跳扩散最优控制的随机最大值原理及在金融中的应用(英文)  

A Stochastic Maximum Principle for Optimal Controlof Jump Diffusions and Applications to Finance

作　　者：史敬涛[1] 吴臻[1] 

机构地区：[1]山东大学数学学院,济南250100

出　　处：《应用概率统计》2011年第2期127-137,共11页Chinese Journal of Applied Probability and Statistics

基　　金：supported by the China Postdoctoral Science Foundation Funded Project(20100481278);the Postdoctoral Innovation Foundation Funded Project of Shandong Province(201002026);the National Natural Sciences Foundations of China(11026185),the National Natural Sciences Foundations of China(10921101);the National Natural Sciences Foundations of Shandong Province(ZR2010AQ004),the National Natural Sciences Foundations of Shandong Province(2008BS01024);the Independent Innovation Foundations of Shandong University(IIFSDU,2009TS036,2010TS060);supported by the National Basic Research Program of China(973Program,2007CB814904);the Science Fund for Distinguished Young Scholars of Shandong Province(JQ200801);the Science Fund for Distinguished Young Scholars of Shandong University(2009JQ004)

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.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.

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 

分 类 号：O211.63[理学—概率论与数理统计] O231.3[理学—数学]