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. Copyright © 2006 John Wiley & Sons, Ltd.