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 Ni=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 Li, i=1,2, with retention limits bi,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 Li, i=1,2,, we discuss optimal bi,i=1,2.
Optimal Expected Utility of Wealth for Two Dependent Classes of Insurance Business
GOSIO, CRISTINA;LARI, ESTER CESARINA;RAVERA, MARINA
2013-01-01
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 Ni=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 Li, i=1,2, with retention limits bi,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 Li, i=1,2,, we discuss optimal bi,i=1,2.
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