Optimal combinational quota-share and excess-of-loss reinsurance policies in a dynamic setting

In this paper, we describe a large insurance company's surplus by a Brownian motion with positive drift, which is the approximation of a classical risk process. The problem of minimizing the probability of ruin by controlling the combinational quota-share and excess-of-loss reinsurance strategy is considered. We show that the optimal combinational reinsurance strategy must be the pure excess-of-loss reinsurance strategy. Moreover, we give an explicit solution for the optimal reinsurance strategy.