Excess-of-loss reinsurance under taxes and fixed costs

We consider the problem of dividend optimization for an insurance company which can use the excess-of-loss reinsur- ance to control its risk. The decrease of risk results in a loss of potential profits in view of the necessity to diverge a part of the premiums to the reinsurance company. In addition to reinsurance the decision is made about the time and the amount of dividends to be paid out to shareholders. Each time when the dividends are paid a set-up cost of K is incurred independent of the amount distributed. In addition the dividends are taxed at the rate of 1 − k ,0 <k< 1. The resulting problem becomes a mixed regular-impulse stochastic control problem for a controlled diffusion process. We solve this problem and find the optimal policy. We give an economic interpretation to the solution obtained. The solution reveals an interesting dependence of the optimal policy on the parameters of the model. We also discuss an extension of this problem to the case when there are restrictions on the level of reinsurance available and show how one can construct the value function and the optimal policy in this case.

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