{
  "id": "1403.7831",
  "version": "v1",
  "published": "2014-03-30T23:20:09.000Z",
  "updated": "2014-03-30T23:20:09.000Z",
  "title": "Uniform asymptotics for the tail probability of weighted sums with heavy tails",
  "authors": [
    "Chenhua Zhang"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper studies the tail probability of weighted sums of the form $\\sum_{i=1}^n c_i X_i$, where random variables $X_i$'s are either independent or pairwise quasi-asymptotical independent with heavy tails. Using $h$-insensitive function, the uniform asymptotic equivalence of the tail probabilities of $\\sum_{i=1}^n c_iX_i$, $\\max_{1\\le k\\le n}\\sum_{i=1}^k c_iX_i$ and $\\sum_{i=1}^n c_iX_i^+$ is established, where $X_i$'s are independent and follow the long-tailed distribution, and $c_i$'s take value in a broad interval. Some further uniform asymptotic results for the weighted sums of $X_i$'s with dominated varying tails are obtained. An application to the ruin probability in a discrete-time insurance risk model is presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-30T23:20:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A60",
      "62P05",
      "62E20",
      "91B30"
    ],
    "keywords": [
      "tail probability",
      "weighted sums",
      "heavy tails",
      "discrete-time insurance risk model",
      "uniform asymptotic results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.7831Z"
    }
  }
}