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

This paper investigates optimal investment and reinsurance policies for an insurance company under a correlated risk model with common Poisson shocks. The goal of the insurance company is to minimize the ultimate ruin probability. By the dynamic programming principle, the Hamilton–Jacobi–Bellman (HJB for short) equation associated with this control problem is obtained. Since there is no explicit solution to the HJB equation, this paper alternates to find the minimal exponential upper bound of the ruin probability. The exponential upper bound of ruin probability is also called Lundberg inequality. Minimizing Lundberg inequality is equal to finding the maximal Lundberg coefficient. It turns out that the optimal investment and reinsurance polices are constant policies. Some numerical examples are given to illustrate the impact of the dependent structure and the investment chance on the upper bound.