{
  "id": "1705.03724",
  "version": "v1",
  "published": "2017-05-10T12:28:23.000Z",
  "updated": "2017-05-10T12:28:23.000Z",
  "title": "Optimal stopping and a non-zero-sum Dynkin game in discrete time with risk measures induced by BSDEs",
  "authors": [
    "Miryana Grigorova",
    "Marie-Claire Quenez"
  ],
  "journal": "Stochastics: An International Journal of Probability and Stochastic Processes, Taylor \\& Francis: STM, Behavioural Science and Public Health Titles, 2016, 89 (1)",
  "doi": "10.1080/17442508.2016.1166505",
  "categories": [
    "math.PR",
    "q-fin.CP",
    "q-fin.RM"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-10T12:28:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "non-zero-sum dynkin game",
      "discrete time",
      "risk measures",
      "optimal stopping",
      "discrete stopping time"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Taylor-Francis"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}