{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:59:07Z","timestamp":1787324347690,"version":"build-2736575974"},"reference-count":17,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2015,1]]},"abstract":"<jats:p>This paper studies stopping problems of the form $V=\\inf_{0 \\leq \\tau \\leq T} \\mathbb{E}[U(\\frac{\\max_{0\\le s \\le T} Z_s }{Z_\\tau})]$ for strictly concave or convex utility functions U in a family of increasing functions satisfying certain conditions, where Z is a geometric Brownian motion and T is the time of the nth jump of a Poisson process independent of Z. We obtain some properties of $V$ and offer solutions for the optimal strategies to follow. This provides us with a technique to build numerical approximations of stopping boundaries for the fixed terminal time optimal stopping problem presented in [J. Du Toit and G. Peskir, Ann. Appl. Probab., 19 (2009), pp. 983--1014].<\/jats:p>","DOI":"10.1137\/130946800","type":"journal-article","created":{"date-parts":[[2015,5,26]],"date-time":"2015-05-26T11:30:30Z","timestamp":1432639830000},"page":"1328-1345","source":"Crossref","is-referenced-by-count":0,"title":["Time-Randomized Stopping Problems for a Family of Utility Functions"],"prefix":"10.1137","volume":"53","author":[{"given":"Iker","family":"Perez","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Huiling","family":"Le","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2015,5,26]]},"reference":[{"key":"atypb1","unstructured":"V. I. Arnold,\n                      Ordinary Differential Equations\n                      , Springer-Verlag, Berlin, Heidelberg, New York, 2006."},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4149(02)00104-7"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1093\/rfs\/11.3.597"},{"key":"atypb4","first-page":"317","author":"Dai M.","year":"2010","journal-title":"New York"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1214\/009117906000000638"},{"key":"atypb6","first-page":"95","author":"Du Toit J.","year":"2008","journal-title":"Heidelberg"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1214\/08-AAP566"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1137\/060673916"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1137\/110838352"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1137\/S0040585X97978075"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.2307\/3318509"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139903426083"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177728720"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1111\/j.0960-1627.2005.00214.x"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1080\/17442500601040461"},{"key":"atypb17","doi-asserted-by":"crossref","unstructured":"G. Peskir and A. Shiryaev,\n                      Optimal Stopping and Free-Boundary Problems\n                      , Birkha\u0308user Verlag, Basel, 2006.","DOI":"10.1007\/978-3-7643-7390-0"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1080\/14697680802563732"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/130946800","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:22:17Z","timestamp":1787322137000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/130946800"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,1]]},"references-count":17,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2015,1]]}},"alternative-id":["10.1137\/130946800"],"URL":"https:\/\/doi.org\/10.1137\/130946800","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,1]]}}}