自动化学报2007，Vol.33Issue(10)：1043-1047,5.
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
Stochastic Maximum Principle for a Kind of Risk-sensitive Optimal Control Problem and Application to Portfolio Choice
摘要
Abstract
In this paper, we mainly study a kind of risk-sensitive optimal control problem motiwted 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 γ. 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.关键词
Stochastic maximum principle/ risk-sensitive control/ convex variational technique/ portfolio choiceKey words
Stochastic maximum principle/ risk-sensitive control/ convex variational technique/ portfolio choice分类
信息技术与安全科学引用本文复制引用
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):1043-1047,5.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 （10671112）
