{
  "id": "math/0509367",
  "version": "v1",
  "published": "2005-09-16T04:21:51.000Z",
  "updated": "2005-09-16T04:21:51.000Z",
  "title": "Game theoretic derivation of discrete distributions and discrete pricing formulas",
  "authors": [
    "Akimichi Takemura",
    "Taiji Suzuki"
  ],
  "journal": "J. Japan Statist. Soc., Vol.37, No.1, 2007, 87-104",
  "categories": [
    "math.PR",
    "math.ST",
    "q-fin.TR",
    "stat.TH"
  ],
  "abstract": "In this expository paper we illustrate the generality of game theoretic probability protocols of Shafer and Vovk (2001) in finite-horizon discrete games. By restricting ourselves to finite-horizon discrete games, we can explicitly describe how discrete distributions with finite support and the discrete pricing formulas, such as the Cox-Ross-Rubinstein formula, are naturally derived from game-theoretic probability protocols. Corresponding to any discrete distribution with finite support, we construct a finite-horizon discrete game, a replicating strategy of Skeptic, and a neutral forecasting strategy of Forecaster, such that the discrete distribution is derived from the game. Construction of a replicating strategy is the same as in the standard arbitrage arguments of pricing European options in the binomial tree models. However the game theoretic framework is advantageous because no a priori probabilistic assumption is needed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-09-16T04:21:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "discrete distribution",
      "discrete pricing formulas",
      "game theoretic derivation",
      "finite-horizon discrete game",
      "game theoretic probability protocols"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......9367T"
    }
  }
}