{
  "id": "1111.1659",
  "version": "v3",
  "published": "2011-11-07T17:44:27.000Z",
  "updated": "2015-03-12T14:53:21.000Z",
  "title": "Exponential moments of affine processes",
  "authors": [
    "Martin Keller-Ressel",
    "Eberhard Mayerhofer"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/14-AAP1009 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Applied Probability 2015, Vol. 25, No. 2, 714-752",
  "doi": "10.1214/14-AAP1009",
  "categories": [
    "math.PR"
  ],
  "abstract": "We investigate the maximal domain of the moment generating function of affine processes in the sense of Duffie, Filipovi\\'{c} and Schachermayer [Ann. Appl. Probab. 13 (2003) 984-1053], and we show the validity of the affine transform formula that connects exponential moments with the solution of a generalized Riccati differential equation. Our result extends and unifies those preceding it (e.g., Glasserman and Kim [Math. Finance 20 (2010) 1-33], Filipovi\\'{c} and Mayerhofer [Radon Ser. Comput. Appl. Math. 8 (2009) 1-40] and Kallsen and Muhle-Karbe [Stochastic Process Appl. 120 (2010) 163-181]) in that it allows processes with very general jump behavior, applies to any convex state space and provides both sufficient and necessary conditions for finiteness of exponential moments.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-04-30T14:47:28.000Z",
      "title": "Exponential Moments of Affine Processes",
      "abstract": "We investigate the maximal domain of the moment generating function of affine processes in the sense of Duffie, Filipovic and Schachermayer (2003), and show the validity of the affine transform formula that connects exponential moments with the solution of a generalized Riccati differential equation. Our result extends and unifies preceding ones by Glasserman and Kim (2010), Filipovic and Mayerhofer (2009), Kallsen and Muhle-Karbe (2008) and Spreij and Veerman (2010) in that it allows processes with completely general jump behavior, applies to any convex state space and provides both sufficient and necessary conditions for finiteness of exponential moments.",
      "comment": "30 pages. Added Section on Applications in Mathematical Finance",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-03-12T14:53:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "affine processes",
      "connects exponential moments",
      "generalized riccati differential equation",
      "affine transform formula",
      "general jump behavior"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.1659K"
    }
  }
}