Financial Bounds for Insurance Claims

In this paper insurance claims are priced using an indifference pricing principle. We first revisit the traditional economic framework and then extend it to include the presence of a complete financial market. In this context we derive lower bounds for claims’ prices, and these bounds correspond to the market prices of some explicitly known financial payoffs. In particular we show that the discounted expected value is no longer valid as a classical lower bound for insurance prices in general, and has to be corrected by a covariance term which reflects the interaction between the insurance claim and the financial market. The paper is illustrated by examples with equity-linked insurance contracts subject to financial and mortality risk. Key-words: Cost-efficiency, Jensen’s inequality, Fréchet bounds, Indifference pricing. Carole Bernard, Department of Statistics and Actuarial Science at the University of Waterloo (email: [email protected]). Corresponding author : Steven Vanduffel, Vrije Universiteit Brussel. (e-mail: [email protected]). Both authors gratefully acknowledge the program “Brains Back to Brussels” that funded an extended research visit of C. Bernard at VUB in Brussels during which this paper was completed. S. Vanduffel acknowledges the financial support of the BNP Paribas Fortis Chair in Banking. C. Bernard also acknowledges support from the Natural Sciences and Engineering Research Council of Canada. The authors would like to thank participants in seminars in Ulm, Rennes, Louvain-la-Neuve, Maastricht, Brussels (ULB), Rio, and Waterloo for interesting suggestions.