Trapping the Ultimate Success

Alexander Gnedin and Zakaria Derbazi
Additional contact information
Alexander Gnedin: School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, UK
Zakaria Derbazi: School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, UK

Mathematics, 2022, vol. 10, issue 1, 1-19

Abstract: We introduce a betting game where the gambler aims to guess the last success epoch in a series of inhomogeneous Bernoulli trials paced randomly in time. At a given stage, the gambler may bet on either the event that no further successes occur, or the event that exactly one success is yet to occur, or may choose any proper range of future times (a trap). When a trap is chosen, the gambler wins if the last success epoch is the only one that falls in the trap. The game is closely related to the sequential decision problem of maximising the probability of stopping on the last success. We use this connection to analyse the best-choice problem with random arrivals generated by a Pólya-Lundberg process.

Keywords: best choice problem; optimal stopping time; last record; trapping strategy (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/1/158/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/1/158/ (text/html)

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:gam:jmathe:v:10:y:2022:i:1:p:158-:d:718112

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().