Generalized Gambler’s Ruin Problem: Explicit Formulas via Siegmund Duality

Paweł Lorek ()
Additional contact information
Paweł Lorek: University of Wrocław

Methodology and Computing in Applied Probability, 2017, vol. 19, issue 2, 603-613

Abstract: Abstract We give explicit formulas for ruin probabilities in a multidimensional Generalized Gambler’s ruin problem. The generalization is best interpreted as a game of one player against d other players, allowing arbitrary winning and losing probabilities (including ties) depending on the current fortune with particular player. It includes many previous other generalizations as special cases. Instead of usually utilized first-step-like analysis we involve dualities between Markov chains. We give general procedure for solving ruin-like problems utilizing Siegmund duality in Markov chains for partially ordered state spaces studied recently in context of Möbius monotonicity.

Keywords: Generalized gambler’s ruin problem; Markov chains; Absorption probability; Siegmund duality; Möbius monotonicity; Partial ordering; 60J10; 60G40; 60J80 (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s11009-016-9507-6 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:metcap:v:19:y:2017:i:2:d:10.1007_s11009-016-9507-6

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/11009

DOI: 10.1007/s11009-016-9507-6

Access Statistics for this article

Methodology and Computing in Applied Probability is currently edited by Joseph Glaz

More articles in Methodology and Computing in Applied Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().