{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:41:57Z","timestamp":1787319717954,"version":"build-2736575974"},"reference-count":21,"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>This paper studies the optimal switching problem for a general one-dimensional diffusion with multiple (more than two) regimes. This is motivated in the real options literature by the investment problem of a firm managing several production modes while facing uncertainties. A viscosity solutions approach is employed to carry out a fine analysis on the associated system of variational inequalities, leading to sharp qualitative characterizations of the switching regions. These characterizations, in turn, reduce the switching problem into one of finding a finite number of threshold values in a state that would trigger switchings. The results of our analysis take several qualitatively different forms depending on model parameters, and the issue of when and where it is optimal to switch is addressed. The general results are then demonstrated by the three-regime case, where a quasi-explicit solution is obtained, and a numerical procedure to find these critical values is devised in terms of the expectation functionals of hitting times for one-dimensional diffusions.<\/jats:p>","DOI":"10.1137\/070709372","type":"journal-article","created":{"date-parts":[[2009,6,25]],"date-time":"2009-06-25T18:04:45Z","timestamp":1245953085000},"page":"2217-2253","source":"Crossref","is-referenced-by-count":45,"title":["Optimal Switching over Multiple Regimes"],"prefix":"10.1137","volume":"48","author":[{"given":"Huy\u00ean","family":"Pham","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vathana Ly","family":"Vath","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xun Yu","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2009,6,25]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1007\/s00245-004-0792-z"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2006.08.004"},{"key":"R3","unstructured":"E. Bayraktar and M. Egami,\n                      On the Optimal Switching Problem for One-Dimensional Diffusions\n                      , preprint, University of Michigan, Ann Arbor, MI, 2007."},{"key":"R4","unstructured":"A. Bensoussan and J. L. Lions,\n                      Contr\u00f4le impulsionnel et in\u00e9quations variationnelles\n                      , Dunod, Paris, 1982."},{"key":"R5","doi-asserted-by":"crossref","unstructured":"A. Borodin and P. Salminen,\n                      Handbook of Brownian Motion\u2014Facts and Formulae\n                      , Birkh\u00e4user, Basel, 1996.","DOI":"10.1007\/978-3-0348-7652-0"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012992229835"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1086\/296288"},{"key":"R8","unstructured":"R. Carmona and M. Ludkovski,\n                      Optimal Switching with Applications to Energy Tolling Agreements\n                      , preprint, Princeton University, Princeton, NJ, 2005."},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4149(03)00076-0"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1142\/S0219622006002039"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1086\/261619"},{"key":"R12","unstructured":"B. Djehiche, S. Hamad\u00e8ne, and A. Popier,\n                      A Finite Horizon Optimal Switching Problem\n                      , preprint, Universit\u00e9 du Maine, Le Mans, France, 2007."},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1214\/aoap\/998926992"},{"key":"R14","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-Verlag, Berlin, 1981, pp. 73\u2013238.","DOI":"10.1007\/BFb0097499"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1137\/060669024"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1287\/moor.1060.0228"},{"key":"R17","unstructured":"Y. Hu and S. Tang,\n                      Multi-dimensional BSDE with oblique reflection and optimal switching\n                      , Probab. Theory Related Fields, to appear."},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1137\/050638783"},{"key":"R19","doi-asserted-by":"crossref","unstructured":"H. Pham,\n                      On the smooth-fit property for one-dimensional optimal switching problem\n                      , S\u00e9minaire de Probabilit\u00e9s XL, Springer-Verlag, Berlin, 2007, pp. 187\u2013199.","DOI":"10.1007\/978-3-540-71189-6_8"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1080\/17442509308833860"},{"key":"R21","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\/070709372","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:51:23Z","timestamp":1787316683000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/070709372"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,1]]},"references-count":21,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2009,1]]}},"alternative-id":["10.1137\/070709372"],"URL":"https:\/\/doi.org\/10.1137\/070709372","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,1]]}}}