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

Published Online:https://doi.org/10.1287/moor.2022.1314

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].

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