Optimal excess of loss reinsurance-barrier dividend strategies with investment

: The optimal barrier dividend problem under excess of loss reinsurance strategy has rarely been studied so far. We combine the risk factors such as market friction and terminal residual value with risk investment and risk control strategy, and study the resulting optimal investment - excess of loss reinsurance - barrier dividend problem. Based on the dynamic programming principle, we establish the Hamilton - Jacobi - Bellman equation, and obtain the explicit solutions for the optimal investment - excess of loss reinsurance strategy. The optimal dividend function is solved by the differential - integral method. The existence and uniqueness of the optimal dividend boundary is proved.