Optimal Proportional Reinsurance With Dependent Risks Under A Value-at-Risk Constraint

In this article, we investigate the optimal reinsurance strategy in a risk model with two dependent classes of insurance business under a VaR constraint, where the two claim number processes are correlated through a common shock component. The problem is formulated as a constrained utility maximization problem over a period of time. Using the technique of dynamic programming, we derive the Hamilton-Jacobi-Bellman equation. The method of Lagrange multiplier is used to tackle the constraint. Finally we use numerical experiments to demonstrate the effect of the risk constraint on the optimal strategy.