Maximizing the discounted survival probability in Vardi's casino

Robert Chen, Ilie Grigorescu, Larry Shepp

Research output: Contribution to journalArticle

Abstract

We are in a subfair casino, with fortune f 0 ∈ and we want to turn it into a fortune of size 1 in discounted time. We may stake any amount 00. We assume that every such gamble has a pay-off with fixed expected value cs, with -10;b,c) = max s,rE S,R f0B τX(f τ = 1), 0n-1,φ n], n≥1, φ 0 = 0 between critical fortunes φ n ↑ 1.

Original languageEnglish (US)
Pages (from-to)623-638
Number of pages16
JournalStochastics
Volume83
Issue number4-6
DOIs
StatePublished - Aug 2011

Fingerprint

Gamble
Survival Probability
Expected Value

Keywords

  • bold play
  • optimal strategy
  • Vardi casino

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation

Cite this

Maximizing the discounted survival probability in Vardi's casino. / Chen, Robert; Grigorescu, Ilie; Shepp, Larry.

In: Stochastics, Vol. 83, No. 4-6, 08.2011, p. 623-638.

Research output: Contribution to journalArticle

Chen, Robert ; Grigorescu, Ilie ; Shepp, Larry. / Maximizing the discounted survival probability in Vardi's casino. In: Stochastics. 2011 ; Vol. 83, No. 4-6. pp. 623-638.
@article{b4e509cd14d44ada8f4c63f0db5301f3,
title = "Maximizing the discounted survival probability in Vardi's casino",
abstract = "We are in a subfair casino, with fortune f 0 ∈ and we want to turn it into a fortune of size 1 in discounted time. We may stake any amount 00. We assume that every such gamble has a pay-off with fixed expected value cs, with -10;b,c) = max s,rE S,R f0B τX(f τ = 1), 0n-1,φ n], n≥1, φ 0 = 0 between critical fortunes φ n ↑ 1.",
keywords = "bold play, optimal strategy, Vardi casino",
author = "Robert Chen and Ilie Grigorescu and Larry Shepp",
year = "2011",
month = "8",
doi = "10.1080/17442508.2011.552980",
language = "English (US)",
volume = "83",
pages = "623--638",
journal = "Stochastics",
issn = "1744-2508",
publisher = "Gordon and Breach Science Publishers",
number = "4-6",

}

TY - JOUR

T1 - Maximizing the discounted survival probability in Vardi's casino

AU - Chen, Robert

AU - Grigorescu, Ilie

AU - Shepp, Larry

PY - 2011/8

Y1 - 2011/8

N2 - We are in a subfair casino, with fortune f 0 ∈ and we want to turn it into a fortune of size 1 in discounted time. We may stake any amount 00. We assume that every such gamble has a pay-off with fixed expected value cs, with -10;b,c) = max s,rE S,R f0B τX(f τ = 1), 0n-1,φ n], n≥1, φ 0 = 0 between critical fortunes φ n ↑ 1.

AB - We are in a subfair casino, with fortune f 0 ∈ and we want to turn it into a fortune of size 1 in discounted time. We may stake any amount 00. We assume that every such gamble has a pay-off with fixed expected value cs, with -10;b,c) = max s,rE S,R f0B τX(f τ = 1), 0n-1,φ n], n≥1, φ 0 = 0 between critical fortunes φ n ↑ 1.

KW - bold play

KW - optimal strategy

KW - Vardi casino

UR - http://www.scopus.com/inward/record.url?scp=84859479999&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84859479999&partnerID=8YFLogxK

U2 - 10.1080/17442508.2011.552980

DO - 10.1080/17442508.2011.552980

M3 - Article

VL - 83

SP - 623

EP - 638

JO - Stochastics

JF - Stochastics

SN - 1744-2508

IS - 4-6

ER -