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CAS Ratemaking Seminar March, 2004 WC-5 Latest Developments in Retrospective Rating Ideas for Future Development Ira Robbin, PhD Senior Pricing Actuary Partner RE

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Ground Rules and Disclaimers The purpose of this session is to promote actuarial discussion of possible improvements in NCCI Retro Rating Plans. Anti-trust guidelines will be scrupulously obeyed. No statements of Partner Re’s corporate position will be made or should be inferred.

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Cautions Examples are for illustrative purposes only. Do not use the results from any example in real-world applications.

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Three Ideas Refining ICRLL Filing an Advisory Agg Model Adding Terrorism and CAT Loadings Table M ELPF

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ICRLL Review Insurance Charge Reflecting Loss Limitation Logical modification of regular insurance charge calculation procedure Limited Loss Ratio Equations Ratio Difference Value Difference Single Table M Adjust Table M column (ELG)

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ICRLL Ratio and Value Difference Expected Limited LR

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Loss Group Adjustment LUGS= Losses Used in Group Selection LUGS = E[L]*M S/H *M k M S/H State/Hazard Group multiplier M k per accident loss limit multiplier M k = (1+.8LER)/(1-LER) LER = ELPF/ELR

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Impact of LG Adjustment Assume M S/H = 1. Then: LUGS > E[L] > E[LL] Larger $ Loss Smaller LG # Smaller LG # Smaller Ins Charges

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ICRLL vs “Correct” Solution ICRLL uses theoretically correct value difference and ratio difference equations ICRLL approximates limited loss distribution by using distribution for a larger risk Correct solution: Limited Loss Table Ms Table M for each per occ loss limit

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Unlimited and Limited Loss Table Ms

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Limited Loss Table Ms vs Table L

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ICRLL Approx of Insurance Charge Values Approximation good for intermediate r ICRLL use of larger risk gives smaller charges Per occ limitation should reduce charges Calibration of ICRLL rating values May over-reduce charges for small r $ savings for small min should not change when a loss limit is introduced ICRLL may incorrectly show $ savings reductions May or may not reduce charges enough for large r

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Understated Savings Example

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Charges for Tiny Loss Limits Let the loss limit approach zero Charges should approach charges for the accident count distribution ICRLL charges approach those of a very large risk Conclusion: ICRLL has incorrect asymptotic behavior as loss limit decreases

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Actual vs Theoretical Error ICRLL theoretical potential error Low loss limits Low entry ratios High entry ratios ICRLL actual error? Needs further study! Tolerance for inaccuracy

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For Greater Accuracy: Promulgate Limited Loss Table Ms Theoretically right Horribly impractical Interpolate between Unlimited Table M and Count Table M Has correct asymptotic behavior Use LER as interpolation weight? Still seems impractical File an Aggregate Model

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The Model Solution Solution considered in early 90s Rejected due to need for paper tables Concern about regulatory approval Prior to Internet and Windows 95 Need Count and Severity Distributions Should closely reproduce current Table M Not a trivial task, but not impossible Refine the model used to develop Table M Develop practical software File as advisory Table M software

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Model Solution:Pros and Cons Theoretically correct and most accurate Practical Modeling problems difficult, not impossible Internet or CD implementation feasible A Solution in Search of a Problem ICRLL generally accurate enough For greater accuracy, use consultants or in-house actuaries Too costly Difficulties with regulatory approval

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CAT and Terrorism Loadings Some actual CAT & Terrorism may be implicitly in Table M and ELPFs May also be part of flat load in ELPFs Current expectation of CAT &Terror not in Table M or ELPF Property CAT models WC CAT potential is signficant

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CAT and Terrorism: Property vs WC Wind less a concern in WC Quake loss in WC varies with time of day Terrorism may be more of a concern in WC Attacks on people that may cause modest property damage Chemical and biological threats

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Occ and Agg Terrorism Exposure Single event explosion Large occ exposure Chemical or biological attack May not immediately generate WC losses Could eventually spawn large number of WC cases

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Method for Loading ELPF? One idea: Compute ELF as per current method Weight with severe CAT distribution Example: Regular ELF = 10% CAT ELF = 50% CAT weight = 2% Final ELF =.98*10%+.02*50% = 10.8%

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How to Load Table M? Model exposure by peril and size of risk Number of locations Number of workers per location Distribution of # injured and severity of injuries for each CAT and Terror peril per location Generate simulated WC CAT and Terror losses and probabilities Model regular loss with current Table M Convolve

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Modeling Issues Source for parameters Property CAT models Experts and consultants Model equations Validation of results Some validation for CAT models Minimal validation of Terrorism models High degree of difficulty

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Practical Issues Need to exclude actual CAT and Terror claims from regular data Claim coding needed to identify CAT &Terror Ideal CAT & Terror weight By location: state and zip Size of risk and public profile Density and vulnerability of workers WC data doesn’t capture key factors Regulatory issues

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Pros and Cons Ought to reflect known exposures in the Retro plan No way to determine right model or select parameters – no data Too costly and impractical No real need exists Market already charges vulnerable risks Models available from consultants

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Conclusion Balance: accuracy vs practicality Uses of Retro parameters and tables Large Deductible and Dividend plans XS of OCC and AAD pricing Roles of key players Dual role of NCCI Consultants Regulators Questions and Comments

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