An application of prophet regions to optimal stopping with a random number of observations
Let X 1 ,X 2 , ... be any sequence of nonnegative integrable random variables, and let N∈{1,2 , ...} be a random variable with known distribution, independent of X 1 ,X 2 , ... The optimal stopping value sup t E(X t I(N≥ t)) is considered for two players: one who has advance knowledge of the value o...
Saved in:
| Published in | Optimization Vol. 53; no. 4; pp. 331 - 338 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Philadelphia
Taylor & Francis Group
01.08.2004
Taylor & Francis LLC |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0233-1934 1029-4945 |
| DOI | 10.1080/02331930410001716829 |
Cover
| Abstract | Let X
1
,X
2
, ... be any sequence of nonnegative integrable random variables, and let N∈{1,2 , ...} be a random variable with known distribution, independent of X
1
,X
2
, ... The optimal stopping value sup
t
E(X
t
I(N≥ t)) is considered for two players: one who has advance knowledge of the value of N, and another who does not. Sharp ratio and difference inequalities relating the two players' optimal values are given in a number of settings. The key to the proofs is an application of a prophet region for arbitrarily dependent random variables by Hill and Kertz [T.P. Hill and R.P. Kertz (1983). Stop rule inequalities for uniformly bounded sequences of random variables. Trans. Amer. Math. Soc., 278, 197-207]. |
|---|---|
| AbstractList | Let X
1
,X
2
, ... be any sequence of nonnegative integrable random variables, and let N∈{1,2 , ...} be a random variable with known distribution, independent of X
1
,X
2
, ... The optimal stopping value sup
t
E(X
t
I(N≥ t)) is considered for two players: one who has advance knowledge of the value of N, and another who does not. Sharp ratio and difference inequalities relating the two players' optimal values are given in a number of settings. The key to the proofs is an application of a prophet region for arbitrarily dependent random variables by Hill and Kertz [T.P. Hill and R.P. Kertz (1983). Stop rule inequalities for uniformly bounded sequences of random variables. Trans. Amer. Math. Soc., 278, 197-207]. Let X1, X2,... be any sequence of nonnegative integrable random variables, and let N epsilon {1, 2,...} be a random variable with known distribution, independent of X1, X2,... The optimal stopping value sup, E(X1I(N greater than or equal to t)) is considered for two players: one who has advance knowledge of the value of N, and another who does not. Sharp ration and difference inequalities relating the two players' optimal values are given in a number of settings. The key to the proofs is an application of a prophet region for arbitrarily dependent random variables by Hill and Kertz (1983). Stop rule inequalities for uniformly bounded sequences of random variables. |
| Author | Allaart, Pieter C. |
| Author_xml | – sequence: 1 givenname: Pieter C. surname: Allaart fullname: Allaart, Pieter C. |
| BookMark | eNqNkEtPAyEYRYnRxLb6D1wQ96O85oEb0zS-kiZudOOGMDNMSzMFBGrtv5e2rkyjrkjgnPvx3SE4NtYoAC4wusKoQteIUIo5RQwjhHCJi4rwIzDAiPCMcZYfg8EWyRLDTsEwhAVCBBeEDcDb2EDpXK8bGbU10HbQeevmKkKvZukmwGihdVEvZQ9DtM5pM4NrHedQQi9Na5fQrJa18lvX1kH5j11UOAMnneyDOv8-R-D1_u5l8phNnx-eJuNp1tCKxkw1jBBcY5J3CpesLnKsypqXPD1wJlmNqpzUhWRY5rSVLZF52dJC8oYkjjE6Apf73PTx95UKUSzsyps0UhDMGS2LkieI7aHG2xC86oTzaSW_ERiJbYniUIlJu_mhNTru1ote6v4v-XYva9NZv5Rr6_tWRLnpre9SdY0Ogv5v_C8Jh0QRPyP9AvGjnrI |
| CODEN | OPTZDQ |
| CitedBy_id | crossref_primary_10_1080_07362990600629140 crossref_primary_10_1081_SAP_200056671 |
| Cites_doi | 10.1214/aop/1176992175 10.1214/aos/1024691094 10.2307/3212720 10.1081/SQA-120025030 10.1090/conm/125/1160620 10.1214/aop/1176993237 10.1081/SQA-120022089 10.1007/BF00535745 10.1007/BF00538887 10.1214/aop/1176990548 10.1137/1117078 10.1007/978-3-322-84825-3 10.1090/S0002-9947-1983-0697070-7 |
| ContentType | Journal Article |
| Copyright | Copyright Taylor & Francis Group, LLC 2004 Copyright Taylor & Francis Group Aug 2004 |
| Copyright_xml | – notice: Copyright Taylor & Francis Group, LLC 2004 – notice: Copyright Taylor & Francis Group Aug 2004 |
| DBID | AAYXX CITATION 7SC 7TB 8FD FR3 H8D JQ2 L7M L~C L~D |
| DOI | 10.1080/02331930410001716829 |
| DatabaseName | CrossRef Computer and Information Systems Abstracts Mechanical & Transportation Engineering Abstracts Technology Research Database Engineering Research Database Aerospace Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional |
| DatabaseTitle | CrossRef Aerospace Database Technology Research Database Computer and Information Systems Abstracts – Academic Mechanical & Transportation Engineering Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Engineering Research Database Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | Aerospace Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering |
| EISSN | 1029-4945 |
| EndPage | 338 |
| ExternalDocumentID | 695528051 10_1080_02331930410001716829 10051660 |
| Genre | Feature |
| GroupedDBID | .7F .DC .QJ 0BK 0R~ 123 29N 30N 4.4 5VS AAENE AAJMT AALDU AAMIU AAPUL AAQRR ABCCY ABFIM ABHAV ABJNI ABLIJ ABPAQ ABPEM ABTAI ABXUL ABXYU ACAGQ ACGEJ ACGFS ACIWK ACTIO ADCVX ADGTB ADXPE AEISY AENEX AEOZL AEPSL AEYOC AFKVX AGDLA AGMYJ AGROQ AHDZW AHMOU AIJEM AJWEG AKBVH AKOOK ALCKM ALMA_UNASSIGNED_HOLDINGS ALQZU AMEWO AQRUH AVBZW AWYRJ BLEHA CAG CCCUG CE4 COF CRFIH CS3 DKSSO DMQIW DU5 EBS EJD E~A E~B GTTXZ H13 HZ~ H~P IPNFZ J.P KYCEM M4Z NA5 O9- P2P PQQKQ QCRFL RIG RNANH ROSJB RTWRZ S-T SNACF TBQAZ TDBHL TEJ TFL TFT TFW TOXWX TTHFI TUROJ TWF UT5 UU3 ZGOLN ~S~ 07G 1TA AAGDL AAHIA AAIKQ AAKBW AAYXX ACGEE ADYSH AEUMN AFRVT AGCQS AGLEN AIYEW AMPGV AMVHM AMXXU BCCOT BPLKW C06 CITATION DWIFK HF~ IVXBP LJTGL NUSFT TAQ TFMCV UB9 UU8 V3K V4Q 7SC 7TB 8FD FR3 H8D JQ2 L7M L~C L~D TASJS |
| ID | FETCH-LOGICAL-c383t-ec4221b125fe174b651e7b979ec494a4b0852b6a41a53dad2a57d36a9c2e7b443 |
| ISSN | 0233-1934 |
| IngestDate | Wed Aug 13 07:34:11 EDT 2025 Tue Jul 01 03:52:06 EDT 2025 Thu Apr 24 22:50:28 EDT 2025 Wed Dec 25 09:03:09 EST 2024 Mon May 13 12:09:11 EDT 2019 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 4 |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c383t-ec4221b125fe174b651e7b979ec494a4b0852b6a41a53dad2a57d36a9c2e7b443 |
| Notes | SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 |
| PQID | 219437679 |
| PQPubID | 27961 |
| PageCount | 8 |
| ParticipantIDs | proquest_journals_219437679 crossref_citationtrail_10_1080_02331930410001716829 crossref_primary_10_1080_02331930410001716829 informaworld_taylorfrancis_310_1080_02331930410001716829 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 8/1/2004 2004-08-00 20040801 |
| PublicationDateYYYYMMDD | 2004-08-01 |
| PublicationDate_xml | – month: 08 year: 2004 text: 8/1/2004 day: 01 |
| PublicationDecade | 2000 |
| PublicationPlace | Philadelphia |
| PublicationPlace_xml | – name: Philadelphia |
| PublicationTitle | Optimization |
| PublicationYear | 2004 |
| Publisher | Taylor & Francis Group Taylor & Francis LLC |
| Publisher_xml | – name: Taylor & Francis Group – name: Taylor & Francis LLC |
| References | Hill TP (bib9) 1992; 125 Krengel U (bib11) 1978 bib14 bib12 bib13 bib10 Schmitz N (bib15) 2000 bib7 bib8 bib5 bib3 bib4 bib1 bib2 Harten F (bib6) 1997 |
| References_xml | – ident: bib4 doi: 10.1214/aop/1176992175 – ident: bib2 doi: 10.1214/aos/1024691094 – ident: bib13 doi: 10.2307/3212720 – ident: bib1 doi: 10.1081/SQA-120025030 – volume: 125 start-page: 191 year: 1992 ident: bib9 publication-title: Contemp. Math. doi: 10.1090/conm/125/1160620 – ident: bib3 doi: 10.1214/aop/1176993237 – ident: bib14 doi: 10.1081/SQA-120022089 – ident: bib7 doi: 10.1007/BF00535745 – ident: bib5 doi: 10.1007/BF00538887 – ident: bib10 doi: 10.1214/aop/1176990548 – ident: bib12 doi: 10.1137/1117078 – volume-title: Prophet Theory year: 2000 ident: bib15 – volume-title: Prophetentheorie year: 1997 ident: bib6 doi: 10.1007/978-3-322-84825-3 – ident: bib8 doi: 10.1090/S0002-9947-1983-0697070-7 – volume-title: Probability on Banach Spaces, Marcel Dekker year: 1978 ident: bib11 |
| SSID | ssj0021624 |
| Score | 1.6232989 |
| Snippet | Let X
1
,X
2
, ... be any sequence of nonnegative integrable random variables, and let N∈{1,2 , ...} be a random variable with known distribution, independent... Let X1, X2,... be any sequence of nonnegative integrable random variables, and let N epsilon {1, 2,...} be a random variable with known distribution,... |
| SourceID | proquest crossref informaworld |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 331 |
| SubjectTerms | AMS 2000 Subject Classifications: 60G40 Game theory Mathematical models Optimal stopping Optimization Prophet inequality Random horizon Random variables Studies |
| Title | An application of prophet regions to optimal stopping with a random number of observations |
| URI | https://www.tandfonline.com/doi/abs/10.1080/02331930410001716829 https://www.proquest.com/docview/219437679 |
| Volume | 53 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1Nj9MwELXQ7gUOiE9RFpAP3KqgJnac-Jhl0w1om0TBhWovkeO6EhIUBEFC_HrGsZNN1ap8XKIqjp028zKecf3eIPQyVkZkjM-8TSypR6VinvQ32vOVYmxGFIQIZkF_kbNsSd-uwtVNMc6OXdI2r9Svg7yS_7EqnAO7GpbsP1h2GBROwGewLxzBwnD8Kxsn-TQpy54MbDbwlFVRZqmYVullRw8WxbQoxZuF0TwQhcnhLyFnFxn4gyrJL4rFNF8uztPK9C3O36XVe8srHsesBXiVz46uOeAD0CMt26f8aHbUuNXWfv2ADrvXrMXFXimPoVyx9UIBIR5EeTbr19ZLmj0zlFsdyN6NWs1fBxc68omOkrXnq93mRhgfhp9R32n3xG4FZEcaOy_q-fLqqhbpSuy2dlMx42EYxDNDpT8Nosj8X3-aZBfXH4bc22ddfePh1_QsSiOzfuAb7EQpOxq2e3N2F4iIe-iuyyBwYuFwH93S2wfozkhX8iG6TnI8AgYu5tgBAztgYFFgBwzcAwMbYOAEW2BgCwzTdwyMR2g5T8XrzHNFNDxFYtJ6WtEg8BuIYzcass-Ghb6OGh5xaOBU0gZi7qBhkvoyJGu5DmQYrQmTXAVwHaXkMTrZftnqJwjHxG9gXoWgTjU0iDhXOtIzroz4_Dpi4QSR_qHVyinMm0Inn2q_F6I98KgnyBt6fbUKK3-4noztUbcdgDcWuwd71O3PdoLiI73I8Rue9Rav3cv_vYaJnhohJP70aOsZun3zzj1DJ-23H_o5RLFt88Ih9DdnuYLG |
| linkProvider | Library Specific Holdings |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LTxsxEB5RONAeWl4VaVrwgashXnu96yNCRCkkOYGEuKxsr1dIlGxEHKnqr-94H1FCaZDa83q8D49nvpkdfwNwktpAMqZ6tEi1oEJbSTUrHGXWStnjFiFCSOiPxnJwK67u4raacNaUVYYYuqiJIipbHTZ3SEa3JXFn6GdQczAQZw3fSxqpd7AVI3QPSs5740XMxWTV1zZIUBQR7em5v8yy4p1WuEv_sNWVA-p_AtM-el138ng69-bU_nrB6vhf77YDHxt4Ss5rfdqFDTfZgw9LpIX7cH8-IUu_vUlZEHym6YPzJHR5QC0mviQlmqInnCkQF4QjWSQkfIkm6Brz8onUjUiCbGkWeeHZAdz2L28uBrTp0EAtRraeOiuiiBkESYXD0MbImLnEqEThBSW0MAjoIiO1YDrmuc4jHSc5l1rZCMcJwT_D5qScuEMgKWcGjTYiBmtElChlXeJ6ygZm8zyRcQd4uzKZbejLQxeNHxlrWU5f-XIdoAupaU3f8cZ4vrzoma_SJkXd4-RVicz_9B1I10jx9TfstmqVNdZjlqEXEYFlR33594mPYXtwMxpmw-_j6y68rwuOQt3iV9j0z3P3DbGUN0fVbvkNDsoNRg |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LT-QwDLZYkBB74Lloh2cOXAOTJk2bIwJGPEccQEJcqiRNhQQzHS1BWvHrcfoYDc-V2HPj9BHH_uw6nwF2UhtIxlSXFqkWVGgrqWaFo8xaKbvcIkQICf2Lvjy-Fqc38c3EKf5QVhli6KImiqhsddjco7xoK-L20M2g4mAczhq6lzRSP2BGIjoJRX282x-HXExWbW2DBEUR0R6e-2SWV87pFXXpO1Nd-Z_eAuj2yeuyk_vdJ2927fMbUsf_ebVFmG_AKdmvtWkJptxwGX5OUBauwO3-kEz89CZlQfCRRnfOk9DjAXWY-JKUaIgGOFOgLQgHskhI9xJN0DHm5YDUbUiCbGnGWeHHX3DdO7o6OKZNfwZqMa711FkRRcwgRCocBjZGxswlRiUKLyihhUE4FxmpBdMxz3Ue6TjJudTKRjhOCL4K08Ny6H4DSTkzaLIRL1gjokQp6xLXVTbwmueJjDvA24XJbENeHnpoPGSs5Tj94Mt1gI6lRjV5xz_G88k1z3yVNCnqDicfSmT-r-9A-oUU__qG661WZY3teMzQh4jAsaPWvj_xNsxeHvay85P-2TrM1dVGoWhxA6b9nye3iUDKm61qr7wAoIML6g |
| 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=AN+APPLICATION+OF+PROPHET+REGIONS+TO+OPTIMAL+STOPPING+WITH+A+RANDOM+NUMBER+OF+OBSERVATIONS&rft.jtitle=Optimization&rft.au=Allaart%2C+Pieter+C&rft.date=2004-08-01&rft.pub=Taylor+%26+Francis+LLC&rft.issn=0233-1934&rft.eissn=1029-4945&rft.volume=53&rft.issue=4&rft.spage=331&rft_id=info:doi/10.1080%2F02331930410001716829&rft.externalDBID=NO_FULL_TEXT&rft.externalDocID=695528051 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0233-1934&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0233-1934&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0233-1934&client=summon |