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Journal of Statistical Theory and Practice

, Volume 2, Issue 2, pp 199–219 | Cite as

Gambler’s Ruin with Catastrophes and Windfalls

  • B. Hunter
  • A. C. Krinik
  • C. Nguyen
  • J. M. Switkes
  • H. F. von Bremen
Article

Abstract

We compute ruin probabilities, in both infinite-time and finite-time, for a Gambler’s Ruin problem with both catastrophes and windfalls in addition to the customary win/loss probabilities. For constant transition probabilities, the infinite-time ruin probabilities are derived using difference equations. Finite-time ruin probabilities of a system having constant win/loss probabilities and variable catastrophe/windfall probabilities are determined using lattice path combinatorics. Formulae for expected time till ruin and the expected duration of gambling are also developed. The ruin probabilities (in infinite-time) for a system having variable win/loss/catastrophe probabilities but no windfall probability are found. Finally, the infinite-time ruin probabilities of a system with variable win/loss/catastrophe/windfall probabilities are determined.

Key-words

Gambler’s Ruin Catastrophe Birth-Death Process 

AMS Subject Classification

60J10 

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Copyright information

© Grace Scientific Publishing 2008

Authors and Affiliations

  • B. Hunter
    • 1
  • A. C. Krinik
    • 2
  • C. Nguyen
    • 2
  • J. M. Switkes
    • 2
  • H. F. von Bremen
    • 2
  1. 1.Department of MathematicsUniversity of CaliforniaDavisUSA
  2. 2.Department of Mathematics and StatisticsCalifornia State Polytechnic UniversityPomonaUSA

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