A Level-Set Approach for Stochastic Optimal Control Problems Under Controlled-Loss Constraints

Géraldine Bouveret () and Athena Picarelli ()
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Géraldine Bouveret: Nanyang Technological University
Athena Picarelli: Università di Verona

Journal of Optimization Theory and Applications, 2020, vol. 186, issue 3, No 3, 779-805

Abstract: Abstract We study a family of optimal control problems under a set of controlled-loss constraints holding at different deterministic dates. The characterization of the associated value function by a Hamilton–Jacobi–Bellman equation usually calls for strong assumptions on the dynamics of the processes involved and the set of constraints. To treat this problem in the absence of those assumptions, we first convert it into a state-constrained stochastic target problem and then solve the latter by a level-set approach. With this approach, state constraints are managed through an exact penalization technique.

Keywords: Hamilton–Jacobi–Bellman equations; Viscosity solutions; Optimal control; Expectation constraints; 93E20; 49L20; 49L25; 35K55 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10957-020-01724-8

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