Improved analytical bounds for gambler's ruin probabilities

DOI10.1007/s11009-005-6656-4zbMath1078.60016OpenAlexW2049187745MaRDI QIDQ2487761

Werner Hürlimann

Publication date: 8 August 2005

Published in: Methodology and Computing in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11009-005-6656-4

zbMATH Keywords

random walkgamblingextremal distribution\(s\)-convex stochastic order

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Stopping times; optimal stopping problems; gambling theory (60G40) Probabilistic games; gambling (91A60)

Related Items (5)

Moment bounds on discrete expected stop-loss transforms, with applications ⋮ Gambler's ruin probability -- a general formula ⋮ Extinction in a branching process: why some of the fittest strategies cannot guarantee survival ⋮ Deciding when to quit the gambler's ruin game with unknown probabilities ⋮ Local Moment Matching and S-convex Extrema

Cites Work

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• Extremal generators and extremal distributions for the continuous \(s\)-convex stochastic orderings
• A rule of thumb (not only) for gamblers
• Some new classes of stochastic order relations among arithmetic random variables, with applications in actuarial sciences
• Bounds on gambler's ruin probabilities in terms of moments
• On \(s\)-convex stochastic extrema for arithmetic risks
• The s-convex orders among real random variables, with applications

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