2017/05/10 by Miryana Grigorova, Marie-Claire Quenez · 2 citations
Mathematics · Economics, Econometrics and Finance · #math.PR #q-fin.RM
paper · pdf · doi:10.1080/17442508.2016.1166505
published as Stochastics: An International Journal of Probability and Stochastic Processes, Taylor \& Francis: STM, Behavioural Science and Public Health Titles, 2016, 89 (1)
arxiv created 2017/05/10 · arxiv updated 2017/05/11
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.