{
  "id": "2004.10697",
  "version": "v1",
  "published": "2020-04-22T17:06:11.000Z",
  "updated": "2020-04-22T17:06:11.000Z",
  "title": "The running maximum of the Cox-Ingersoll-Ross process with some properties of the Kummer function",
  "authors": [
    "Stefan Gerhold",
    "Friedrich Hubalek",
    "Richard B. Paris"
  ],
  "categories": [
    "math.PR",
    "math.CA"
  ],
  "abstract": "We derive tail asymptotics for the running maximum of the Cox-Ingersoll-Ross process. The main result is proved by the saddle point method, where the tail estimate uses a new monotonicity property of the Kummer function. This auxiliary result is established by a computer algebra assisted proof. Moreover, we analyse the coefficients of the eigenfunction expansion of the running maximum distribution asymptotically.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-22T17:06:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C15",
      "41A60",
      "60G17"
    ],
    "keywords": [
      "running maximum",
      "cox-ingersoll-ross process",
      "kummer function",
      "saddle point method",
      "computer algebra assisted proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}