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

TL;DR

This paper explores the connection between maximum principle and dynamic programming in risk-sensitive stochastic control, providing theoretical relations and applying them to a financial portfolio optimization problem.

Contribution

It establishes the relationship between maximum principle and dynamic programming for risk-sensitive control under smooth value functions, with an application to finance.

Findings

Relations among adjoint processes, Hamiltonian, and value function are derived.

Application to a linear-quadratic portfolio optimization problem.

Provides theoretical insights for risk-sensitive control methods.

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.