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Stochastic Optimal Control Models for the Insurance Company with Bankruptcy Return |
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PP: 273-282 |
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Author(s) |
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Qingbin Meng,
Zhendong Li,
Menghai Wang,
Xin Zhang,
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Abstract |
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| In this paper we consider the optimal control problem for a insurance company. Our objective is to maximize the expectation
of discounted dividends and its terminal value which represents the company liquidation value upon the time of bankruptcy. The surplus
of the insurance company is governed by the Brownian motion with a constant drift and a diffusion term. The company can manage
its risk exposure simultaneously through proportional reinsurance. Apart from the proportional reinsurance, the insurance company
also pays out dividends with bounded dividends rate. With the help of the stochastic dynamic programming approach, we solve the
control problem of maximizing the expectation of discounted dividends and the terminal value. We first construct a solution to the
HJB equation and then verify that the solution of the HJB equation is indeed the optimal value function for our problem. We also give
explicit expressions of the optimal strategies. |
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