Generalized Risk-Sensitive Optimal Control and Hamilton-Jacobi-Bellman Equation
- Authors
- Moon, Jun
- Issue Date
- May-2021
- Publisher
- IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
- Keywords
- Optimal control; Viscosity; Indexes; Differential equations; Stochastic processes; Dynamic programming; Europe; Backward stochastic differential equations (BSDE); Hamilton& #8211; Jacobi& #8211; Bellman (HJB) equations; risk-sensitive optimal control; viscosity solutions
- Citation
- IEEE TRANSACTIONS ON AUTOMATIC CONTROL, v.66, no.5, pp.2319 - 2325
- Indexed
- SCIE
SCOPUS
- Journal Title
- IEEE TRANSACTIONS ON AUTOMATIC CONTROL
- Volume
- 66
- Number
- 5
- Start Page
- 2319
- End Page
- 2325
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/141977
- DOI
- 10.1109/TAC.2020.3004717
- ISSN
- 0018-9286
- Abstract
- 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.
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