A Stochastic Maximum Principle for Relaxed Control with General Risk Measure and Its Application in Finance

Author(s)

,
&

Abstract

This paper deals with optimal relaxed control problem where the cost functional is a general risk measure instead of an expectation. We develop a stochastic maximum principle for this kind of optimal control problems using a variational method. Then, under the expectation optimization objective, a dynamic programming principle is studied and its connections to the adjoint process is shown. At last, the result is applied to two examples. One is a linear quadratic problem and the other is an optimal investment problem.

Keywords:

Measure valued control process stochastic maximum principle

Author Biographies

  • Shuaiqi Zhang

    School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China

  • Jie Xiong

    Department of Mathematics, and SUSTech International Center for Mathematics, Southern University of Science and Technology, Shenzhen 518055, China

  • Xin Zhang

    School of Mathematics, Southeast University Nanjing, Nanjing 211189, China

About this article

Abstract View

  • 1545

Pdf View

  • 85

DOI

10.4208/cmaa.2025-0017