1. Main design concepts
Contents
1. Perform simulation using ASIR tt a Analyse results of simulation run Figure 2 1 ASIR the Cycle of use o wee p p see gt 369 This chapter is concerned with the first stage entering data for a simulation The next chapter explains how a user performes a simulation once the data has been entered There are two purpose built interactive systems which help the user with the task of supplying data for a simulation These systems are called IMIDES and EDITOR IMIDES standing for Insurance Model Interactive Data Entry System provides a fully prompted intelligent data entry and verification system storing the coded data in computer files which reside on the users own disc area EDITOR enables a user to inspect and change any data item stored in any of these files and when the editing session is complete EDITOR will store the amended data either in a new data file or back in the old one at the user s behest The use of these two systems is now explained in the remainder of this chapter 2 1 Interactive data entry using the IMLDES system The data requirement for the ASIR model is comprehensive and many of the data items provide multiple specifications and are linked to other data items Were it not for the IMIDES system the task of supplying data for a simulation run could be a formidable one IMIDES has been specially designed to ease the task of the user in supplying all the data nec2. An example of each of the reports produced by the main ASIR program appears in Appendix F of the User s Manual 3 2 Modes of operation The random number seed can effectively determine the mode in which the ASIR model operates and three distinct modes of operation can be obtained These are discussed briefly in the following sections 381 3 2 1 Single shot In most cases a user will only be interested in obtaining a single set of results from a simulation run Here the single shot mode is the most appropriate mode to achieve this goal The user should specify a positive value for the random number seed reference number 106 and this will generate a single repeatable set of random numbers which will be used by ASIR to generate the requisite probability distributions used for sampling claims This will be satisfactory in most cases but there will still be a random element in the results To circumvent this the user could also ensure that the IRISK 4 N parameter for each risk class was set to a negative number This would provide zero variance results forcing each of the probability distribution generators within the model to return the mean of the distribution every time they were sampled 3 2 2 Sensitivity analysis In more extensive explorations the user may wish to explore the effect on the insurance company s of systematic changes in the input data Put another way the user may want to ask a range of what
3. number of the risk class For some data items all those stored as two dimensional arrays there is also a sub reference number which the EDITOR will also prompt for if necessary In this example the requested item reference 422 has three data items within it and so the EDITOR will ask Sub reference for item 422 99 for all 0 As can be seen from the appendix the sub reference for the particular data item wanted is 3 With this information the EDITOR can pinpoint the single value requested by the user The EDITOR will retrieve this information and will print out the value as currently held for example Old value 0 25 The EDITOR then asks the user whether he wishes to alter this value If the user responds with Y to the question Change Y N N the EDITOR prompts for the New value The EDITOR will store the user s response and will return to the Item Reference 0 to finish editing 422 prompt ready for the next item to be edited As a time saver the EDITOR will always remember the user s last response to a particular question and will display this as part of the prompt as shown above 375 If the user simply responds with a RETURN the EDITOR will substitute the pre viously entered value as the default This applies to all the prompts given to select a particular item of data for editing One variation to the above dialogue occurs if the user specifies 99 in response to the sub
4. companies over a time span of several years rather than days or months The methodology adopted for this model is therefore basically that of the continuous variable time path approach in which the effects of many events are summed integrated to give the cash flow over each time slice or period However a number of simulated discrete events are superimposed on this underlying continuity these correspond to important relatively infrequent discontinuities in the cash flow which significantly affect the state of an insurance company Examples are the raising of Published in the serie Etudes et Dossiers N 52 and N 57 November 1981 and June 1982 The Geneva Association 364 capital and payment of dividends payment of taxes and payment of large claims chapters 13 14 and 8 of the User s Manual Thus the model is based on aggregative techniques supplemented by the use of discrete event simulation where it is thought more appropriate 1 1 2 Stochastic and deterministic In the main computer simulation which is designed to be run without user interaction the calculating procedures referred to in 1 1 1 must consist of sets of rules formulated in computer language which express a the functional dependence of cash flows on current and past values of variables and on the environment and b the functions transforming cash flow to new values of state variables Such sets of rules may consist entirely of
5. each active company and the countries where they are held also the parameters specifying investment strategy and any data changes during the simulation 7 Dividends and capital strategy data comprising capital raising parameters and dividend payment parameters for each active company 8 Operating environment data comprising inflation and interest rates exchange rates and share and property indices for each country also real growth rates for each risk class and tax rates for each country Appendix A 1 of the User s Manual here paragraph 4 which is also the reference guide to the ASIR EDITOR contains a complete list of the input data required for a simulation The three digit item reference number used within the EDITOR always starts with the number of the division in which the data belongs thus for example all risks and reinsurance data are stored in arrays which are given reference numbers between 400 and 499 1 2 2 Simulated Data Data generated as the simulation proceeds can be segregated into four main divisions S1 Data generated each period from the outcome of the risks business including numbers and amounts of claims incurred and claims paid new levels of policies in force technical reserves and reserve deposits income from premiums commis sions eXpenses interest payments and claims payments hence new levels of current assets and liabilities S2 Data generated each period from the outcome of investm
6. or unas sessable 3 the sums insured are extremely large Two alternatives are available for sampling the incurrence of a claim for a VLR 367 1 A very small probability of a claim occurring may be specified say 0001 Each period a simple Bernoulli trial is carried out with probability p of success If this sampling results in a claim its amount and times of settle ment are sampled according to specified distributions VLR claims may be settled in up to three separate payments However this method has the dis advantage that many simulation runs may have to be undertaken before such a claim is generated 2 A claim may be forced to occur at a specified time The amount and settle ment times are then sampled as in the first alternative This forced occur rence alternative must be used if it is desired to simulate coinsurance of a VLR by several insurance companies the VLR with proportionate premiums and claim amounts is entered as a separate risk class for each company 1 5 Random numbers Sampling from statistical distributions in this simulation is carried out by specially designed subroutines which depend only on the generation of a sequence of pseudo random numbers Software for this is provided as standard in all modern computer systems as is the capability of setting different random number seeds if required which enables different sequences of pseudo random numbers to be generated in each s
7. reference number 441 which operates in the same way as the ICSA array above IMIDES suggests a default value of 23 in this case 3 Summary Company Results these give for each active company a statement of the aggregate underwriting performance a profit and loss account and a sum mary balance sheet The MD3 array reference number 330 controls the printing of this report IMIDES suggests a default value of 20 for this report 4 Detailed Company Results these give for each active company a detailed balance sheet a statement of unrealized gains and losses on the investments portfolio and a sources and uses of fund statement The printing of this report is controlled by the IBDET array in the input data reference number 331 IMIDES suggests a default value of 21 for this report 5 Reinsurers Reports the final report produced by the ASIR model gives an underwriting report looked at from the reinsurers viewpoint These reports are produced automatically for each active company accepting reinsurance business and are produced on channels MD2 1 MD2 2 MD2 NC see 3 1 1 for an explanation of these terms As with ASIRRG the simulation will proceed for as many years as was requested in the input data unless one of the companies becomes insolvent before this time is reached When the simulation is complete and all the reports produced ASIR will return control back to the computer s operating system
8. the data the simulation itself will start As with ASIRRG any error messages that occur will be sent to the channel selected by data item MD There is a wide range of output reports available from the ASIR program and these are grouped into five categories 1 Claims Settlement Analyses these give for each risk class a detailed breakdown of the claims settlement run off arising from each underwriting year The printing 380 of this report is controlled by the ICSA array reference number 440 a non zero entry in this array causes ASIR to produce a Claims Settlement Analysis report for that risk class which will be output on the channel number specified by that entry IMIDES suggests a default value of 22 for each element of the ICSA array if this report is requested However it is quite permissible to allocate dif ferent channel numbers to different risk classes if the user wants to have the results from different risk classes printed completely separately 2 Detailed Underwriting Reports these give for each risk class a statement of the underwriting performance for each year of the simulation This statement subdivided into operating periods if this has been specified by the user provides figures both gross and net of reinsurance giving details of the operation of any treaties that may be in force for that risk class A summary revenue account is also provided The printing of this report is controlled by the IDET array
9. with ASIRRG 3 1 1 The ASIRRG program The ASIRRG program is a summary Report Generator hence the RG in the name The program is started by issuing the command RUN ASIRRG ASIRRG will first prompt for Name of file containing data to which the user should respond with the name of the file in his disc area which contains the data appropriate for the simulation to be carried out If the data is spread across more than one file the user should initially respond with the name of the first file ASIRRG will load this file discover that it only has part of the data it requires and will repeat the file name prompt This process will repeat for two or three times until a complete set of data is loaded 379 ASIRRG will then proceed to perform the simulation and will terminate when the specified number of years has elapsed or if one of the companies goes insolvent whichever occurs first If any errors arise during the execution of the job a message will be output to the output channel selected by the data item MD reference number 110 which is normally allocated to the user s terminal The IMIDES system will enter a default value of 5 for this channel Error messages produced by ASIRRG are listed and explained in Appendix E of the User s Manual During the execution of a job ASIRRG also makes use of work files allocated to a range of channels in the sequence MD2 1 MD2 2 MD2 NC where MD2 is a base channel su
10. 4 24 430 5 15 25 430 6 16 26 REINS 30 40 FORTRAN Variable Description Min time occ to report Time occ to scnd pmt Meantime p 5 3 Propn paid Min time occ to settle Time occ to third pmt Meantime 5 Propn paid Max sum insured 0 if open end Max sum insured or EML Least sum insured or EML For prop reins Average sum insured or EML Time delay parameters Time span between changes in premium rates Mean delay between premium due and premiums received Delay between commissions due and paid Expenses parameters New business age commissions and expenses Renewals age commissions and expenses Fixed expenses Average expenses per renewable policy Average expenses per claim reported Parameters for numbers of policies age renewable policies renewed each period age policies cancelled during term Optional capacity contraint sets max premium to solvency multiple EITHER gross premium income in year 1 if positive OR minus number of policies in force at end of year 1 if negative and IPOL 0 OR number of policies in force grows with growth parameters if zero and IPOL gt 0 Reinsurance treaty parameters 1 10 for treaty 1 11 20 for treaty 2 21 30 for treaty 3 Reinsurance premium as age of direct premium age commission age profit commission age of claims paid by reinsurer QT Net retention by ceding company ST Lower limit of net loss covered EL Payment l
11. CRD 80 CEXPNS 80 Name of simulation run Description of special features Number of simulated companies including shadow Number of countries and currencies Length of simulation run in years Number of simulation periods per year Random number seed Output channel number for error messages Output channel number for lineprinter ASIRRG only Base channel number for temporary binary files ASIRRG only Country names Currency names Units of currency for flows Units of currency for levels Country of incorporation of companies Initial capital Initial share premium Number of branches for each company Country of operation of each branch Initial level of cash Initial level of liquid deposits Initial level of overdraft Initial level of tax payable Initial level of dividends declared Initial level of tax credit Initial level of fixed expenses 385 Item Reference 330 331 400 401 410 411 412 420 421 386 411 1 411 2 411 3 411 4 412 1 412 2 420 1 420 2 420 3 420 4 420 5 420 6 420 7 420 8 420 9 RISKP 14 40 421 1 421 2 421 3 421 4 421 5 421 6 FORTRAN Variable Description MD3 9 IBDET 9 IRR 10 IPOL 40 PREM 40 DECPRM 4 40 DXCPRM 6 40 IRISK 9 40 Output channel number for summary company results ASIR only Output channel number for detailed company results ASIR only Number of direct risk classes for each company i
12. The Geneva Papers on Risk and Insurance 7 No 25 October 1982 364 390 From the User s Manual 1 Main design concepts 1 1 Theoretical basis of model This chapter introduces the technical side of the ASIR model starting with the general philosophy behind the simulation approach and then moving on to look at the key statistical assumptions that govern the behaviour of what is probably the most important part of any insurance model the risk portfolio 1 1 1 Discrete and continuous There are two basic sets of elements in any simulation model a a set of state variables whose values completely describe the system at any stage typically for a financial system the items in a company s balance sheet and b a set of procedures for calculating a new set of values at any stage N 1 from those at stage N for a financial system these can be subdivided into 1 procedures for determining cash flow and 2 decisions for converting the cash flow into other balance sheet items such as investments The definition of stage N in b ts crucial We could simulate an insurance company by treating for example the receipt of each premium and the payment of each claim as discrete events and proceed from one event to the next Since insurance companies work on the principle of the law of large numbers simulation at such a level of detail would be impracticable if it is desired to simulate the state of insurance
13. algebraic equations Alternatively if algebraic equations are combined with conditional statements and random sampling from statistical distributions they may be probabilistic A model without any proba bilistic rules is completely deterministic this approach has been used to simulate premium income and expenses the return on investments and the management of the investment portfolio However the random nature of the risks business requires a stochastic model so amounts and numbers of claims and therefore technical loss reserves are generated by probabilistic rules In other words what determines the cash flow generated by payment of claims are statistical distributions whereas what determines all other cash flows are exogenously determined fixed parameters which includes all decision parameters Thus while most rules used in the model are deterministic the nature of the model is stochastic since the amounts of claim payments indirectly affect the values of all state variables Results obtained by running the model should be regarded as indicating a range of possible outcomes for a given set of exogenous parameters rather than a definite answer 1 2 Structure of the data There are two main types of data in the model Input Data Data generated as the simulation proceeds 1 2 1 Input Data The input data can be segregated into eight main divisions 1 General information comprising the name and descripti
14. ass A D A Which investment class number 4 x amp EDITOR will change the data in item references 610 611 612 613 614 620 621 622 623 also 420 432 and 632 so that investment class numbers 4 5 become 5 6 k k amp 377 OK to proceed Y N Y Y REMINDER You will need to enter data into the above items for the new investment class 4 If the user signified his acceptance the EDITOR would move all the data as indicated and would check the contents of the CHANGE array 632 moving any of these references affected by the change as appropriate As can be appreciated the super edit facility provides a powerful enhancement to the capabilities of the EDITOR system An extension of the super edit facility is designed to handle the operating environ ment data in arrays with reference numbers in the range 800 to 811 If any of these arrays are selected for editing the EDITOR will first list the entire environment specification for the particular array and country specified The user can then edit the data with three options at his disposal 1 A option this allows interpolation points to be added The EDITOR will prompt for the year for which a point is to be added and for the value of the environ mental parameter at that time 2 M option this allows the user to modify an existing interpolation point The EDITOR will prompt for the year to be modified and for new value at that time 3 D option this enables exis
15. ated with the EDITOR 383 A wide range of simulations can then be carried out using this stock of information The user could for example keep a set of standard operating environments in this library If there was a need to evaluate quickly the working of a new insurance arrangement the details could be fed in with IMIDES as a new risk class and this could be tested against the existing company set up and operating environments both of which would already be on record within the library As use of the model increased and more information stored use of the ASIR model would become more and more efficient This idea is depicted in Fig 3 1 below ___ EDITOR J J Io o J I o J o o 7 V l I Ic ASIR Ic gt gt IMIDES IE FILE 1 E ASIR ASIRRG gt gt R LIBRARY IR gt gt Key C company files E environment files R risk files Figure 3 1 The ASIR File Library 384 From the User s Manual 4 Data requirements for ASIR 4 1 List of input data variables and Editor reference guide Item Reference 100 101 102 103 104 105 106 110 111 112 FORTRAN Variable Description NAME NFEAT IC KK YEARS INT IRAN MD MDi MD2 KUNTRY 4 20 KURNCY 3 20 KUNF 20 KUNL 20 KHOME 9 CAPTAL 9 SHAPRM 9 NBRNCH 9 NBKEY 80 CASH 80 STERM 80 ODRAFT 80 TAXN 80 DIVID 9 TAX
16. e EDITOR there is a super edit facility which is invoked whenever a user wishes to deal with the special arrays NBRNCH IRR ITRETY IRV or any of the arrays governing the operating environment This facility is described further in section 2 2 1 i 374 To start the EDITOR the user issues the command RUN EDITOR After printing an introductory message the EDITOR will ask Name of file to be edited to which the user should respond with the name of the file he wishes to edit The EDITOR will then load the data from that file into temporary working storage and will then prompt for Item Reference 0 to finish editing 0 All the data within the EDITOR are referred to initially by a three digit reference number all of which appear in Appendix A 1 Suppose that a user wishes to alter the data item referring to delay between commissions due and paid for one of the risk classes This is within item 422 as can be seen from Appendix A 1 of the User s Manual here paragraph 4 and so the user would respond with 422 to the above prompt The EDITOR will then ask Risk class number 0 so that it can retrieve the information from the correct risk class for this item As the response to this the user should give the sequential risk class within the data file If for example the risk class wanted was the second risk class of company 2 and companies 0 and 1 had three risk classes each the user would respond with 8 as the
17. ed reinsurance gross loss recoveries Key to solvency margin calculation Key to valuation of investments Keys to EEC unit of currency age weighting for each currency used Solvency calculation parameters Parameter 1 Parameter 2 Parameter 3 Parameter 4 Parameter 5 Number of investment classes for each company Integer investment parameters Item Reference 611 612 613 614 620 621 622 623 630 610 1 610 2 610 3 610 4 610 5 610 6 611 1 5 9 611 2 6 10 611 3 7 11 611 4 8 12 612 1 4 7 612 2 5 8 612 3 6 9 613 1 613 2 613 3 614 1 614 2 614 3 614 4 621 1 621 2 621 3 621 4 622 1 622 2 623 1 623 2 FORTRAN Variable Description PINSHA 12 40 PINBND 9 40 PINPTY 3 40 PINCST 4 40 KEYDEC 40 DECINV 4 40 DECBND 2 40 DECSHA 2 40 NYRCH 31 Key to country where investment held Number of different types of share Number of different types of bond Maturity of bond 1 Maturity of bond 2 Maturity of bond 3 Parameters for shares 1 4 for share 1 5 8 for share 2 9 12 for share 3 Purchase price Current market value Gross dividend yield Beta value Parameters for bonds 1 3 for bond 1 4 6 for bond 2 7 9 for bond 3 Purchase price Coupon Present value Parameters for property Purchase price Current market value Rental income as age of purchase price Expenses parameters age expense for share transactions age expense for bond transactions age exp
18. ense for property transactions Fixed expense for this investment class Key to investment strategy behaviour Parameters for overall investment strategy Parameter for shareholders funds age of total investments as bonds age of total investments as shares Ratio of current assets to current liabilities Parameters for bonds investment strategy age of total bonds as bond type 1 age of total bonds as bond type 2 Parameters for shares investment strategy age of total shares as share type 1 age of total shares as share type 2 Years in which data changes First element total number of different years in which changes take place Subsequent elements year number for set of changes 391 Item Reference FORTRAN Variable Description 631 NCHNG 30 Number of changes in data in each year specified above 632 KEYCH 200 Key to investment strategy change digits 7654321 as follows 765 item reference number 43 sub reference number 21 Country Company Risk Investment number 633 CHNG 200 New value for data changed 700 NDECYR 9 Number of years between possible capital issues 701 DECCAP 9 Solvency threshold factor 702 DECDIV 9 Parameters for interim dividends 703 DECDFV 9 Parameters for final dividends 800 INFLT 29 20 Inflation rate interpolation points 801 EINFLT 30 20 Inflation rate data 802 ISHARE 29 20 Share index interpolation points 803 SHARES 30 20 Share index data 804 INTRST 29 20 Interest rate inter
19. ents held including net income from interest received new market values of investments net additions to investments portfolios hence new balance sheet levels 366 S3 Data generated at end of each simulation year to form the underwriting revenue account and the profit and loss account of each company also solvency margin and accounting ratios i e the year s results S4 Data parameters updated at the end of each period or other time interval for example monetary items such as expenses or average claims which are updated by inflation factors As far as possible only simulated data for the current year is held within the model and is superseded after the required output of results Parameters for risks investments and decisions however remain fixed and are only altered if updated as in S4 above or if the CHANGE facility is used The main simulated variables and arrays are listed in Appendix A 2 of the User s Manual 1 3 Key statistical assumptions Central to the operation of any insurance company is the portfolio of insured risks and this is reflected in the model At the core of the simulation is a number of direct insurance risk classes the results of which drive the rest of the model In this section we consider only those classes which contain a large number of policies In modelling these risk classes there is a fundamental assumption namely that underlying each risk class is a set of stable
20. eposits Unearned premium reserve of proportional treaty reinsurers for treaties 1 to 30 covering risk classes 1 to 10 Initial level of reinsurer s UPR Premium reserve deposits proportional treaties for treaties 1 to 30 covering risk classes 1 to 10 Initial level of premium reserve deposits Number of bands in user specified claims amount distribution 389 Item Reference 481 482 485 486 487 500 501 510 511 520 521 530 531 540 600 610 390 481 1 486 1 501 1 501 2 FORTRAN Variable Description ABANDS 16 10 CUMFAM 15 10 NSB 10 SBANDS 11 10 CUMSET 10 10 KUPR 20 UPR 2 20 KLR 20 PLR 20 KRULES 9 KBAL 9 KEEC 10 WEEC 9 SOLVNT S5 9 IRV 9 IN VEST 6 40 Endpoints of band widths in user specified claims amount distribution Minimum claim amount Cumulative percentages of claims by number in each amount band Number of bands in user specified distribution of times between incurrence and settlement Endpoints of band widths in user specified times to settlement distribution Minimum time between incurrence and settlement Cumulative percentages of claims by number in each time settlement band Key to method for calculation of UPR reserve Parameters for UPR calculation Proportional term Proportion of premium allowable as reinsurance Key to method for calculation of loss reserve Maximum proportion of reserve allowable as estimat
21. essary for a simulation run It does this by carrying out a dialogue with the user in the form of a careful structured question and answer session IMIDES will provide a descriptive prompt for each and every component of data which is needed for a particular simulation run and will invite the user for his response This response will be checked against the range of permissible answers and if correct will be accepted and IMIDES will then move on to the next question If the answer was not acceptable IMIDES will print an explanatory message and invite the user to enter another response IMIDES provides the user with an intelligent system because the questions asked will depend on the answers to previous questions For example if the user has specified that a particular risk class has two reinsurance treaties IMIDES will only ask the user to enter details for two treaties for that risk class As the user enters details for each treaty IMIDES will check what type of treaty is specified and will ask only those questions relevant to that type of reinsurance business As an additional aid to the user IMIDES will provide for most of the items of data a default answer and this will be printed enclosed in square brackets as part of the prompt If the user is willing to accept the default he needs only to press the RETURN key on the keyboard instead of having to enter the number in full A further feature that can assist the user is t
22. for the random number seed This will instruct ASIR to generate a different random number seed each time a simulation run is performed the actual seed chosen will be based on the date and time of day that the simulation is performed to the nearest tenth of a second At present the user must perform the requisite number of simulations and aggregate the results manually but a later release of the model will automate this process 382 3 3 The LISTER facility There is a utility program which enables a user to obtain a neat and comprehensive listing of the entire contents of any data file produced by IMIDES or the EDITOR The LISTER is started by issuing the command RUN LISTER which will then prompt for Name of file to be listed type CR to finish The user should respond with the name of the file he wishes to see The LISTER will then ask Output to TTY or LPT LPT TTY LPT If the user wishes the listing to be sent to the computer s line printer he should respond with LPT or just RETURN If the listing is to appear on the terminal the user should respond with TTY The LISTER will then ask Section of file to be listed 0 to finish 1 2 7 8 99 for all Any single section of data can be listed out with the section numbers being the same as those used by IMIDES see 2 1 When the section has been listed the same prompt will reappear When the user has finished listing out parts of t
23. he help facility which will explain the possible answers to questions requiring a coded key as the response e g the key to the type of loss reserve estimation To start IMIDES the user must be logged in to the timesharing computing system and should type the command RUN IMIDES 370 on the terminal IMIDES will respond with an introductory message followed by the prompt Do you wish to create a complete set of data Y N Y IMIDES organises the total set of data into the eight sections outlined earlier general information basic country and currency data basic company data risks and reinsurance data reserves and solvency rules data investments and investment strategy data dividends and capital strategy data operating environment data OS ge ee a These sections are grouped further to obtain three divisions COMPANY DATA sections 1 3 6 and 7 ENVIRONMENT DATA sections 1 2 5 and 8 RISKS DATA sections 1 and 4 As shown above the first question put by IMIDES asks the user whether he wishes to enter the complete set of data or whether he wants to enter just one or two divisions At the end of the prompt is the letter Y in square brackets which indicates that the default assumed by IMIDES unless told otherwise is Y If the user responds with N IMIDES will ask in turn whether the user wants to enter company data environment data or risks data The user can specify any one
24. he file he should respond with zero whereupon the LISTER will return to the file name prompt Alternatively the user can ask for the entire file to be listed out by entering 99 as the section number In this case after the listing is produced the LISTER will return to the file name prompt straight away When the user has finished with the LISTER he should type just a RETURN in response to the file name prompt and the LISTER will return control to the computer s operating system An example of LISTER output appears in Appendix F of the User s Manual 3 4 Maintaining a user library The structure of the ASIR model makes it particularly easy for the user to organise his work in a systematic fashion IMIDES can produce data in named files with a separate file for each type of data The EDITOR can select any type of file for editing and produce a new file with amended data Finally the simulation programs ASIR and ASIRRG can accept any grouping of compatible data files and perform a simulation from the data contained therein 7 With this capability the concept emerges of an ASIR file library for each user This library will contain a collection of files describing particular companies particular portfolios of risks to underwrite and different kinds of environment against which to operate The user can supplement the information in his library by adding new files with IMIDES Existing files can be amended and new ones gener
25. he random number generator used by the main simulation program If the number entered here is zero or positive that number will be used directly as the seed and a repeatable set of random numbers will be produced each time the simulation is run If a negative number is used then the random number generator will be seeded by looking up the time of day when the simulation is run This will therefore produce a different set of random numbers each time the simulation is run However in both cases the actual seed used is printed at the beginning of the results listing The different modes of opera tion obtainable from the ASIR model through the use of random number seeds is explored further in the next chapter Default output channels for results the ASIR model needs to know where output from a simulation is to go so that it can inform the computer s operating system In this section there are three channel numbers which can be specified although IMIDES will insert default values if the user responds with Y to this question The three channel members required are i error messages default on DECsystem 10 is 5 the terminal ii lineprinter output default on DECsystem 10 is 3 iit base number for temporary files used in ASIRRG or reinsurers results in ASIR default on DECsystem 10 is 30 At later stages within IMIDES the user will also be asked to specify which channel numbers are to be used for the various reports p
26. if questions to see how the modelled company s react to different circumstances In that case the random number seed should be set to a positive value so that ASIR will produce the same stream of random numbers every time the model is run This will enable the user to change one or more of the input data items from one run to the next and be sure that the changes in the results produced is solely due to the change in the input data and not because a different set of claims experience was simulated In this sensitivity analysis mode the user can see exactly how sensitive the system being modelled is to a change in input data Some of the data items may have only a minor effect on the operating results whilst others may have a devastating effect In real life it would be the latter group that should be of most concern to insurance company practitioners 3 2 3 Stochastic modelling In some circumstances the user may want to get an idea of the range of possible results that can arise from a given set of input data This recognises the fact that just as in real life there can be many outcomes from a given set of risks The results from one ASIR simulation run is just one possible outcome just as the state of the real world at any time is just one of the very many possibilities that could have arisen To carry out a range of simulations using the same input data but with different risk outcomes the user should enter a negative value
27. imit on any one risk QT Limit of reinsurers liability on any one risk ST Upper limit of net loss covered EL age cover EL 387 Item Reference 431 432 440 441 450 460 461 462 388 430 7 17 27 430 8 18 28 430 9 19 29 430 10 20 30 ITRETY 9 KTRETY 120 ICSA 40 IDET 40 ITYPE 4 10 SIMNUM 10 82 460 1 to 15 460 42 to 56 KNOWN 10 5 461 1 IBNR 10 5 462 1 462 3 462 4 462 5 FORTRAN Variable Description age of outstanding losses retained as loss reserve deposits age of premiums retained as UPR deposit age interest paid on reserve deposits age of last qtr s prem counted as this qtr s ceded prem QT or ST Deposit premium as age of reinsurance premium EL Number of treaties accepted by each company Keys to treaties accepted digits 7654321 as follows 7 treaty 1 2 or 3 65 risk class number 01 to 40 4 ceding company 0 to 9 3 key to treaty type 21 gt investment class where reinsurer holds reserves Output channel number for claims settlement analysis ASIR only Output channel number for detailed underwriting report ASIR only Names of types of business Numbers of outstanding claims reported and settled risk classes 1 to 10 Numbers reported in years 1 to 15 Numbers settled in years 1 to 15 Number of claims known outstanding risk classes 1 to 10 Number known outstanding at beginning of simulation IBNR claims and flags for u
28. imula tion run The use of the random number seed to give different modes of operation of the ASIR model is discussed more fully in section 3 2 There are three major techniques that can be used for sampling subroutines which one is actually used for a given distribution depends on the form of the cumulative distribution function and on considerations governing efficient use of the computer A considerable amount of research has been carried out in recent years in this area the results of which have been used in the programming of the sampling subroutines Technical note These techniques are the inverse transformation method the enve lope rejection method and the composition method Details can be found in any standard text on simulation Monte Carlo methods 368 From the User s Manual 2 Preparing data for a simulation There are three stages involved in using the ASIR model In the first stage the user must enter data appropriate for the particular simulation which is to be carried out The second stage consists of carrying out the simulation itself whilst the third stage sees the user studying the results which ASIR has produced In many cases examining the results of a simulation run will lead the user to carry out further simulations and there is typically found a cycle of use as depicted in Fig 2 1 below START a Edit existing data Enter new data using IMIDES using EDITOR S cd
29. in the broad grouping of data into divisions and sections IMIDES also subdivides the data during entry into checkpoint blocks At the beginning of each such block IMIDES prints a message like checkpoint block 1 1 starts The user will then be asked for a group of data items and then a message like checkpoint block 1 1 finish your command type h for help will appear There are four valid responses to this prompt 1 P or just RETURN this instructs IMIDES to proceed normally to the next block of data to be input This is the default response 2 B this instructs IMIDES to backtrack to the beginning of the checkpoint block so that any data entered incorrectly can be entered again This is especially useful if the user has made a mistake in entering a fundamental item of data such as the number of risk classes insured by each company 3 A this instructs IMIDES to abort the session immediately Any data entered up to that point will be lost 4 H this instructs IMIDES to print a helpful text explaining the operation of checkpoint blocks After the text is printed the prompt shown above will be repeated The checkpoint facility thus gives the user an elementary method of editing the data just entered before proceeding further It is not possible however to backtrack more than one checkpoint block When all the data in the IMIDES session has been entered satisfactorily IMIDES wi
30. ll print the message END OF IMIDES DATA INPUT 373 and will confirm the creation of the data file or files by printing a message like File ENV27 created for each file named during the initial dialogue IMIDES will then terminate relinquishing control back to the computer s operating system An example of a short IMIDES terminal session is included in Appendix F of the User s Manual 2 2 Interactive editing using the EDITOR As seen in the preceding section IMIDES provides the user with a fully prompted system for the entry of a complete division of data which is subsequently stored in a named data file within the user s own disc area The EDITOR is another purpose built interactive system which enables the user to inspect and edit any of the data contained in any of the files It provides the only effective means of performing this useful task because the data files used within ASIR contain binary data they are in fact unformatted FORTRAN data files and standard computer text editors will not make any sense of them With the EDITOR a user can check the values of individual data items or columns within an array After each selected value is displayed the user has the option to change the value if he should so wish When an editing session is complete the user can instruct the EDITOR to overwrite the existing data file with the new data or the modified data can be saved in a new file The EDITOR is particula
31. named file to hold the edited data Once the EDITOR has satisfactorily disposed of the information it holds it prints a confirmatory message and then asks Do you wish to edit another file Y N N A Y reply will return the user to the beginning of the EDITOR program and he will be asked for the name of the next file to be edited A N reply will terminate the EDITOR which will relinquish control back to the computer s operating system 2 2 1 The Super Edit facility Most of the data items stand completely by themselves and can be edited without regard to any other item of data A few data items are somewhat more important and affect many other items of data for example the IRISK 6 N item mentioned above determines how many treaties are associated with a given risk class If this data item 376 is incorrect the data in the REINS array reference number 430 will be interpreted incorrectly or may be ignored altogether There are a handful of items which are fundamental in nature They are as follows NBRNCH reference 303 IRR reference 400 ITRETY reference 431 IRV reference 600 The reason for their special importance is because they control the interpretation of whole groups of arrays The IRV array for example governs the number of investment classes held by each active company The data in all the other arrays in the 6XX series is then organised based on this informati
32. ncluding shadow Initial number of policies in force Initial premiums Parameters for calculation of new premiums onstant proportional increase Constant proportional weighting for inflation in year f Constant proportional weighting for inflation in year t 1 Constant proportional weighting for inflation in year t 2 Parameters for linking premium rates to claims experience Credibility factor Target loss ratio Integer risk class parameters 1st digit type of business 2nd digit key to length of claims runoff Country where risks taken Investment class where reserves held Distributions flag 1st digit claims number 2nd digit claims amount Key to loss reserve estimation Key to number of treaties and types Treaty 1 Four digit code AABB AA currency of premium paid to Treaty 2 reinsurer BB currency of claims paid by Treaty 3 reinsurer Claims distribution parameters Group risk VLR RISK Yage incidence of Prob of occurrence claims time of ist occ age large claims 0 0 time of second occ Mean size of large Size of avg claim claims SD of large claims SD of claims Mean size of small Time occ to first pmt claims SD of small claims Propn paid Item Reference 422 423 424 430 421 7 421 8 421 9 421 10 421 11 421 12 421 13 421 14 422 1 422 2 422 3 423 1 423 2 423 3 423 4 423 5 RISKN 4 40 424 1 424 2 424 3 424 4 430 1 11 21 430 2 12 22 430 3 13 23 430 4 1
33. on If to continue the example further company 1 has two investment classes company 2 has one investment class and company 3 has two investment classes then the data in IRV IRV 1 2 IRV 2 1 IRV 3 2 will control the interpretation of all the data stored in arrays 610 611 612 613 and so on The first two columns of these rows will be assigned to company 1 the third column to company 2 and columns 4 and 5 to company 3 If the user were to edit the IRV array and leave the other arrays untouched the allocation of investment classes between the active companies would be completely altered It would be unreasonable to expect a user to edit manually all the arrays affected by a change to one of the four arrays mentioned above The EDITOR therefore contains a super edit facility which is invoked whenever these four arrays are selected for editing This facility first explains the present allocation of branches risk classes treaties accepted investment classes and then asks whether this is to be changed The user can increase or decrease the allocation to a particular company or leave it unchanged If in the above example the number of investment classes for company 2 were increased from 1 to 2 the super edit facility would conduct the following Item reference number 0 to finish editing 422 600 Company 0 2 Company 2 has one investment class investment class 3 Change Y N N Y Add or Delete an investment cl
34. on of the simulation run the random number seed the numbers of companies countries and years simulated the number of simulation periods per year and some machine dependent output parameters 365 2 Basic country and currency data comprising names of countries and names and units of currencies 3 Basic company data comprising for each simulated company except the shadow company the country of registration and the initial levels of share capital and premium current assets and liabilities and also the number of branches and the country and yearly fixed expenses of each branch finally some machine dependent parameters for any company results produced 4 Risks and reinsurance data comprising the number of direct insurance risk classes for each company including the shadow company and the parameters specifying the precise nature of each of these classes the number of rein surance treaties accepted by each active company and the parameters specifying them also machine dependent parameters for any required detailed results 5 Reserves and solvency rules data comprising parameters for the calculation of technical reserves in each country of operation and parameters for the calculation of the required solvency margin in each country of registration also parameters for calculating the EEC unit of currency if required 6 Investments and investment strategy data comprising the initial levels and yields of investments for
35. polation points 805 RATE 30 20 Interest rate data 806 IPROP 29 20 Property index interpolation points 807 PROPTY 30 20 Property index data 808 IGROW 29 40 Growth rate for risk business interpolation points 809 GROWTH 30 40 Growth rate for risk business data 810 IEXCH 29 20 Exchange rate interpolation points 811 EXCH 30 20 Exchange rate data 815 EINTDF 10 20 Interest rate differentials 815 1 age differential below basic I R for short term interest rates 815 2 age differential above basic I R for overdrafts 815 3 age differential above basic I R for bond type 1 815 4 age differential above basic I R for bond type 2 815 5 Yage differential above basic I R for bond type 3 820 Tax rate data 820 1 TAXES 4 20 Company profits tax rate corporation rate 820 2 Imputed tax rate on franked investment income income tax 820 3 Capital gains tax rate 820 4 Miscellaneous taxes rate 392
36. pplied within the input data reference number 112 and NC is the number of active companies The IMIDES system will enter a default value of 30 for this base number The results from the ASIRRG program are produced as a time series report listing comprising 1 ratio measures of underwriting performance both gross and net of reinsurance 2 a listing of some two dozen key measures of underwriting and total company performance encompassing premiums claims underwriting revenue profit and loss account capital issues balance sheet and solvency This record is output from the ASIRRG program on the output channel selected by the data item MD1 reference number 111 which is normally allocated to the computer system s line printer However any suitable device available to the operating system can be selected The IMIDES system will enter a default value of 3 for this channel When ASIRRG has completed the output of its results it relinquishes control back to the computer s operating system An example of the output from the ASIRRG program is given in Appendix F of the User s Manual 3 1 2 The ASIR program When the user wishes to obtain more detailed results from the ASIR model the main simulation program ASIR itself should be run To start ASIR the user should enter the command RUN ASIR The ASIR program will prompt for the Name of file containing data in the same manner as that for ASIRRG and when it has all
37. probability distributions from which random _ samples of claims numbers and amounts can be made ASIR does not attempt to deal directly with joint probability distributions of claims numbers and amounts and times to settlement it is difficult to conceptualize such distributions and even more difficult to supply the necessary data parameters Instead ASIR generates claims numbers and amounts from marginal distributions and assumes that the time to settlement is cor related with the size of claim The data required to specify these distributions has been kept to a minimum however users should find this relatively straightforward approach offers a great deal of flexibility and gives considerable scope for experimenta tion in specifying different types of risk classes with widely differing characteristics Claims modelling is described in detail in Chapter 8 of the User s Manual 1 4 Group vs VLR risks In the previous section we considered risk classes comprising a number of policies having underlying probability distributions of claims numbers and amounts Risk classes of this type are called GROUP risks and follow the law of large numbers It is also possible to simulate VLR risks very large risks such as the insurance of a Concorde or an oilrig The characteristics of such risk class are as follows 1 there is only one policy i e only one item insured 2 the probability of a claim being incurred is either extremely small
38. reference prompt In this case the EDITOR will step through all the sub reference items for the array and column specified In the above example the user is dealing with the 8th column i e the 8th risk class of the array RISK This array has three sub reference values i e it has three rows If the user enters the value 99 as the sub reference the EDITOR will print each row of the array in turn and await a response If the user simply enters RETURN the value for that row remains unchanged If the user enters a numerical value this new value will replace the old one for that row A typical dialogue would appear something like Sub reference for item 422 99 for all 0 99 Sub reference 1 1 000 Sub reference 2 0 500 0 25 Sub reference 3 0 250 Item reference 0 to finish editing 422 Here the user has changed the value of sub reference 2 referring to the mean delay between premiums due and premiums received from 0 5 to 0 25 but has left the other two values unchanged When the user has finished all his edits he should respond with a zero as the item reference number The EDITOR will then ask Do you wish to overwrite existing file Y N N A Y response will replace the disc copy of the file with the new data which has been held up to this point in temporary working storage A N reply will however invoke the further prompt Name of new file for data allowing the user to create a new
39. rly useful in the case where a user wishes to run a number of simulations changing a small number of data items in between each run In this application the user would create an initial set of data using IMIDES and from this he could create a series of related files using the EDITOR There is one fundamental difference between using IMIDES and using the EDITOR IMIDES is a fully prompted intelligent system that provides the user with substantial help during the data entry process and checks to see that all responses made by the user are correct and consistent It is perfectly possible to use IMIDES without knowing anything about the way in which the data is organised within the ASIR model The EDITOR on the other hand performs virtually no checking what soever Any item of data can be altered to take on virtually any value even if the new value is inconsistent with other data within the file or is just totally unsuitable Such errors will only be detected during the simulation which will abort prematurely with an appropriate error message When running the EDITOR the user must there fore ensure that he is making valid alterations to the data In many cases the user will need to know something about the way in which ASIR organises data within the simulation arrays all this information is given in earlier chapters of the Weer s Manual and should not present any real difficulties There is an exception to the above assertion Within th
40. roducted in the course of a simulation 372 IMIDES will now proceed to go through each of the data sections requested by the user at the beginning of the session For each component of data IMIDES will provide a fully descriptive prompt and will in most cases provide a default answer indicated within square brackets IMIDES will then await the user s response When this is forthcoming it will be checked for consistency before IMIDES moves on to the next question If the answer is incorrect IMIDES will print am error message of the form Invalid answer response should lie in range 1 9 and will repeat the original question until the answer provided by the user is within the limits it expects Sometimes these limits are fixed e g the maximum number of countries currencies is always 20 sometimes they depend on the answer to previous questions e g if the user has indicated a maximum of three countries currencies not more than three investment classes can be entered for each active company Where ASIR requires a single data item to encompass a number of component data items e g IRISK 6 N which gives as a three digit code the number of treaties for risk class N and the type of treaty for each IMIDES will either ask an explicit series of questions or will deduce the values implicitly from other information it has In either case the data item will be filled in automatically without the user having to intervene With
41. ser specified initial technical reserves risk classes 1 to 10 Number of claims incurred before simulation start but not yet reported Flag 999 for user initialized UPR Flag 999 user specified estimated loss reserves year 2 onwards Flag 999 for user initialized loss reserve Item Reference 463 464 465 470 471 472 473 474 480 463 1 to 15 464 1 464 2 to 15 465 1 470 1 to 15 471 1 474 2 to 15 472 1 473 1 474 1 FORTRAN Variable Description SIMCLM 10 41 SIMLR 10 41 SIMUPR 10 5 RIMCLM 30 41 RIMLR 30 41 RIMDLR 30 5 RIMUPR 30 5 RIMDEP 30 5 NAB 10 Amounts of outstanding claims gross of reinsurance risk classes 1 to 10 Amounts of outstanding claims paid in years 1 to 15 Estimated gross loss reserve for outstanding claims risk classes 1 to 10 Initial loss reserve Estimates for claims outstanding at beginning of years 2 to 15 Unearned premium reserve risk classes 1 to 10 Initial UPR Amounts of outstanding claims paid by reinsurers treaties 1 to 30 covering risk classes 1 to 10 Amounts paid in years 1 to 15 Estimated total claims amounts outstanding payable by reinsurer on treaties 1 to 30 covering risk classes 1 to 10 Reinsurer s initial loss reserve Estimates for claims payments outstanding at beginning of years 2 to 15 Loss reserve deposits for treaties 1 to 30 covering risk classes 1 to 10 Initial level of loss reserve d
42. ting interpolation points to be deleted The EDITOR will prompt for the year to be removed When editing of that particular environmental specification is complete the EDITOR will reorganise the environment arrays accordingly and store the new data An example of a short editing session is given in Appendix F of the User s Manual 378 From the User s Manual 3 Running the ASIR mode Once the user has entered the data necessary for a simulation actually running the model is very straightforward This chapter describes how the two simulation programs ASIR and ASIRRG are run and also explains the operation of a utility called LISTER 3 1 The simulation programs ASIR and ASIRRG There are two main simulation programs within the ASIR model ASIR and ASIRRG They perform precisely the same calculations and obtain the same answers but present their results differently When a user first starts working with a set of data it is recommended that the ASIRRG program be used first in preference to the main simulation program ASIR This is because ASIRRG is more economical of computer resources but provides sufficient information to enable the user to correct any errors that might occur in the input data When the simulation is shown to work satisfactorily the user can turn to the ASIR program which produces results in far greater detail The differences between ASIR and ASIRRG are now explained in the following sections dealing first
43. try IMIDES will always start with section 1 In this section the user should specify the following items 1 Name of simulation run this name is limited to four characters only and can be used as a short identification It will appear at the start of any results printed out by the model The name is stored internally within all the data files produced by IMIDES and does not have to be the same as the name of the file itself Simulation Description this can be up to 48 characters long and provides a less restricted way for the user to label a data file The simulation description also appears at the beginning of any printed listings produced by the ASIR system Number of active companies this specifies the number of active companies within the simulation and must not exceed nine The shadow company is not included within this total Number of countries and currencies this specifies the maximum number of countries and currencies within a simulation Length of simulation run in years this determines the maximum length of a simulation run and can be set to any number required The computer costs incurred in running a simulation run will be proportional to the length of the simulation Number of simulation periods per year the basic accounting unit is the year but simulations can be carried in smaller time steps of six months or three months if necessary Random number seed this provides the seed for t
44. two or even all three divisions The next question is All data to be placed in one file Y N Y If the user answers Y then all the data as a result of the session will be placed in a single data file The alternative response N will place different divisions in different files The second response is preferred if the user wants to create a well organised library of files In this case the user could create and maintain a number of files containing specifications of risks portfolios A simulation could then be carried out using any compatible selection from this library Creating a user library in this way is explained in the next chapter IMIDES will next ask for the names of the file or files in which the data is to be stored Any name is acceptable provided that it is consistent with the requirements of the computer s operating system for the naming of files For example the DEC system 10 series of computers allows a maximum of six characters in a file name and these characters can only be letters or digits When selecting names users should keep track of the file names already used because IMIDES does not check to see whether a name has been used previously and will overwrite any existing files which have the same name 371 Once this initial dialogue is completed IMIDES will move on to ask for the data to be used in the particular simulation run Whatever divisions of data have been selected for data en
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