Optimal Expected Utility of Wealth for Two Dependent Classes of Insurance Business

Cristina Gosio, Ester C. Lari, Marina Ravera

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Department of Economics and Business, University of Genova, Genova, Italy.

DOI: 10.4236/tel.[phone]                

Abstract

We consider a modified version of the classical Cramer-Lundberg risk model. In particular, we assume two classes of insurance business dependent through the claim number process N_i, i=1,2: we consider that the number of claims is generated by a bivariate Poisson distribution (N₁, N₂). We also consider the presence of a particular kind of reinsurance contract, supposing that the first insurer concludes an Excess of Loss reinsurance limited by L_i, i=1,2, with retention limits b_i, i=1,2, for the respective classes of insurance business. The aim of this paper is to maximize the expected utility of the wealth of the first insurer, having the retention limits as decision variables. We assume an exponential utility function and, fixed L_i, i=1,2, we discuss optimal b_i, i=1,2.

Keywords

Bivariate Poisson Distribution; Excess of Loss; Exponential Utility Function; Reinsurance; Retention Limits; Risk Theory

Conflicts of Interest

The authors declare no conflicts of interest.

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