Risk-Averse Optimal Control in Continuous Time by Nesting Risk Measures

• 成果类型: Article
• 署名作者: Pichler, Alois; Schlotter, Ruben
• 署名单位: Technische Universitat Chemnitz
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2022.1314
• 发表日期: 2023
• 页码: 1657-1678
• 关键词: nonlinear expectations; consistent; PROGRAMS

摘要

This paper extends dynamic control problems from a risk-neutral to a risk-averse setting. We establish a limit for consecutive risk-averse decision making by consistently and adequately nesting coherent risk measures. This approach provides a new perspective on multistage optimal control problems in continuous time. For the limiting case, we elaborate a new dynamic programming principle, which is risk averse, and give risk-averse Hamilton-Jacobi-Bellman equations by generalizing the infinitesimal generator. In doing so, we provide a constructive explanation of the driver g in g-expectation, a dynamic risk measure based on backward stochastic differential equations.