随机微分对策与 Hamilton-Jacobi-Bellman-Isaacs 方程的粘性解
概率论
2011-02-19 v1 辛几何
摘要
本文借助倒向随机微分方程（BSDEs）理论研究零和双人随机微分对策。一方面，我们将 Fleming 和 Souganidis 开创性工作的结果推广，考虑由受控 BSDE 定义的成本泛函，并允许 admissible 控制过程依赖于对策开始前发生的事件（这意味着成本泛函成为随机变量）；另一方面，BSDE 方法的应用，特别是 Peng 引入的随机“倒向半群”概念，使得我们可以直接证明对策上下值函数的动态规划原理，而无需借助附加逼近。上下值函数分别被证明为上下 Hamilton-Jacobi-Bellman-Isaacs 方程的唯一粘性解。为此，Peng 的 BSDE 方法从随机控制理论框架被转译到随机微分对策框架。
引用
@article{arxiv.math/0702131,
title = {Stochastic Differential Games and Viscosity Solutions of Hamilton-Jacobi-Bellman-Isaacs Equations},
author = {Rainer Buckdahn and Juan Li},
journal= {arXiv preprint arXiv:math/0702131},
year = {2011}
}
备注
The results were presented by Rainer Buckdahn at the "12th International Symposium on Dynamic Games and Applications" in Sophia-Antipolis (France) in June 2006; They were also reported by Juan Li at 2nd Workshop on "Stochastic Equations and Related Topics" in Jena (Germany) in July 2006 and at one seminar in the ETH of Zurich in November 2006