{
  "id": "1709.01691",
  "version": "v1",
  "published": "2017-09-06T06:51:18.000Z",
  "updated": "2017-09-06T06:51:18.000Z",
  "title": "Heavy tail and light tail of Cox-Ingersoll-Ross processes with regime-switching",
  "authors": [
    "Tongtong Hou",
    "Jinghai Shao"
  ],
  "comment": "19 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "This work is denoted to studying the tail behavior of Cox-Ingersoll-Ross (CIR) processes with regime-switching. One essential difference shown in this work between CIR process with regime-switching and without regime-switching is that the stationary distribution for CIR process with regime-switching could be heavy-tailed. Our results provide a theoretical evidence of the existence of regime-switching for interest rates model based on its heavy-tailed empirical evidence. In this work, we first provide sharp criteria to justify the existence of stationary distribution for the CIR process with regime-switching, which is applied to study the long term returns of interest rates. Then under the existence of the stationary distribution, we provide a criterion to justify whether its stationary distribution is heavy-tailed or not.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-06T06:51:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "light tail",
      "cox-ingersoll-ross processes",
      "regime-switching",
      "stationary distribution",
      "heavy tail"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}