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

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.
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Stochastics: An International Journal of Probability and Stochastic Processes, Taylor & Francis: STM, Behavioural Science and Public Health Titles, 2016, 89 (1), 〈10.1080/17442508.2016.1166505〉
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Miryana Grigorova, Marie-Claire Quenez. Optimal stopping and a non-zero-sum Dynkin game in discrete time with risk measures induced by BSDEs. Stochastics: An International Journal of Probability and Stochastic Processes, Taylor & Francis: STM, Behavioural Science and Public Health Titles, 2016, 89 (1), 〈10.1080/17442508.2016.1166505〉. 〈hal-01519215〉

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