{
  "id": "1404.2218",
  "version": "v4",
  "published": "2014-04-08T17:14:03.000Z",
  "updated": "2014-11-27T16:36:53.000Z",
  "title": "Reflected Backward Stochastic Differential Equations for a Finite State Markov Chain Model and Applications to American Options",
  "authors": [
    "Dimbinirina Ramarimbahoaka",
    "Zhe Yang",
    "Robert J. Elliott"
  ],
  "comment": "34 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we introduce a new kind of reflected backward stochastic differential equations (RBSDEs) driven by a martingale, in a Markov chain model but not driven by Brownian motion and give existence and uniqueness results for the new equations. Then we discuss American options in a finite state Markov chain model, in the presence of a stochastic discount function (SDF) and using the theory of the new RBSDEs. We show that there exists a constrained super-hedging strategy for an American option, which is unique in our framework as the solution to an RBSDE.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-08-14T20:40:25.000Z",
      "title": "American Options and Reflected Backward Stochastic Differential Equations for a Finite State Markov Chain Model",
      "abstract": "In this paper, we discuss American options in a finite state Markov chain model, in the presence of a stochastic discount function (SDF) and using the theory of reflected backward stochastic differential equations (RBSDEs). We prove an existence and uniqueness theorem for an RBSDE driven by a martingale, in the Markov chain model. We show that there exists a constrained super-hedging strategy for an American option, which is unique in our framework as the solution to an RBSDE.",
      "comment": "32 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2014-11-27T16:36:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite state markov chain model",
      "reflected backward stochastic differential equations",
      "american option"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.2218R"
    }
  }
}