Generalized Risk-Sensitive Optimal Control and Hamilton-Jacobi-Bellman Equation

• 成果类型: Article
• 署名作者: Moon, Jun
• 署名单位: Hanyang University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3004717
• 发表日期: 2021
• 页码: 2319-2325
• 关键词: Optimal control; viscosity; indexes; Differential equations; Stochastic processes; dynamic programming; Europe; Backward stochastic differential equations (BSDE); Hamilton– Jacobi– Bellman (HJB) equations; risk-sensitive optimal control; VISCOSITY SOLUTIONS

摘要

In this article, we consider the generalized risk-sensitive optimal control problem, where the objective functional is defined by the controlled backward stochastic differential equation (BSDE) with quadratic growth coefficient. We extend the earlier results of the risk-sensitive optimal control problem to the case of the objective functional given by the controlled BSDE. Note that the risk-neutral stochastic optimal control problem corresponds to the BSDE objective functional with linear growth coefficient, which can be viewed as a special case of the article. We obtain the generalized risk-sensitive dynamic programming principle for the value function via the backward semigroup associated with the BSDE. Then we show that the corresponding value function is a viscosity solution to the Hamilton-Jacobi-Bellman equation. Under an additional parameter condition, the viscosity solution is unique, which implies that the solution characterizes the value function. We apply the theoretical results to the risk-sensitive European option pricing problem.