Gambler’s Ruin with Catastrophes and Windfalls
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-wordsGambler’s Ruin Catastrophe Birth-Death Process
AMS Subject Classification60J10
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