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Speaker: Yang Zhou, Professor, South China Normal University
Date: Jan 10, 2022
Location: Tencent Meeting, ID:675902352
Sponsor: School of Mathematics, Shandong University
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.
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