We consider an optimal control problem of a property insurance company withproportional reinsurance strategy. The insurance business brings in catastropherisk, such as earthquake and flood. The catastrophe risk could be partlyreduced by reinsurance. The management of the company controls the reinsurancerate and dividend payments process to maximize the expected present value ofthe dividends before bankruptcy. This is the first time to consider thecatastrophe risk in property insurance model, which is more realistic. Weestablish the solution of the problem by the mixed singular-regular control ofjump diffusions. We first derive the optimal retention ratio, the optimaldividend payments level, the optimal return function and the optimal controlstrategy of the property insurance company, then the impacts of the catastropherisk and key model parameters on the optimal return function and the optimalcontrol strategy of the company are discussed.
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