| Optimal Proportional Reinsurance for Controlled Risk Process which is Perturbed by Diffusion |
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| 作者姓名： | Zhi-bin Liang |
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| 作者单位： | [1]Institute of Mathematics and Computer Science, Nanjing Normal University, Nanjing 210097, China [2]School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China |
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| 基金项目： | Supported by the National Natural Science Foundation of China （No. 10571092）;Acknowledgment The author would like to thank the anonymous referees for their careful reading and helpful comments on an earlier version of this paper, which led to a considerable improvement of the presentation of the work. |
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| 摘 要： |
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| 关 键 词： | 最佳比例 可控理论 随机控制 方程式 |
| 收稿时间： | 4 January 2006 |
| 修稿时间： | 2006-01-042006-09-25 |
Optimal Proportional Reinsurance for Controlled Risk Process which is Perturbed by Diffusion |
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| Zhi-bin Liang.Optimal Proportional Reinsurance for Controlled Risk Process which is Perturbed by Diffusion[J].Acta Mathematicae Applicatae Sinica,2007,23(3):477-488. |
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| Authors: | Zhi-bin Liang |
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| Institution: | (1) Institute of Mathematics and Computer Science, Nanjing Normal University, Nanjing, 210097, China;(2) School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071, China |
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| Abstract: | In this paper, we study optimal proportional reinsurance policy of an insurer with a risk process which is perturbed by a diffusion. We derive closed-form expressions for the policy and the value function, which are optimal in the sense of maximizing the expected utility in the jump-diffusion framework. We also obtain explicit expressions for the policy and the value function, which are optimal in the sense of maximizing the expected utility or maximizing the survival probability in the diffusion approximation case. Some numerical examples are presented, which show the impact of model parameters on the policy. We also compare the results under the different criteria and different cases. |
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| Keywords: | Stochastic control Hamilton-Jacobi-Bellman equation jump-diffusion brownian motion diffusion approximation proportional reinsurance |
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