{
  "id": "2212.07474",
  "version": "v1",
  "published": "2022-12-14T19:45:40.000Z",
  "updated": "2022-12-14T19:45:40.000Z",
  "title": "A Characterization of Bounded Stochastic Dominance",
  "authors": [
    "Bar Light",
    "Andres Perlroth"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Stochastic dominance orders are commonly used in the theory and practice of risk management and decision making under uncertainty. We provide a novel characterization for the $n$-th degree bounded stochastic dominance order which compares the $n$-th lower partial moment of the random variables under consideration on a bounded domain. This characterization establishes a connection between the risk tolerance of decision makers and bounded stochastic dominance orders, and hence, it provides a decision theoretic interpretation for these stochastic orders. As a by-product of our results, we provide non-trivial inequalities for $n$-convex functions and rankings over lotteries for decision makers with a globally bounded Arrow-Pratt measure of risk aversion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-14T19:45:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "characterization",
      "th degree bounded stochastic dominance",
      "decision makers",
      "th lower partial moment",
      "degree bounded stochastic dominance order"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}