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Control Optim."],"published-print":{"date-parts":[[2016,1]]},"abstract":"<jats:p>We revisit a stochastic control problem of optimally modifying the underlying spectrally negative L\u00e9vy process. A strategy must be absolutely continuous with respect to the Lebesgue measure, and the objective is to minimize the total costs of the running and controlling costs. Under the assumption that the running cost function is convex, we show the optimality of a refraction strategy. We also obtain the convergence of the optimal refraction strategies and the value functions, as the control set is enlarged, to those in the relaxed case without the absolutely continuous assumption. Numerical results are further given to confirm these analytical results.<\/jats:p>","DOI":"10.1137\/15m1051208","type":"journal-article","created":{"date-parts":[[2016,5,5]],"date-time":"2016-05-05T10:58:39Z","timestamp":1462445919000},"page":"1126-1156","source":"Crossref","is-referenced-by-count":18,"title":["Optimality of Refraction Strategies for Spectrally Negative L\u00e9vy Processes"],"prefix":"10.1137","volume":"54","author":[{"given":"Daniel","family":"Hern\u00e1ndez-Hern\u00e1ndez","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jos\u00e9-Luis","family":"P\u00e9rez","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kazutoshi","family":"Yamazaki","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2016,5,5]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2003.07.005"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1214\/105051606000000709"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1007\/s102030200001"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2015.01.011"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1017\/asb.2013.17"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1137\/080715883"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012904443737"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1007\/s00440-010-0289-4"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1287\/opre.26.4.620"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2013.12.044"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2014.07.020"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9965.1993.tb00085.x"},{"key":"atypb13","first-page":"97","author":"Kuznetsov A.","year":"2013","journal-title":"Heidelberg"},{"key":"atypb14","doi-asserted-by":"crossref","unstructured":"A. E. Kyprianou,\n                      Fluctuations of Le\u0301vy Processes with Applications\n                      , 2nd ed., Universitext, Springer-Verlag, Berlin, 2014.","DOI":"10.1007\/978-3-642-37632-0"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1214\/08-AIHP307"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1331216839"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1214\/07-AAP504"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4068(97)00013-X"},{"key":"atypb19","unstructured":"P. E. Protter,\n                      Stochastic Integration and Differential Equations\n                      , 2nd ed., Stoch. Model. Appl. Probab. 21, Springer-Verlag, Berlin, 2005."},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1287\/moor.11.1.125"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/15M1051208","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:01:42Z","timestamp":1787320902000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/15M1051208"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,1]]},"references-count":20,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2016,1]]}},"alternative-id":["10.1137\/15M1051208"],"URL":"https:\/\/doi.org\/10.1137\/15m1051208","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,1]]}}}