Relationship between Maximum Principle and Dynamic Programming Principle for Risk-Sensitive Stochastic Optimal Control Problems with Applications

2025/07/09 by Dong, Huanqing, Jingtao Shi, Shi, Jingtao
Computer Science · Decision Sciences · Economics, Econometrics and Finance · #35K15 #49N10 #60H10 #93E20 #Adaptive Dynamic Programming Control #FOS: Mathematics #Optimization and Control (math.OC) #Risk and Portfolio Optimization #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2507.06504

openalex publication_date 2025/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with the relationship between maximum principle and dynamic programming principle for risk-sensitive stochastic optimal control problems. Under the smooth assumption of the value function, relations among the adjoint processes, the generalized Hamiltonian function, and the value function are given. As an application, a linear-quadratic risk-sensitive portfolio optimization problem in the financial market is discussed.

Citations

• A Risk-Sensitive Global Maximum Principle for Controlled Fully Coupled FBSDEs with Applications
• Stochastic maximum principle, dynamic programming principle, and their relationship for fully coupled forward-backward stochastic control systems
• Connection between MP and DPP for Stochastic Recursive Optimal Control Problems: Viscosity Solution Framework in General Case
• A Stochastic Maximum Principle for Risk-Sensitive Mean-Field Type\n Control

Related

• Relationships Between the Maximum Principle and Dynamic Programming for Infinite Dimensional Non-Markovian Stochastic Control Systems
• Dynamic programming in convex stochastic optimization
• The Relationship between Maximum Principle and Dynamic Programming Principle for Stochastic Recursive Control Problem with Random Coefficients
• Relationship between maximum principle and dynamic programming principle for recursive optimal control problem of stochastic evolution equations
• Relationships Between the Maximum Principle and Dynamic Programming for Infinite Dimensional Stochastic Control Systems