Optimal insurance risk control with multiple reinsurers

An optimal insurance risk control problem is discussed in a general situation where several reinsurance companies enter into a reinsurance treaty with an insurance company. These reinsurance companies adopt variance premium principles with different parameters. Dividends with fixed costs and taxes are paid to shareholders of the insurance company. Under certain conditions, a combined proportional reinsurance treaty is shown to be optimal in a class of plausible reinsurance treaties. Within the class of combined proportional reinsurance strategies, analytical expressions for the value function and the optimal strategies are obtained.