{
  "id": "2402.19203",
  "version": "v2",
  "published": "2024-02-29T14:33:20.000Z",
  "updated": "2024-07-22T14:02:53.000Z",
  "title": "On non-negative solutions of stochastic Volterra equations with jumps and non-Lipschitz coefficients",
  "authors": [
    "Aurélien Alfonsi",
    "Guillaume Szulda"
  ],
  "categories": [
    "math.PR",
    "q-fin.MF"
  ],
  "abstract": "We consider one-dimensional stochastic Volterra equations with jumps for which we establish conditions upon the convolution kernel and coefficients for the strong existence and pathwise uniqueness of a non-negative c\\`adl\\`ag solution. By using the approach recently developed in arXiv:2302.07758, we show the strong existence by using a nonnegative approximation of the equation whose convergence is proved via a variant of the Yamada--Watanabe approximation technique. We apply our results to L\\'evy-driven stochastic Volterra equations. In particular, we are able to define a Volterra extension of the so-called alpha-stable Cox--Ingersoll--Ross process, which is especially used for applications in Mathematical Finance.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-07-22T14:02:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "non-lipschitz coefficients",
      "non-negative solutions",
      "levy-driven stochastic volterra equations",
      "one-dimensional stochastic volterra equations",
      "strong existence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}