Abstract: To better reflect the insurance prectice and help insurance company making more robust strategy, we assume that the number of claims follows the compound Poisson-Geometric process, and investigate the optimal investment-reinsurance-hybrid dividend problem under the assumption that the insurance's reserve price follows a diffusion process. Based on the criterion of maximizing the expected total present value of dividends, the optimal desicion model is utiliting dynamic programming priciple, and the optimal policy is obtained through solving the HJB equation. The closed-form optimal investment-reinsurance-hybrid dividend strategies have been derived under the special case: the loss rate of reinsurance premiums is equal to the dividend discount rate. Finally, some numerical examples and their economic analyses are provided to illustrate the reasonability of the obtained theoretical results.

Key words: compound Poisson-Geometric process, diffusion process, investment strategy, reinsurance policy, hybrid dividend, HJB equation, deviation coefficient