{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:40:51Z","timestamp":1787323251719,"version":"build-2736575974"},"reference-count":28,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"8","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>We study finite horizon optimal stopping problems for continuous-time Feller\u2013Markov processes. The functional depends on time, state, and external parameters and may exhibit discontinuities with respect to the time variable. Both left- and right-hand discontinuities are considered. We investigate the dependence of the value function on the parameters, on the initial state of the process, and on the stopping horizon. We construct $\\varepsilon$-optimal stopping times and provide conditions under which an optimal stopping time exists. We demonstrate how to approximate this optimal stopping time by solutions to discrete-time problems. Our results are applied to the study of impulse control problems with finite time horizon, decision lag, and execution delay.<\/jats:p>","DOI":"10.1137\/080737848","type":"journal-article","created":{"date-parts":[[2010,9,16]],"date-time":"2010-09-16T18:19:15Z","timestamp":1284661155000},"page":"4874-4909","source":"Crossref","is-referenced-by-count":23,"title":["Finite Horizon Optimal Stopping of Time-Discontinuous Functionals with Applications to Impulse Control with Delay"],"prefix":"10.1137","volume":"48","author":[{"given":"Jan","family":"Palczewski","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"\u0141ukasz","family":"Stettner","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,9,16]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1287\/moor.20.3.709"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1080\/10451120290008557"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1080\/1045112021000015331"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2006.08.004"},{"key":"R5","unstructured":"A. Bensoussan and J.L. Lions,\n                      Applications des In\u00e9quations Variationnelles en contr\u00f4le Stochastique\n                      , Dunod, Paris, 1978."},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1016\/0022-1236(81)90043-4"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1007\/BF01877497"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2008.07.007"},{"key":"R9","doi-asserted-by":"crossref","unstructured":"E. B. Dynkin,\n                      Markov Processes\n                      , Springer, Berlin, 1965.","DOI":"10.1007\/978-3-662-00031-1"},{"key":"R10","doi-asserted-by":"crossref","unstructured":"N. El Karoui,\n                      Les aspects probabilistes du contr\u00f4le stochastique\n                      , in Ninth Saint Flour Probability Summer School\u20141979, Lecture Notes in Math. 876, Springer, Berlin, 1981, pp. 73\u2013238.","DOI":"10.1007\/BFb0097499"},{"key":"R11","doi-asserted-by":"crossref","unstructured":"N. El Karoui, J. P. Lepeltier, and B. Marchal,\n                      Optimal stopping of controlled Markov processes\n                      , in Advances in Filtering and Optimal Stochastic Control, Lecture Notes in Control and Inform. Sci. 42, Springer, Berlin, 1982, pp. 106\u2013112.","DOI":"10.1007\/BFb0004529"},{"key":"R12","first-page":"97","volume":"13","author":"El Karoui N.","year":"1992","journal-title":"Probab. Math. Statist.","ISSN":"https:\/\/id.crossref.org\/issn\/0208-4147","issn-type":"print"},{"key":"R13","first-page":"708","volume":"16","author":"Fakeev A. G.","year":"1971","journal-title":"Teor. Verojatnost. i Primenen."},{"key":"R14","unstructured":"W. H. Fleming and H. M. Soner,\n                      Controlled Markov Processes and Viscosity Solutions\n                      , Springer, New York, 1993."},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2009.05.005"},{"key":"R16","first-page":"115","volume":"13","author":"Mackevicius V.","year":"1973","journal-title":"Liet. Mat. Rink."},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1137\/0318052"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1007\/BF00533481"},{"key":"R19","unstructured":"P. A. Meyer,\n                      Markov Processes\n                      , Research and Training School, Indian Statistical Institute, Kolkata, India, 1969."},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012900376013"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1007\/s00245-007-9034-5"},{"key":"R22","unstructured":"M. Robin,\n                      Contr\u00f4le impulsionnel avec retard pour des processes de Markov\n                      , in \u00c9cole d'\u00c9t\u00e9 de Calcul des Probabilit\u00e9s de Saint-Flour, Ann. Sci. Univ. Clermont 61, Math. 14, Universit\u00e9 Blaise Pascal, Clermont-Ferrand, France, 1976, pp. 115\u2013128."},{"key":"R23","unstructured":"M. Robin,\n                      Controle impulsionnel des processus de Markov\n                      , Thesis, University of Paris, IX, Paris, 1978."},{"key":"R24","unstructured":"W. Rudin,\n                      Principles of Mathematical Analysis\n                      , 3rd ed., McGraw\u2013Hill, New York, 1976."},{"key":"R25","unstructured":"\u0141. Stettner,\n                      Penalty method for finite horizon stopping problems\n                      , SIAM J. Control Optim., submitted."},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1080\/17442508108833167"},{"key":"R27","unstructured":"\u0141. Stettner and J. 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Zabczyk,\n                      Stopping problems in stochastic control\n                      , in Proceedings of the International Congress of Mathematicians, Vol. II, PWN, Warsaw, North\u2013Holland, Amsterdam, 1984, pp. 1425\u20131437."}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/080737848","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:50:52Z","timestamp":1787320252000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/080737848"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":28,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1137\/080737848"],"URL":"https:\/\/doi.org\/10.1137\/080737848","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1]]}}}