{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:42:49Z","timestamp":1787319769170,"version":"build-2736575974"},"reference-count":34,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2009,1]]},"abstract":"<jats:p>-1We consider the problem of optimal multiple switching in a finite horizon when the state of the system, including the switching costs, is a general adapted stochastic process. The problem is formulated as an extended impulse control problem and solved using probabilistic tools such as the Snell envelope of processes and reflected backward stochastic differential equations. Finally, when the state of the system is a Markov process, we show that the associated vector of value functions provides a viscosity solution to a system of variational inequalities with interconnected obstacles.<\/jats:p>","DOI":"10.1137\/070697641","type":"journal-article","created":{"date-parts":[[2009,9,18]],"date-time":"2009-09-18T18:20:03Z","timestamp":1253298003000},"page":"2751-2770","source":"Crossref","is-referenced-by-count":87,"title":["A Finite Horizon Optimal Multiple Switching Problem"],"prefix":"10.1137","volume":"48","author":[{"given":"Boualem","family":"Djehiche","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Said","family":"Hamad\u00e8ne","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alexandre","family":"Popier","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2009,9,18]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1080\/17442500802327360"},{"key":"R2","unstructured":"K. A. Brekke and B. \u00d8ksendal,\n                      The high contact principle as a sufficiency condition for optimal stopping\n                      , in Stochastic Models and Option Values, D. Lund and B. \u00d8ksendal, eds., North\u2013Holland, Amsterdam, 1991, pp. 187\u2013208."},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012992229835"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1086\/296288"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1080\/13504860802170507"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1041903216"},{"key":"R7","unstructured":"C. Dellacherie and P. A. Meyer,\n                      Probabilit\u00e9s et Potentiel\n                      , V-VIII, Hermann, Paris, 1980."},{"key":"R8","unstructured":"S. J. Deng and Z. Xia,\n                      Pricing and Hedging Electric Supply Contracts: A Case with Tolling Agreements\n                      , preprint, Georgia Institute of Technology, Atlanta, 2005."},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1142\/S0219024909005312"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1086\/261619"},{"key":"R11","doi-asserted-by":"crossref","unstructured":"A. Dixit and R. S. Pindyck,\n                      Investment Under Uncertainty\n                      , Princeton University Press, Princeton, NJ, 1994.","DOI":"10.1515\/9781400830176"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1109\/TAES.2002.1039427"},{"key":"R13","doi-asserted-by":"crossref","unstructured":"K. Duckworth and M. Zervos,\n                      A problem of stochastic impulse control with discretionary stopping\n                      , in Proceedings of the 39th IEEE Conference on Decision and Control, IEEE Control Systems Society, Piscataway, NJ, 2000, pp. 222\u2013227.","DOI":"10.1109\/CDC.2000.912763"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1214\/aoap\/998926992"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1007\/s00245-009-9071-3"},{"key":"R16","doi-asserted-by":"crossref","unstructured":"N. El Karoui,\n                      Les aspects probabilistes du contr\u00f4le stochastique\n                      , in Ecole d'\u00e9t\u00e9 de Probabilit\u00e9s de Saint-Flour, Lecture Notes in Math. 876, Springer-Verlag, New York, 1980.","DOI":"10.1007\/BFb0097499"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1024404416"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9965.00022"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1214\/105051605000000412"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.3150\/bj\/1161614951"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2004.12.002"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1080\/1045112021000036545"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1287\/moor.1060.0228"},{"key":"R24","unstructured":"S. Hamad\u00e8ne and I. Hdhiri,\n                      On the Starting and Stopping Problem with Brownian and Independent Poisson Noise\n                      , preprint, Universit\u00e9 du Maine, Le Mans, France, 2006."},{"key":"R25","doi-asserted-by":"crossref","unstructured":"I. Karatzas and S. E. Shreve,\n                      Methods of Mathematical Finance\n                      , Springer-Verlag, New York, 1998.","DOI":"10.1007\/b98840"},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012997315816"},{"key":"R27","unstructured":"E. Pardoux and S. Peng,\n                      Backward SDEs and quasilinear PDEs\n                      , in Stochastic Partial Differential Equations and Their Applications, B. L. Rozovskii and R. B. Sowers, eds., Lecture Notes in Control and Inform. Sci. 176, Springer-Verlag, Berlin, 1992."},{"key":"R28","doi-asserted-by":"crossref","unstructured":"D. Revuz and M. Yor,\n                      Continuous Martingales and Brownian Motion\n                      , Springer-Verlag, Berlin, 1991.","DOI":"10.1007\/978-3-662-21726-9"},{"key":"R29","doi-asserted-by":"publisher","DOI":"10.1007\/s00186-008-0231-z"},{"key":"R30","first-page":"107","volume":"987","author":"Shirakawa H.","year":"1997","journal-title":"S${\\bar u}$rikaisekikenky${\\bar u}$sho K${\\bar o}$ky${\\bar u}$roku"},{"key":"R31","doi-asserted-by":"publisher","DOI":"10.1080\/17442509308833860"},{"key":"R32","doi-asserted-by":"publisher","DOI":"10.2307\/3665939"},{"key":"R33","unstructured":"L. Trigeorgis,\n                      Real Options: Managerial Flexibility and Strategy in Resource Allocation\n                      , MIT Press, Cambridge, MA, 1996."},{"key":"R34","doi-asserted-by":"publisher","DOI":"10.1137\/S036301290038111X"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/070697641","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:52:29Z","timestamp":1787316749000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/070697641"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,1]]},"references-count":34,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2009,1]]}},"alternative-id":["10.1137\/070697641"],"URL":"https:\/\/doi.org\/10.1137\/070697641","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,1]]}}}