{
  "id": "1409.6255",
  "version": "v1",
  "published": "2014-09-22T17:29:51.000Z",
  "updated": "2014-09-22T17:29:51.000Z",
  "title": "Martingale Inequalities for the Maximum via Pathwise Arguments",
  "authors": [
    "Jan Obloj",
    "Peter Spoida",
    "Nizar Touzi"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We study a class of martingale inequalities involving the running maximum process. They are derived from pathwise inequalities introduced by Henry_Labordere et al. (2013) and provide an upper bound on the expectation of a function of the running maximum in terms of marginal distributions at n intermediate time points. The class of inequalities is rich and we show that in general no inequality is uniformly sharp - for any two inequalities we specify martingales such that one or the other inequality is sharper. We then use our inequalities to recover Doob's L^p inequalities. For p in (0,1] we obtain new, or refined, inequalities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-22T17:29:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G44"
    ],
    "keywords": [
      "inequality",
      "martingale inequalities",
      "pathwise arguments",
      "intermediate time points",
      "running maximum process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.6255O"
    }
  }
}