{
  "id": "1501.03638",
  "version": "v1",
  "published": "2015-01-15T11:37:06.000Z",
  "updated": "2015-01-15T11:37:06.000Z",
  "title": "Positive Harris recurrence and exponential ergodicity of the basic affine jump-diffusion",
  "authors": [
    "Peng Jin",
    "Barbara Rüdiger",
    "Chiraz Trabelsi"
  ],
  "comment": "21 papes",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we find the transition densities of the basic affine jump-diffusion (BAJD), which is introduced by Duffie and G\\^{a}rleanu [D. Duffie and N. G\\^{a}rleanu, Risk and valuation of collateralized debt obligations, Financial Analysts Journal 57(1) (2001), pp. 41--59] as an extension of the CIR model with jumps. We prove the positive Harris recurrence and exponential ergodicity of the BAJD. Furthermore we prove that the unique invariant probability measure $\\pi$ of the BAJD is absolutely continuous with respect to the Lebesgue measure and we also derive a closed form formula for the density function of $\\pi$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-15T11:37:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "60J60"
    ],
    "keywords": [
      "basic affine jump-diffusion",
      "positive harris recurrence",
      "exponential ergodicity",
      "unique invariant probability measure",
      "financial analysts journal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150103638J"
    }
  }
}