TITLE:
Optimal Expected Utility of Wealth for Two Dependent Classes of Insurance Business
AUTHORS:
Cristina Gosio, Ester C. Lari, Marina Ravera
KEYWORDS:
Bivariate Poisson Distribution; Excess of Loss; Exponential Utility Function; Reinsurance; Retention Limits; Risk Theory
JOURNAL NAME:
Theoretical Economics Letters,
Vol.3 No.2,
April
30,
2013
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, 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 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.