# American Institute of Mathematical Sciences

October  2008, 4(4): 801-815. doi: 10.3934/jimo.2008.4.801

## On maximizing the expected terminal utility by investment and reinsurance

 1 School of Mathematics and Computer Sciences, Anhui Normal University, Wuhu, Anhui, 241003, China 2 School of Finance and Statistics, East China Normal University, Shanghai, 200241, China 3 School of Finance and Statistics,, East China Normal University, Shanghai, 200241, China

Received  June 2007 Revised  August 2008 Published  November 2008

In this paper, optimal problems for the insurer who can invest on risky market and purchase reinsurance are considered. The surplus process of the insurer is a kind of perturbed classical risk model with stochastic premium income. The investment return generating process of the risky market is a drifted Brownian motion plus a compound Poisson process. The objective function in this paper is to maximize the expected utility of wealth of the insurer at terminal time, say $T$. By solving the Hamilton-Jacobi-Bellman equations related to our optimal control problems, the closed form expression for optimal strategy and the value function is derived, which indicates that the value function for an insurer to purchase both investment and reinsurance is always better than the one for the insurer to purchase only either investment or reinsurance.
Citation: Lin Xu, Rongming Wang, Dingjun Yao. On maximizing the expected terminal utility by investment and reinsurance. Journal of Industrial & Management Optimization, 2008, 4 (4) : 801-815. doi: 10.3934/jimo.2008.4.801
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