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: LPMA
Marie-Claire Quenez: LPMA

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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. Hamad{\`e}ne 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.

Date: 2017-05
New Economics Papers: this item is included in nep-gth
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Published in Stochastics: An International Journal of Probability and Stochastic Processes, Taylor \& Francis: STM, Behavioural Science and Public Health Titles, 2016, 89 (1)

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1705.03724

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