On the Optimal Control Problem for New Business

In actuary research field, optimal dividends problems for insurance companies are widely studied and recently, this area has become one of the hottest topics because that it is not only has the theoretical but also the practical importance. In this paper, the optimal control problem for the insurance which pursues new businesses is studied. The objective of our paper is to maximize the exponential utility function. Our contribution is that the explicit control policy and the maximal discounted utility are obtained by solving the HJB (Hamilton-Jaccobi-Bellman) equation.