{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T11:50:02Z","timestamp":1759665002781,"version":"3.38.0"},"reference-count":8,"publisher":"Cambridge University Press (CUP)","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2014,9]]},"abstract":"<jats:p>We consider a class of optimal stopping problems involving both the running maximum as well as the prevailing state of a linear diffusion. Instead of tackling the problem directly via the standard free boundary approach, we take an alternative route and present a parameterized family of standard stopping problems of the underlying diffusion. We apply this family to delineate circumstances under which the original problem admits a unique, well-defined solution. We then develop a discretized approach resulting in a numerical algorithm for solving the considered class of stopping problems. We illustrate the use of the algorithm in both a geometric Brownian motion and a mean reverting diffusion setting.<\/jats:p>","DOI":"10.1017\/s0001867800011691","type":"journal-article","created":{"date-parts":[[2016,3,29]],"date-time":"2016-03-29T10:50:01Z","timestamp":1459248601000},"page":"818-836","source":"Crossref","is-referenced-by-count":1,"title":["Optimal Stopping of the Maximum Process"],"prefix":"10.1017","volume":"51","author":[{"given":"Luis H. R.","family":"Alvarez","sequence":"first","affiliation":[]},{"given":"Pekka","family":"Matom\u00e4ki","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2016,2,4]]},"reference":[{"volume-title":"Optimal Stopping and Free-boundary Problems","year":"2006","key":"S0001867800011691_ref26"},{"volume-title":"Handbook of Brownian Motion\u2014Facts and Formulae","year":"2002","key":"S0001867800011691_ref7"},{"key":"S0001867800011691_ref5","first-page":"93","volume":"7","year":"1997","journal-title":"Statistica Sinica"},{"key":"S0001867800011691_ref15","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1080\/17442500601111429","volume":"79","year":"2007","journal-title":"Stochastics"},{"key":"S0001867800011691_ref19","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1080\/17442500601075780","volume":"79","year":"2007","journal-title":"Stochastics"},{"volume-title":"Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables","year":"1964","key":"S0001867800011691_ref1"},{"volume-title":"Brownian Motion and Stochastic Calculus","year":"1988","key":"S0001867800011691_ref17"},{"first-page":"309","volume-title":"The Maximality Principle Revisited: On Certain Optimal Stopping Problems","year":"2007","key":"S0001867800011691_ref22"}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0001867800011691","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,5]],"date-time":"2019-09-05T22:16:20Z","timestamp":1567721780000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0001867800011691\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,9]]},"references-count":8,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2014,9]]}},"alternative-id":["S0001867800011691"],"URL":"https:\/\/doi.org\/10.1017\/s0001867800011691","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"type":"print","value":"0021-9002"},{"type":"electronic","value":"1475-6072"}],"subject":[],"published":{"date-parts":[[2014,9]]}}}