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Stochastics
An International Journal of Probability and Stochastic Processes
Volume 83, 2011 - Issue 4-6: Optimal stopping with Applications
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Original Articles

Maximizing the discounted survival probability in Vardi's casino

Robert Chen Department of Mathematics, University of Miami, Coral Gables, FL, USAView further author information
,
Ilie Grigorescu Department of Mathematics, University of Miami, Coral Gables, FL, USACorrespondence[email protected]
&
Larry Shepp Department of Statistics, Rutgers University, Piscataway, NJ, USAView further author information
Pages 623-638 | Received 21 Jun 2010, Accepted 06 Jan 2011, Published online: 10 Mar 2011

References

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  • Chen , M.-R. , Chung , P.-S. , Hsiau , S.-R. and Yao , Y.-C. 2008 . On nonoptimality of bold play for subfair red-and-black with a rational-valued house limit . J. Appl. Probab. , 45 : 1024 – 1038 .
  • Chen , R. 1977 . Subfair primitive casino with a discount factor . Z. Wahr. verw. Gebiete , 39 : 167 – 174 .
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  • Dubins , L.E. and Savage , L.J. 1965 . How To Gamble If You Must, Inequalities for Stochastic Processes , New York : McGraw-Hill .
  • Grigorescu , I. , Chen , R. and Shepp , L. 2007 . Optimal strategy for the Vardi casino with interest payments . J. Appl. Probab. , 44 ( 1 ) : 199 – 211 .
  • J. Lou, Gambling theory and stock option models, Ph.D. thesis, Rutgers, 2009
  • Shepp , L. 2002 . A model for stock price fluctuations based on information . IEEE Trans. Inf. Theory , 48 : 1372 – 1378 .
  • Shepp , L. 2006 . “ Bold play and the optimal policy for Vardi's casino ” . In Random Walk, Sequential Analysis And Related Topics , 150 – 156 . Hackensack, NJ : World Scientific Publishing .
  • Yao , Y.-C. 2007 . Explicit optimal strategy for the Vardi casino with limited playing time . J. Appl. Probab. , 44 : 831 – 837 .
  • Yao , Y.-C. and Chen , M.-R . 2008 . Strong optimality of bold play for discounted Dubins-Savage gambling problems with time-dependent parameters . J. Appl. Probab. , 45 ( 2 ) : 403 – 416 .

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