{
  "id": "1911.06079",
  "version": "v1",
  "published": "2019-11-14T13:07:35.000Z",
  "updated": "2019-11-14T13:07:35.000Z",
  "title": "Mean-field reflected backward stochastic differential equations",
  "authors": [
    "Boualem Djehiche",
    "Romuald Elie",
    "Said Hamadène"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we study a class of reflected backward stochastic differential equations (BSDEs) of mean-field type, where the mean-field interaction in terms of the distribution of the $Y$-component of the solution enters in both the driver and the lower obstacle. We consider in details the case where the lower obstacle is a deterministic function of $(Y,\\E[Y])$ and discuss the more general dependence on the distribution of $Y$. Under mild Lipschitz and integrability conditions on the coefficients, we obtain the well-posedness of such a class of equations. Under further monotonicity conditions, we show convergence of the standard penalization scheme to the solution of the equation, which hence satisfies a minimality property. This class of equations is motivated by applications in pricing life insurance contracts with surrender options.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-14T13:07:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "reflected backward stochastic differential equations",
      "mean-field reflected backward stochastic differential",
      "lower obstacle",
      "standard penalization scheme",
      "pricing life insurance contracts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}