Risk-Averse Optimal Control in Continuous Time by Nesting Risk Measures
将动态控制问题从风险中性扩展到风险厌恶，通过嵌套一致风险度量建立连续时间多阶段最优控制的新视角，推导风险厌恶动态规划原理和HJB方程，并解释g-期望中的驱动项g。
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. Funding: This work was supported by Deutsche Forschungsgemeinschaft [Project-ID 416228727 – SFB 1410].