{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:48:39Z","timestamp":1787320119709,"version":"build-2736575974"},"reference-count":21,"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":[[2009,1]]},"abstract":"<jats:p>This paper is concerned with stock loan valuation in which the underlying stock price is dictated by geometric Brownian motion with regime switching. The stock loan pricing is quite different from that for standard American options because the associated variational inequalities may have infinitely many solutions. In addition, the optimal stopping time equals infinity with positive probability. Variational inequalities are used to establish values of stock loans and reasonable values of critical parameters such as loan sizes, loan rates, and service fees in terms of certain algebraic equations. Numerical examples are included to illustrate the results.<\/jats:p>","DOI":"10.1137\/070708998","type":"journal-article","created":{"date-parts":[[2009,4,1]],"date-time":"2009-04-01T18:17:15Z","timestamp":1238609835000},"page":"1229-1250","source":"Crossref","is-referenced-by-count":59,"title":["Valuation of Stock Loans with Regime Switching"],"prefix":"10.1137","volume":"48","author":[{"given":"Qing","family":"Zhang","sequence":"first","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":[[2009,4,1]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.3905\/jod.1998.408011"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1142\/S0219024902001523"},{"key":"R3","doi-asserted-by":"crossref","unstructured":"Y. S. Chow and H. Teicher,\n                      Probability Theory\n                      , Springer-Verlag, New York, 1978.","DOI":"10.1007\/978-1-4684-0062-5"},{"key":"R4","unstructured":"M. Dai, Z. Xu, and X. Y. Zhou,\n                      Optimal Redeeming Strategy of Stock Loans\n                      , working paper, University of Oxford, 2008."},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1137\/1139008"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1088\/1469-7688\/2\/2\/303"},{"key":"R7","unstructured":"X. Guo,\n                      Inside Information and Stock Fluctuations\n                      , Ph.D. thesis, Rutgers University, 1999."},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1080\/713665550"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/996986756"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2005.854657"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.2307\/1912559"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1080\/10920277.2001.10595984"},{"key":"R13","unstructured":"J. C. Hull,\n                      Options, Futures, and Other Derivatives\n                      , 4th ed., Prentice\u2013Hall, Upper Saddle River, NJ, 2000."},{"key":"R14","doi-asserted-by":"crossref","unstructured":"B. \u00d8ksendal,\n                      Stochastic Differential Equations\n                      , 6th ed., Springer-Verlag, New York, 2003.","DOI":"10.1007\/978-3-642-14394-6"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2002.1003827"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9965.2006.00305.x"},{"key":"R17","doi-asserted-by":"crossref","unstructured":"D. D. Yao, Q. Zhang, and X. Y. Zhou,\n                      A regime-switching model for European options\n                      , in Stochastic Processes, Optimization, and Control Theory: Applications in Financial Engineering, Queueing Networks, and Manufacturing Systems, Internat. Ser. Oper. Res. Management Sci. 94, Springer-SBM, New York, 2006, pp. 281\u2013300.","DOI":"10.1007\/0-387-33815-2_14"},{"key":"R18","unstructured":"J. Yong and X. Y. Zhou,\n                      Stochastic Controls: Hamiltonian Systems and HJB Equations\n                      , Springer-Verlag, New York, 1999."},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012999356325"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1023\/B:JOTA.0000037412.23243.6c"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012902405583"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/070708998","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:55:08Z","timestamp":1787316908000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/070708998"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,1]]},"references-count":21,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2009,1]]}},"alternative-id":["10.1137\/070708998"],"URL":"https:\/\/doi.org\/10.1137\/070708998","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,1]]}}}