{
  "id": "2002.01448",
  "version": "v1",
  "published": "2020-02-04T18:21:03.000Z",
  "updated": "2020-02-04T18:21:03.000Z",
  "title": "Cumulants and Martingales",
  "authors": [
    "Peter K. Friz",
    "Jim Gatheral",
    "Radoš Radoičić"
  ],
  "comment": "23 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "A general and computable expression for cumulants of a random variables in a semimartingale context is given, with resulting expressions for characteristic and cumulant generating functions. We have been inspired by a formal forest series for expectations of solutions of the Black-Scholes equation [AGR20]. Our proof is of remarkable simplicity and the result is likely to transcend the financial context from which it originates. A variety of examples are presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-04T18:21:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G44",
      "60H99",
      "60L70"
    ],
    "keywords": [
      "martingales",
      "formal forest series",
      "random variables",
      "financial context",
      "semimartingale context"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}