In this paper, the insurance company invests its wealth in a capital market composed of a riskless asset and a risky asset. The aggregate claim process of the insurance company is modeled by the Gamma process so as to make it closer to the reality. In practice, the insurance company provides not only those policies with large lose coverings but also policies with small ones. The Gamma process can describe this characteristic better than the compound Poisson process. It is assumed that the insurance company can purchase proportional reinsurance or excess-of-loss reinsurance. Two kinds of optimization problems are considered: maximizing the expected utility of the terminal wealth and minimizing the probability of ruin. For the problem of maximizing the expected utility of the terminal wealth, the explicit optimal value functions and optimal strategies are obtained. For the problem of minimizing the ruin probability, a sufficient condition for the optimal value function and the optimal strategy is obtained.

在本文中，保险公司将其财富投资于由无风险资产和风险资产组成的资本市场。保险公司的总索赔流程以Gamma流程为模型，从而使其更接近实际。实际上，保险公司不仅提供那些损失较大的保单，而且还提供较小损失的保单。与复合泊松过程相比，伽玛过程可以更好地描述此特性。假设保险公司可以购买比例再保险或损失超额再保险。考虑了两种优化问题：最大化终端财富的预期效用和最小化破产的可能性。对于使终端财富的预期效用最大化的问题，得到了明确的最优值函数和最优策略。针对最小化破产概率的问题，获得了最优函数和最优策略的充分条件。