| 跳扩散最优控制的随机最大值原理及在金融中的应用 |
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| 引用本文： | 史敬涛,吴臻.跳扩散最优控制的随机最大值原理及在金融中的应用[J].应用概率统计,2011,27(2). |
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| 作者姓名： | 史敬涛 吴臻 |
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| 作者单位： | 山东大学数学学院,济南,250100 |
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| 基金项目： | the China Postdoctoral Science Foundation Funded Project，the Postdoctoral Innovation Foundation Funded Project of Shandong Province，the National Natural Sciences Foundations of China，Shandong Province，the Independent Innovation Foundations of Shandong University，the National Basic Research Program of China (973 Program)，the National Natural Science Foundations of China，Shandong Province，the Science Fund for Distinguished Young Scholars of Shandong Province，Shandong University |
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| 摘 要： | 讨论了由金融市场中投资组合和消费选择问题引出的一类最优控制问题,投资者的期望效用是常数相对风险厌恶(CRRA)情形.在跳扩散框架下,利用古典变分法得到了一个局部随机最大值原理.结果应用到最优投资组合和消费选择策略问题,得到了状态反馈形式的显式最优解.
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| 关 键 词： | 随机最大值原理 最优控制 跳扩散 投资组合和消费选择 CRRA效用 |
A Stochastic Maximum Principle for Optimal Control of Jump Diffusions and Applications to Finance |
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| SHI JINGTAO,Wu ZHEN.A Stochastic Maximum Principle for Optimal Control of Jump Diffusions and Applications to Finance[J].Chinese Journal of Applied Probability and Statisties,2011,27(2). |
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| Authors: | SHI JINGTAO Wu ZHEN |
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| Institution: | Shi Jingtao Wu Zhen(School of Mathematics,Shandong University,Jinan,250100) |
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| Abstract: | An optimal control problem motivated by a portfolio and consumption choice problem in the financial market where the expected utility of the investor is assumed to be the Constant Relative Risk Aversion (CRRA) case is discussed. A local stochastic maximum principle is obtained in the jump-diffusion setting using classical variational method. The result is applied to make optimal portfolio and consumption choice strategy for the problem and the explicit optimal solution in the state feedback form is given. |
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| Keywords: | Stochastic maximum principle optimal control jump diffusions portfolio and consumption choice CRRA utility |
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