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

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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 (*N*_{1}, *N*_{2}). 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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

*Theoretical Economics Letters*, Vol. 3 No. 2, 2013, pp. 90-95. doi: 10.4236/tel.2013.32015.

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