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

Alois Pichler and Ruben Schlotter ()
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Alois Pichler: Faculty of Mathematics, Chemnitz University of Technology, 09111 Chemnitz, Germany
Ruben Schlotter: Faculty of Mathematics, Chemnitz University of Technology, 09111 Chemnitz, Germany

Mathematics of Operations Research, 2023, vol. 48, issue 3, 1657-1678

Abstract: 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.

Keywords: 90C15; 60B05; 62P05; risk measures; optimal control; stochastic processes (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:48:y:2023:i:3:p:1657-1678

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