CONTINUOUS-TIME RED AND BLACK: HOW TO CONTROL A DIFFUSION TO A GOAL.

Victor C. Pestien, William D. Sudderth

Research output: Contribution to journalArticle

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Abstract

A player starts at x in (0, 1) and tries to reach 1. The process (X//T, t greater than equivalent to 0) of his positions moves according to a diffusion process (or, more generally, an Ito process) whose infinitesimal parameters mu , sigma are chosen by the player at each instant of time from a set depending on his current position. To maximize the probability of reaching 1, the player should choose the parameters so as to maximize mu / sigma **2, at least when the maximum is achieved by bounded, measurable functions. This implies that bold (timid) play is optimal for subfair (superfair), continuous-time red-and-black. Furthermore, in superfair red-and-black, the strategy which maximizes the drift coefficient of left brace log X//t right brace minimizes the expected time to reach 1.

Original languageEnglish (US)
Pages (from-to)599-611
Number of pages13
JournalMathematics of Operations Research
Volume10
Issue number4
DOIs
StatePublished - Jan 1 1985

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ASJC Scopus subject areas

  • Mathematics(all)
  • Computer Science Applications
  • Management Science and Operations Research

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