An Application of Game Theory: Property Catastrophe Risk Load

Two well-known methods for calculating risk load -- Marginal Surplus and Marginal Variance -- are applied to output from catastrophe 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 account lo that new account. For renewal situations, 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 two accounts evenly between 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.