{
  "id": "2403.02941",
  "version": "v2",
  "published": "2024-03-05T13:12:17.000Z",
  "updated": "2024-07-11T13:16:17.000Z",
  "title": "Ruin Probability Approximation for Bidimensional Brownian Risk Model with Tax",
  "authors": [
    "Timofei Shashkov"
  ],
  "comment": "23 pages, 16 references",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $\\mathbf{B}(t)=(B_1(t), B_2(t))$, $t\\geq 0$ be a two-dimensional Brownian motion with independent components and define the $\\mathbf{\\gamma}$-reflected process $$\\mathbf{X}(t)=(X_1(t),X_2(t))=\\left(B_1(t)-c_1t-\\gamma_1\\inf_{s_1\\in[0,t]}(B_1(s_1)-c_1s_1),B_2(t)-c_2t-\\gamma_2\\inf_{s_2\\in[0,t]}(B_2(s_2)-c_2s_2)\\right),$$ with given finite constants $c_1,c_2,\\gamma_1,\\gamma_2$ and $\\gamma_1,\\gamma_2\\in[0,1]$. The goal of this paper is to derive the asymptotics of ruin probability $$\\mathbb{P}\\{\\exists_{t\\in[0,T]}: X_1(t)>u,X_2(t)>au\\}$$ as $u\\to\\infty$ for $a\\leq 1$ and $T>0$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-07-11T13:16:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G15",
      "60G70"
    ],
    "keywords": [
      "bidimensional brownian risk model",
      "ruin probability approximation",
      "two-dimensional brownian motion",
      "independent components",
      "finite constants"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}