An Application of Garne Theory : Property Catastrophe Risk Load by

Two well-known methods for calculating risk load -Marginal Surplus and Marginal Variance -are applied to output from caiastrophe modeling software. Risk loads for these “marginal methods” are calculated for sample new and renewal accounts. Differences between new and renewal pricing are examined. For new situations, both current methods allocate the full marginal impact of addition of a new accounl lo that new account. For renewal situalions, a new concept is introduced -“renewal additivity”. Neither marginal method is renewal additive. A new method is introduced, inspired by game theory, which splits the mutual covariance between any hvo accounts evenly behveen those accounts. The new method is extended and generalized to a proportional sharing of mutual covariance between any two accounts. Both new approaches are tested in new and renewal situations. (1) Introduction The calculation of risk load continues to be a topic of interest in the actuarial community -see Bault [l] for a recent survey of well-known alternatives. One area where the CAS literature is somewhat scarce, and the need is great, is calculation of risk loads for property catastrophe insurance. The new catastrophe modeling products produce modeled “occurrence size-of-loss distributions” for a series of simulated events. Using the occurrence size-of-loss distribution, one can easily calculate expected losses, loss variance and standard deviation. Two of the more well-known risk load methods from the CAS titerature -what I call “Marginal Surplus” (MS) from Kreps [3] and “Marginal Variance” (MV) from Meyers [6] -use the marginal change in portfolio standard deviation (respectively variance) due to addition of a new account as a means to calculate the risk load for that new account. However, as we shall see, problems arise when we use these marginal methods in calculating the risk loads for the renewal of the accounts in a portfolio. We apply the MV and MS methods to a simplified occurrence size-of-loss distribution, calculate risk loads both in assembling or building up a potiolio of risks, and in subsequently renewing that por?folio. Then we discuss the differences between build-up and renewal results. 1 wuutd Iike to thank Eric Lemieux and Sean Uingsted for their suppoft, editorial soggestions and review of early drafts. / woufd also like fo fhank Paul Kneuer for bis fhoughtfu/ and insighfful review which improved me paper.