The Research On The Profit Of Participating Insurance Products With Consideration On Reinsurance

In recent years, the with-profit life insurance products experienced a rapid development and became the main body of the insurance industry. In some influential insurance companies, the total premium of with-profit products is more than half of the total premium of all policies. The percentage in some companies is even higher. As a result, the performance of this kind of product is critical for life insurance Company, so it is necessary to do some researches on the product. Meanwhile, the reinsurance market became better and better for life insurance industry and can offer good reinsurance cover for with-profit products, as the participation of WTO for Chinese insurance market came near.In china, the expectation of the profit is the important factor which can affect the motivation of policyholder. If the level of the profit is too low to meet the expectation of the policyholder, some of them will decide to withdraw, it has negative impact on the insurer. Vice versa, if the level of the profit is a bit higher that exceed the endurance of the insurer, it will bring the insurer with some troubles.Based on this, this article tried to solve the problem of profit distributing by optimal control theory, with the consideration of reinsurance together with a profit distribution problem.At first, the article tries to construct a systematic function and value function about the reinsurance and profit distribution. The systematic function is described by a diffusion process. After that, the article discusses the characteristics of these functions in order for the procedure of solving them.Secondly, the article tries to find out the relative HJB (Hamilton-Jacobi-Bellman) equation for the reason of the HJB equation can transform the optimal value function to the problem of solving differential equation. The article takes the advantage of it to discuss the continuous profit assumption and solve the value function firstly. The result of the value function is a combination control decision between reinsurance and profit distribution over the condition of the optimal value function.Lastly, the article tries to discuss the form the optimal value function with the assumption of discrete profit, and the optimal value function in the situation of different premium loading on the insurer and reinsurer.