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On the gambler's ruin problem for a finite Markov chain

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  • El-Shehawey, M.A.

Abstract

In this paper we present closed-form formulas for the solutions of the gambler's ruin problem for a finite Markov chain where probabilities of winning or losing a particular game depending on the amount of the current fortune, from probability boundary conditions' viewpoint, and provide some very simple closed forms which immediately lead to exact and explicit formulas for some special cases, depending on the relationships between the transition probabilities and the boundary condition probabilities.

Suggested Citation

  • El-Shehawey, M.A., 2009. "On the gambler's ruin problem for a finite Markov chain," Statistics & Probability Letters, Elsevier, vol. 79(14), pages 1590-1595, July.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:14:p:1590-1595
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    References listed on IDEAS

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    1. Lefebvre, Mario, 2008. "The gambler's ruin problem for a Markov chain related to the Bessel process," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2314-2320, October.
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