Lecturer: Yang Zhou

Abstract:

A robust control problem is considered in this paper, where the controlled stochastic differential equations include ambiguity parameters and satisfy some mild assumptions, the objective function is expressed as a backward stochastic differential equation with the driver depending on the value function. We establish the existence and uniqueness of the value function in proper space under some mild assumptions. And we provide the verification theorem, which shows that the solution of the associated Hamilton-Jacobi-Bellman-Isaacs equation is the unique value function under some proper assumptions. Moreover, we apply the results to solve two optimal investment problems in markets with ambiguity, one of which is with Heston stochastic volatility model. In particular, we establish some estimations for Heston model with ambiguity parameters.

Introduction to the Lecturer:

Yang Zhou, professor and doctoral supervisor from School of Mathematical Sciences, South China Normal University, has obtained his doctoral degree in South China Normal University in 2007, has been engaged in post-doctoral research in Fudan University from 2009 to 2011, and went to Singapore and South Korea for cooperative visiting research. His research fields include financial mathematics, free boundary problem and stochastic control and his main research directions are American derivatives, optimal portfolio, optimal stopping time problem and free boundary problem in finance. Some research results are issued onMathematics of Operations Research,SIAM Journal on Control and Optimization,Insurance: Mathematics and EconomicsandJournal of Differential Equations. He has presided over a number of programs of National Natural Science Foundation of China and provincial and ministerial funds.

Invitee:

Shi Jingtao, Professor from School of Mathematics

Date:

10:00-11:00, January 10 (Monday)

Venue:

Tencent Meeting ID: 675902352, password: 202201

Hosted by: School of Mathematics, Shandong University