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

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  • Kupper, Michael

    (Center for Mathematical Economics, Bielefeld University)

  • Nendel, Max

    (Center for Mathematical Economics, Bielefeld University)

  • Sgarabottolo, Alessandro

    (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.

Suggested Citation

  • Kupper, Michael & Nendel, Max & Sgarabottolo, Alessandro, 2025. "Hopf-Lax approximation for value functions of L´evy optimal control problems," Center for Mathematical Economics Working Papers 747, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:747
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    File URL: https://pub.uni-bielefeld.de/download/3006255/3006256
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    References listed on IDEAS

    as
    1. Daniel Bartl & Samuel Drapeau & Ludovic Tangpi, 2020. "Computational aspects of robust optimized certainty equivalents and option pricing," Mathematical Finance, Wiley Blackwell, vol. 30(1), pages 287-309, January.
    2. Gerhard Winkler, 1988. "Extreme Points of Moment Sets," Mathematics of Operations Research, INFORMS, vol. 13(4), pages 581-587, November.
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