This paper considers a correlated aggregate claims model with common Poisson shocks, which allows for dependence in n (n ≥ 2) classes of business across m (m ≥ 1) different types of stochastic events. The dependence structure between different claim numbers is connected with the thinning procedure. Under combination of quota-share and excess of loss reinsurance arrangements, we examine the properties of the proposed risk model. An upper bound for the ruin probability determined by the adjustment coefficient is established through martingale approach. We reduce the problem of optimal reinsurance strategy for maximizing the insurer’s adjustment coefficient and illustrate the results by numerical examples.
Common poisson shocks Thinning procedure Ruin probability Adjustment coefficient Optimal reinsurance
Mathematics Subject Classification (2010)
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Bai L, Cai J, Zhou M (2013) Optimal reinsurance policies for an insurer with a bivariate reserve risk process in a dynamic setting. Insurance: Mathematics and Economics 53(3):664–670MathSciNetzbMATHGoogle Scholar