报告题目：The existence and uniqueness of viscosity solutions to generalized Hamilton-Jacobi-Bellman equations

报告时间： 2018年6月22日下午 4:00

报告地点： J9-525 （泰山学者实验室）

报 告 人： 嵇少林教授（山东大学）
报告人简介：
    嵇少林，山东大学教授。1999年获得博士学位，是彭实戈院士创新学术团队成员之一，2011年入选教育部新世纪优秀人才支持计划。研究领域：金融数学、随机控制和非线性期望理论。近年来，嵇少林教授在Review of financial studies, Probability theory and the related fields和SIAM Control and Optimization等杂志上发表了一系列的成果。研究的问题包括模型不确定下的资产定价公式、非线性期望下Neyman - Pearson基本引理和G-布朗运动驱动下的倒向随机微分方程理论。
内容简介：
    In this report, we study the existence and uniqueness of viscosity solutions to generalized Hamilton-Jacobi-Bellman (HJB) equations combined with algebra equations. This generalized HJB equation is related to a stochastic optimal control problem for which the state equation is described by a fully coupled forward-backward stochastic differential equation (FBSDE). By extending Peng's backward semigroup approach to this problem, we obtain the dynamic programming principle (DPP) and show that the value function is a viscosity solution to this generalized HJB equation. As for the proof of the uniqueness of viscosity solution, the analysis method in Barles, Buckdahn and Pardoux -Baeles usually does not work for this fully coupled case. With the help of the uniqueness of the solution to FBSDEs, we propose a novel probabilistic approach to study the uniqueness of the solution to this generalized HJB equation. We obtain that the value function is the minimum viscosity solution to this generalized HJB equation. Especially, when the coefficients are independent of the control variable or the solution is smooth, the value function is the unique viscosity solution. This is a joint work with Mingshang Hu and Xiaole Xue.