Maximizing survival time in a random walk on an interval
A gambler buys N tokens that enable him to play N rounds of the following game. A symmetric random walk on a discrete interval { − r, ..., r} starts from the point 0. The gambler knows only the number of steps made so far, but is unaware of the current position of the walk. Once the walk hits one of...
Saved in:
| Published in: | Stochastic models Vol. 34; no. 2; pp. 154 - 165 |
|---|---|
| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Philadelphia
Taylor & Francis
03-04-2018
Taylor & Francis Ltd |
| Subjects: | |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | A gambler buys N tokens that enable him to play N rounds of the following game. A symmetric random walk on a discrete interval { − r, ..., r} starts from the point 0. The gambler knows only the number of steps made so far, but is unaware of the current position of the walk. Once the walk hits one of the barriers − r or r for the first time in the current round, the round ends with no payoff. The gambler can start a new round by inserting a new token, if there are any tokens left. The gambler can end the game at any time getting the payoff equal to the number of steps made in the current round. We find the optimal stopping strategy for this game and calculate the expected payoff once the optimal strategy is applied. |
|---|---|
| AbstractList | A gambler buys N tokens that enable him to play N rounds of the following game. A symmetric random walk on a discrete interval { - r, ..., r} starts from the point 0. The gambler knows only the number of steps made so far, but is unaware of the current position of the walk. Once the walk hits one of the barriers - r or r for the first time in the current round, the round ends with no payoff. The gambler can start a new round by inserting a new token, if there are any tokens left. The gambler can end the game at any time getting the payoff equal to the number of steps made in the current round. We find the optimal stopping strategy for this game and calculate the expected payoff once the optimal strategy is applied. A gambler buys N tokens that enable him to play N rounds of the following game. A symmetric random walk on a discrete interval { − r, ..., r} starts from the point 0. The gambler knows only the number of steps made so far, but is unaware of the current position of the walk. Once the walk hits one of the barriers − r or r for the first time in the current round, the round ends with no payoff. The gambler can start a new round by inserting a new token, if there are any tokens left. The gambler can end the game at any time getting the payoff equal to the number of steps made in the current round. We find the optimal stopping strategy for this game and calculate the expected payoff once the optimal strategy is applied. |
| Author | Kubicka, Ewa M. Kubicki, Grzegorz Kuchta, Małgorzata Morayne, Michał |
| Author_xml | – sequence: 1 givenname: Ewa M. surname: Kubicka fullname: Kubicka, Ewa M. organization: University of Louisville – sequence: 2 givenname: Grzegorz surname: Kubicki fullname: Kubicki, Grzegorz email: gkubicki@louisville.edu organization: University of Louisville – sequence: 3 givenname: Małgorzata surname: Kuchta fullname: Kuchta, Małgorzata organization: Wrocław University of Technology – sequence: 4 givenname: Michał surname: Morayne fullname: Morayne, Michał organization: Wrocław University of Technology |
| BookMark | eNp9kF9LwzAUxYNMcJt-BCHgc2eSm7bpmzJ0ChNf9DlkaSqZbTKTbnN-elM2X326l8Pv3D9ngkbOO4PQNSUzSgS5pTmwAng1Y4SWM8oJA16eofGgZ5xRPjr1A3SBJjGuCaF5KcQYiRf1bTv7Y90HjtuwszvV4t52BluHFQ7K1b7De9V-Yp8El-TehARdovNGtdFcneoUvT8-vM2fsuXr4nl-v8w0gOgzyKGqRQGirEst-CrnJC8qoTUFXjdARJ3OaEq6MrqqtGgKQgvCKq7YyhRCMJiim-PcTfBfWxN7ufbb4NJKyQgwKGlBIVH5kdLBxxhMIzfBdiocJCVyCEn-hSSHkOQppOS7O_qsa3zo1N6Htpa9OrQ-NOl5baOE_0f8ArwbbUM |
| CitedBy_id | crossref_primary_10_1080_03610926_2019_1662044 |
| Cites_doi | 10.1016/S0899-8256(03)00121-0 10.1007/978-3-662-11281-6 10.1007/978-1-4684-6257-9 10.1287/opre.20.1.37 10.1239/aap/1418396245 10.1093/imamci/dnt021 10.1002/nav.3800130105 10.1002/nav.3800290103 10.1214/EJP.v14-631 10.1016/j.jet.2011.03.003 10.1073/pnas.1400987111 10.1002/nav.3800060203 10.1214/aop/1176988174 10.1007/s00186-017-0594-0 10.1080/03610926.2011.654040 |
| ContentType | Journal Article |
| Copyright | 2018 Taylor & Francis 2018 2018 Taylor & Francis |
| Copyright_xml | – notice: 2018 Taylor & Francis 2018 – notice: 2018 Taylor & Francis |
| DBID | AAYXX CITATION |
| DOI | 10.1080/15326349.2017.1402347 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Statistics Mathematics |
| EISSN | 1532-4214 |
| EndPage | 165 |
| ExternalDocumentID | 10_1080_15326349_2017_1402347 1402347 |
| Genre | Articles |
| GrantInformation_xml | – fundername: National Science Center (Narodowe Centrum Nauki), Poland grantid: NCN Grant DEC-2015/17/B/ST6/01868 funderid: 10.13039/501100004281 |
| GroupedDBID | -~X .7F .QJ 0BK 0R~ 123 29Q 30N 4.4 8V8 AAAVI AAENE AAJMT AALDU AAMIU AAPUL AAQRR ABBKH ABCCY ABDBF ABFIM ABHAV ABJVF ABLIJ ABPEM ABPTK ABQHQ ABTAI ABXUL ACGEJ ACGFS ACIWK ACTIO ADCVX ADGTB ADXPE AEGYZ AEISY AEMOZ AENEX AEOZL AEPSL AEYOC AFKVX AFOLD AFWLO AGDLA AGMYJ AHDLD AIJEM AIRXU AJWEG AKBVH AKOOK AKVCP ALMA_UNASSIGNED_HOLDINGS ALQZU AQRUH AVBZW BLEHA CCCUG CE4 CS3 DGEBU DKSSO DU5 EAP EBR EBS EBU EJD EMK EPL EST ESX E~A E~B FUNRP FVPDL GTTXZ H13 HF~ HZ~ H~P I-F IPNFZ J.P KYCEM M4Z NA5 NHB NY~ O9- RIG RNANH ROSJB RTWRZ S-T SNACF TEJ TFL TFT TFW TH9 TN5 TTHFI TUS TWF UT5 UU3 V1K ZGOLN ~S~ AAYXX ABJNI ABPAQ ABXYU AHDZW AWYRJ CITATION K1G TBQAZ TDBHL TUROJ |
| ID | FETCH-LOGICAL-c338t-3539d86387d7c84b5405698cc134df308d788f71bec99c8f60160294a2be68823 |
| IEDL.DBID | TFW |
| ISSN | 1532-6349 |
| IngestDate | Thu Oct 10 21:53:04 EDT 2024 Thu Nov 21 21:33:50 EST 2024 Tue Jun 13 19:51:28 EDT 2023 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 2 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c338t-3539d86387d7c84b5405698cc134df308d788f71bec99c8f60160294a2be68823 |
| PQID | 2032371613 |
| PQPubID | 216161 |
| PageCount | 12 |
| ParticipantIDs | proquest_journals_2032371613 crossref_primary_10_1080_15326349_2017_1402347 informaworld_taylorfrancis_310_1080_15326349_2017_1402347 |
| PublicationCentury | 2000 |
| PublicationDate | 2018-04-03 |
| PublicationDateYYYYMMDD | 2018-04-03 |
| PublicationDate_xml | – month: 04 year: 2018 text: 2018-04-03 day: 03 |
| PublicationDecade | 2010 |
| PublicationPlace | Philadelphia |
| PublicationPlace_xml | – name: Philadelphia |
| PublicationTitle | Stochastic models |
| PublicationYear | 2018 |
| Publisher | Taylor & Francis Taylor & Francis Ltd |
| Publisher_xml | – name: Taylor & Francis – name: Taylor & Francis Ltd |
| References | cit0011 cit0001 cit0012 Chow Y.S. (cit0003) 1971 cit0008 cit0009 cit0006 cit0017 Fudenberg D. (cit0005) 1998 cit0007 cit0018 cit0004 cit0015 cit0016 cit0002 cit0013 cit0014 |
| References_xml | – ident: cit0004 doi: 10.1016/S0899-8256(03)00121-0 – volume-title: Great Expectations: The Theory of Optimal Stopping year: 1971 ident: cit0003 contributor: fullname: Chow Y.S. – ident: cit0018 doi: 10.1007/978-3-662-11281-6 – ident: cit0017 doi: 10.1007/978-1-4684-6257-9 – ident: cit0009 doi: 10.1287/opre.20.1.37 – ident: cit0013 doi: 10.1239/aap/1418396245 – ident: cit0014 doi: 10.1093/imamci/dnt021 – ident: cit0015 doi: 10.1002/nav.3800130105 – ident: cit0002 doi: 10.1002/nav.3800290103 – ident: cit0008 doi: 10.1214/EJP.v14-631 – volume-title: The Theory of Learning in Games year: 1998 ident: cit0005 contributor: fullname: Fudenberg D. – ident: cit0007 doi: 10.1016/j.jet.2011.03.003 – ident: cit0006 doi: 10.1073/pnas.1400987111 – ident: cit0016 doi: 10.1002/nav.3800060203 – ident: cit0001 doi: 10.1214/aop/1176988174 – ident: cit0011 doi: 10.1007/s00186-017-0594-0 – ident: cit0012 doi: 10.1080/03610926.2011.654040 |
| SSID | ssj0015788 |
| Score | 2.1582592 |
| Snippet | A gambler buys N tokens that enable him to play N rounds of the following game. A symmetric random walk on a discrete interval { − r, ..., r} starts from the... A gambler buys N tokens that enable him to play N rounds of the following game. A symmetric random walk on a discrete interval { - r, ..., r} starts from the... |
| SourceID | proquest crossref informaworld |
| SourceType | Aggregation Database Publisher |
| StartPage | 154 |
| SubjectTerms | Economic models Game theory Optimal stopping time Optimization Random walk Random walk theory |
| Title | Maximizing survival time in a random walk on an interval |
| URI | https://www.tandfonline.com/doi/abs/10.1080/15326349.2017.1402347 https://www.proquest.com/docview/2032371613 |
| Volume | 34 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://sdu.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV07T8MwELagUxl4FBCFgjywBprYceyxglZdykIRbJZjJ1JEmyLSCsSv5y6PigohBhgTyVZ0vsd3zt13hFyGwrrQt6C8QgqPm5B7KlbWcyowIoptIi3eQ47vo7sneTtEmpxB0wuDZZWYQ6cVUUTpq9G4TVw0FXHXYKSBYBzbTPwITB3CDsd-csA2qNfT0eP6PwLoo6wYUwMPlzQ9PD_tshGdNrhLv_nqMgCN9v7h0_fJbo0-6aBSlwOyleQdsjNZU7cWHdJG-FmxNx8SOTHv2Tz7gPhGixV4FdBLiuPoaZZTQyHOucWcvpnZM13Ai5xmZQmlmR2Rh9FwejP26lkLnoUkdemxkCknwRgjF1nJYwRyQklrfcZdyvrSgSTTyIcjV8rKFFlc-oHiJogTASidHZNWvsiTE0IBgSlEahbn3yC5DYRJTIXjMBXOWNUlV42M9UtFqaH9mqm0kY9G-ehaPl2ivp6EXpZ3GWk1eESzX9b2mmPTtXUWGqfGM0gUfXb6h63PSBseZVnGw3qktXxdJedku3Cri1IJPwFS3tQ9 |
| link.rule.ids | 315,782,786,1455,1509,27933,27934,58021,59734,60523 |
| linkProvider | Taylor & Francis |
| linkToHtml | http://sdu.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LT8JAEJ4IHsSDD9SIou7Ba5V2-9g9GoVgBC5i9LZpd9uECMUIROOvd6YPIjHGg17b7KaZx84309lvAM49XxvP1mi8vvAtN_RcS0ZSW0Y6oR9EOhaa6pDd-2DwJG7aRJOzvAtDbZWUQyc5UUR2VpNzUzG6bIm7RC91fO7SPRM7QF_HuOMGFVhHcMyJP3_YeVz-SUCLFDlnqmPRmvIWz0_brMSnFfbSb6d1FoI62__x8TuwVQBQdpVbzC6sxWkdNvtL9tZZHWqEQHMC5z0Q_fB9NBl9YIhjswUeLGiajCbSs1HKQoahzkwn7C0cP7MpPkjZKOuiDMf78NBpD6-7VjFuwdKYp84t7nFpBPpjYAIt3IiwnC-F1jZ3TcJbwqAok8BGrUupRUJELi1HuqETxT4CdX4A1XSaxofAEIRJAmuaRuAQvw1GSsqGIy_xTahlAy5KIauXnFVD2QVZaSkfRfJRhXwaIL-qQs2zckaSzx5R_Je1zVJvqnDQmaLB8RxzRZsf_WHrM9joDvs91bsd3B1DDV-JrKuHN6E6f13EJ1CZmcVpZpGf4AvYYQ |
| linkToPdf | http://sdu.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LS8NAEB5sBdGDj6pYrboHr1GTzWP3WGyLohXBit6WZDeBYJsW26L4653JoygiHvSasEuYnZlvZjPzDcCJ52vj2RqV1xe-5Yaea8lIastIJ_SDSMdC0z3k5X1w-yQ6XaLJaVe9MFRWSTl0UhBF5L6ajHtikqoi7gyN1PG5S20mdoCmjrDjBjVY9gQCFqr0oPe4-JGACikKylTHojVVE89P23yBpy_kpd-cdY5AvY1_-PZNWC_DT9Yu9GULluKsAWv9BXfrtAGrFH8W9M3bIPrhWzpK3xHg2HSObgUVk9E8epZmLGQIdGY8Yq_h8JmN8UHG0ryGMhzuwEOvO7i4tMphC5bGLHVmcY9LI9AaAxNo4UYUyflSaG1z1yT8XBiUZBLYeOZSapEQjcu5I93QiWIfw3S-C_VsnMV7wDAEkxSqaRqAQ-w2iJOUC0de4ptQyyacVjJWk4JTQ9klVWklH0XyUaV8miA_n4Sa5ZcZSTF5RPFf1raqY1OleU4VjY3nmCnafP8PWx_Dyl2np26ubq8PYBXfiLykh7egPnuZx4dQm5r5Ua6PHz7X1wU |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Maximizing+survival+time+in+a+random+walk+on+an+interval&rft.jtitle=Stochastic+models&rft.au=Kubicka%2C+Ewa+M.&rft.au=Kubicki%2C+Grzegorz&rft.au=Kuchta%2C+Ma%C5%82gorzata&rft.au=Morayne%2C+Micha%C5%82&rft.date=2018-04-03&rft.pub=Taylor+%26+Francis&rft.issn=1532-6349&rft.eissn=1532-4214&rft.volume=34&rft.issue=2&rft.spage=154&rft.epage=165&rft_id=info:doi/10.1080%2F15326349.2017.1402347&rft.externalDocID=1402347 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1532-6349&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1532-6349&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1532-6349&client=summon |