Ruin Probability in a Correlated Aggregate Claims Model with Common Poisson Shocks: Application to Reinsurance

Abstract

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.

On Minimizing the Ultimate Ruin Probability of an Insurer by Reinsurance

“…On the other hand, the literature shows that the optimal reinsurance strategy is a pure XL, that is, (1, * ) (see, e.g., [7,8,16]). Possible extensions to the work are the inclusion of investments and dividend payouts as well as considering noncheap reinsurance, whereby, for a given risk, the reinsurer requires more premium and therefore uses a higher safety loading, than the insurer.…”

“…Theorem 2. Suppose Φ ∈ 2 is an increasing strictly concave function satisfying HJB equation (7) subject to the boundary conditions…”

“…Additionally, they obtained an explicit expression for the survival probability under the optimal reinsurance strategy and found it to be larger than that with the aforementioned strategies. Hu and Zhang [7] introduced a general risk model involving dependence structure with common Poisson shocks. Under a combined quotashare and excess-of-loss reinsurance arrangements, they studied the optimal reinsurance strategy for maximizing the insurer's adjustment coefficient and established that excessof-loss reinsurance was optimal from the insurer's point of view.…”

Minimizing Lundberg inequality for ruin probability under correlated risk model by investment and reinsurance

“…In the classical risk model, an upper bound for ruin probability is also called Lundberg inequality. Hu and Zhang [ 22 ] studied optimal reinsurance for minimizing the upper bound of ultimate ruin probability in a correlated risk model with common shocks. The results in [ 22 ] show that the upper bound of the ruin probability in the model with reinsurance chance is less than the one in the model without reinsurance chance.…”

“…Hu and Zhang [ 22 ] studied optimal reinsurance for minimizing the upper bound of ultimate ruin probability in a correlated risk model with common shocks. The results in [ 22 ] show that the upper bound of the ruin probability in the model with reinsurance chance is less than the one in the model without reinsurance chance. Thus, under the correlated risk model, reinsurance business can really reduce the exposure of the insurance company, and this impact can be quantified by comparing the upper bound.…”