带Poisson跳跃的正倒向随机微分对策的最大值原理与动态规划之间的关系  

Relationship between maximum principle and dynamic programming for forward-backward stochastic differential game with Poisson jumps

作　　者：史敬涛[1] 

机构地区：[1]山东大学数学学院,济南250100

出　　处：《中国科学：数学》2016年第9期1305-1328,共24页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11571205;11301011和11201264)资助项目

摘　　要：本文研究了带Poisson跳跃的零和正倒向随机微分对策的最大值原理与动态规划之间的关系;在一定的可微性假设下,建立了对偶过程、广义Hamilton函数和值函数之间的联系;作为主要结果的应用,讨论了金融市场中一类带有模型不确定性的递归效用投资组合优化问题.This paper is concerned with the relationship between maximum principle and dynamic programming for zero-sum forward-backward stochastic differential game with Poisson jumps. Under certain differentiability conditions, relations among the adjoint processes, the generalized Hamiltonian function and the value function are given. A recursive utility portfolio optimization problem under model uncertainty in the financial market is discussed to show the applications of our result.

关 键 词：随机微分对策 正倒向随机微分方程 Poisson跳跃 最大值原理 动态规划 递归效用 模型不确定性 

分 类 号：O211.63[理学—概率论与数理统计] O221.3[理学—数学]