Hopf-Lax approximation for value functions of L´evy optimal control problems

Michael Kupper, Max Nendel and Alessandro Sgarabottolo
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Michael Kupper: Center for Mathematical Economics, Bielefeld University
Max Nendel: Center for Mathematical Economics, Bielefeld University
Alessandro Sgarabottolo: Center for Mathematical Economics, Bielefeld University

No 747, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

Abstract: In this paper, we investigate stochastic versions of the Hopf-Lax formula which are based on compositions of the Hopf-Lax operator with the transition kernel of a Lévy process taking values in a separable Banach space. We show that, depending on the order of the composition, one obtains upper and lower bounds for the value function of a stochastic optimal control problem associated to the drift controlled Lévy dynamics. Dynamic consistency is restored by iterating the resulting operators. Moreover, the value function of the control problem is approximated both from above and below as the number of iterations tends to infinity, and we provide explicit convergence rates and guarantees for the approximation procedure.

Keywords: Hopf-Lax formula; Lévy process; optimal control problem; nonlinear Lie- Trotter formula; Nisio semigroup; Wasserstein perturbation (search for similar items in EconPapers)
Pages: 12
Date: 2025-08-18
New Economics Papers: this item is included in nep-cmp
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Persistent link: https://EconPapers.repec.org/RePEc:bie:wpaper:747

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