| 一个风险敏感最优控制问题的随机最大值原理及在投资选择中的应用 |
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| 引用本文： | 王光臣,吴臻.一个风险敏感最优控制问题的随机最大值原理及在投资选择中的应用[J].自动化学报,2007,33(10):1043-1047. |
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| 作者姓名： | 王光臣 吴臻 |
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| 作者单位： | 1.山东大学数学与系统科学学院 济南 250100 |
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| 基金项目： | Supported by National Natural Science Foundation of China （10671112）, National Basic Research Program of China （973 Program） （2007CB814904）, the Natural Science Foundation of Shandong Province （Z2006A01）, and the Chinese New Century Young Teachers Program The authors would like to thank the referees for a careful reading of this paper and helpful suggestions which made the revised version more readable. |
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| 摘 要： | 在本文, 我们主要研究了一类产生于金融市场中投资选择问题的风险敏感最优控制问题. 用经典的凸变分技术, 我们得到了该类问题的最大值原理. 最大值原理的形式相似于风险中性的情形. 但是, 对偶方程和变分不等式明显地依赖于风险敏感参数 γ. 这是与风险中性情形的主要区别之一. 我们用该结果解决一类最优投资选择问题. 在投资者仅投资国内债券和股票的情况下, 前人用贝尔曼动态规划原理所得的最优投资策略仅是我们结果的特殊形式. 我们也给了一些数值算例和图, 他们显式地解释了最大期望效用和模型中参数的关系.
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| 关 键 词： | 随机最大值原理 风险敏感控制 凸变分技术 投资组合选择 |
| 收稿时间： | 2006-10-16 |
| 修稿时间： | 2006-10-16 |
Stochastic Maximum Principle for a Kind of Risk-sensitive Optimal Control Problem and Application to Portfolio Choice |
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| WANG Guang-Chen,WU Zhen.Stochastic Maximum Principle for a Kind of Risk-sensitive Optimal Control Problem and Application to Portfolio Choice[J].Acta Automatica Sinica,2007,33(10):1043-1047. |
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| Authors: | WANG Guang-Chen WU Zhen |
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| Affiliation: | 1.School of Mathematics and System Sciences, Shandong University, Jinan 250100, P.R.China;2.School of Mathematical Sciences, Shandong Normal University, Jinan 250014, P.R. China |
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| Abstract: | In this paper, we mainly study a kind of risk-sensitive optimal control problem motivated by a kind of portfolio choice problem in certain financial market. Using the classical convex variational technique, we obtain the maximum principle for this kind of problem. The form of the maximum principle is similar to its risk-neutral counterpart. But the adjoint equation and the variational inequality heavily depend on the risk-sensitive parameter 7. This is one of the main difference from the risk-neutral case. We use this result to solve a kind of optimal portfolio choice problem. The optimal portfolio strategy obtained by the Bellman dynamic programming principle is a special case of our result when the investor only invests the home bond and the stock. Computational results and figures explicitly illustrate the relationships between the maximum expected utility and the parameters of the model. |
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| Keywords: | Stochastic maximum principle risk-sensitive control convex variational technique portfolio choice |
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