Abstract
In this paper, the authors consider the optimal investment of the risk model with perturbed diffusion. Insurance companies invest the surplus in risky asset and risk-free asset. This paper discusses the problem of minimizing the ruin probability of insurance company. By solving the corresponding Hamilton-Jacobi-Bellman equations, the optimal investment portfolio and the upper bound of Lundberg of the minimal ruin probability are obtained. Especially,when the claim distribution is exponential distribution, asymptotic optimality and asymptotic uniqueness of strategy A* and R are obtained.
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