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Optimal control on graphs: existence, uniqueness, and long-term behavior

Author

Listed:
  • Olivier Guéant

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Iuliia Manziuk

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

The literature on continuous-time stochastic optimal control seldom deals with the case of discrete state spaces. In this paper, we provide a general framework for the optimal control of continuous-time Markov chains on finite graphs. In particular, we provide results on the long-term behavior of value functions and optimal controls, along with results on the associated ergodic Hamilton-Jacobi equation.

Suggested Citation

  • Olivier Guéant & Iuliia Manziuk, 2020. "Optimal control on graphs: existence, uniqueness, and long-term behavior," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-03252606, HAL.
    • Handle: RePEc:hal:cesptp:hal-03252606
    DOI: 10.1051/cocv/2019071
    Note: View the original document on HAL open archive server: https://hal.science/hal-03252606
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    Cited by:

    1. Alexander Barzykin & Philippe Bergault & Olivier Guéant, 2023. "Algorithmic market making in dealer markets with hedging and market impact," Mathematical Finance, Wiley Blackwell, vol. 33(1), pages 41-79, January.
    2. Philippe Bergault & Olivier Gu'eant, 2023. "Modeling liquidity in corporate bond markets: applications to price adjustments," Papers 2309.04216, arXiv.org, revised Oct 2023.

    More about this item

    Keywords

    Optimal control; graphs; asymptotic analysis; Ergodic Hamilton-Jacobi equation;
    All these keywords.

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