Hopf-Lax approximation for value functions of Lévy optimal control problems

Kupper, Michael; Nendel, Max und Sgarabottolo, Alessandro (2025): Hopf-Lax approximation for value functions of Lévy optimal control problems. In: Proceedings of the American Mathematical Society, Bd. 154: S. 243-254 [Forthcoming]

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.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik > Finanz- und Versicherungsmathematik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 0002-9939
• Sprache: Englisch