The Control Theory About The Optimization Of New Business

In this paper, we first consider the utility function especially the exponential utility. In this case, we can obtain the explicit results. Then, in section 4, we consider the model with investment. There are risk-free asset and risky asset available for investors. Let A_t be the total amount of money invested in the stock market at time t . (b_t ,A_t) are control admissible policy. From the analysis of the HJB equation, the explicit results about the dividends is evident when the claim amount X, Y are all exponential distribution. Then the optimal b can be given theoretically. In section 5 we consider maximizing expected utility of terminal wealth with the admissible policy (b_t ,A_t).