Optimal stopping and a non-zero-sum Dynkin game in discrete time with risk measures induced by BSDEs

Miryana Grigorova and Marie-Claire Quenez
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Miryana Grigorova: Institut für Mathematik [Humboldt] - HU Berlin - Humboldt-Universität zu Berlin = Humboldt University of Berlin = Université Humboldt de Berlin
Marie-Claire Quenez: LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique

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Abstract: We first study an optimal stopping problem in which a player (an agent) uses a discrete stopping time in order to stop optimally a payoff process whose risk is evaluated by a (non-linear) $g$-expectation. We then consider a non-zero-sum game on discrete stopping times with two agents who aim at minimizing their respective risks. The payoffs of the agents are assessed by g-expectations (with possibly different drivers for the different players). By using the results of the first part, combined with some ideas of S. Hamadène and J. Zhang, we construct a Nash equilibrium point of this game by a recursive procedure. Our results are obtained in the case of a standard Lipschitz driver $g$ without any additional assumption on the driver besides that ensuring the monotonicity of the corresponding $g$-expectation.

Keywords: optimal stopping; non-zero-sum Dynkin game; g-expectation; dynamic risk measure; game option; Nash equilibrium (search for similar items in EconPapers)
Date: 2017
New Economics Papers: this item is included in nep-gth
Note: View the original document on HAL open archive server: https://hal.science/hal-01519215v1
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Published in Stochastics: An International Journal of Probability and Stochastic Processes, 2017, 89 (1), ⟨10.1080/17442508.2016.1166505⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01519215

DOI: 10.1080/17442508.2016.1166505

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