{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:35:02Z","timestamp":1787322902168,"version":"build-2736575974"},"reference-count":20,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>In this paper, we discuss a combined singular control problem with discretionary stopping for geometric Brownian motions. By the method of penalization, we solve the degenerate variational inequality associated with this problem. Its solution v coincides with the value function and, by the concavity of v, an optimal control is shown to exist.<\/jats:p>","DOI":"10.1137\/080734856","type":"journal-article","created":{"date-parts":[[2010,3,19]],"date-time":"2010-03-19T18:22:02Z","timestamp":1269022922000},"page":"3781-3804","source":"Crossref","is-referenced-by-count":12,"title":["A Singular Control Problem with Discretionary Stopping for Geometric Brownian Motions"],"prefix":"10.1137","volume":"48","author":[{"given":"Hiroaki","family":"Morimoto","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,3,19]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012900367825"},{"key":"R2","doi-asserted-by":"crossref","unstructured":"M. Bardi and I. Capuzzo-Dolcetta,\n                      Optimal Control and Viscosity Solutions of Hamilton\u2013Jacobi\u2013Bellman Equations\n                      , Birkh\u00e4user Boston, Boston, 1997.","DOI":"10.1007\/978-0-8176-4755-1"},{"key":"R3","unstructured":"A. Bensoussan and J.L. Lions,\n                      Applications des In\u00e9quations Variationnelles en Contr\u00f4le Stochastique\n                      , Dunod, Paris, 1978."},{"key":"R4","unstructured":"A. Bensoussan and J.L. Lions,\n                      Contr\u00f4le Impulsionnel et In\u00e9quations Quasi Variationnelles\n                      , Gauthier-Villars, Paris, 1982."},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012900382667"},{"key":"R6","unstructured":"F. H. Clarke,\n                      Optimization and Nonsmooth Analysis\n                      , John Wiley and Sons, New York, 1983."},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1090\/S0273-0979-1992-00266-5"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1214\/aoap\/1177005209"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1007\/BF00533992"},{"key":"R10","unstructured":"W. H. Fleming and H. M. Soner,\n                      Controlled Markov Processes and Viscosity Solutions\n                      , Springer-Verlag, New York, 1993."},{"key":"R11","unstructured":"D. Gilbarg and N. S. Trudinger,\n                      Elliptic Partial Differential Equations of Second Order\n                      , 2nd ed., Springer-Verlag, Berlin, 1983."},{"key":"R12","unstructured":"N. Ikeda and S. Watanabe,\n                      Stochastic Differential Equations and Diffusion Processes\n                      , North\u2013Holland, Amsterdam, 1981."},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.2307\/1426435"},{"key":"R14","doi-asserted-by":"crossref","unstructured":"I. Karatzas and S. E. Shreve,\n                      Brownian Motion and Stochastic Calculus\n                      , Grad. Texts in Math. 113, Springer-Verlag, New York, 1988.","DOI":"10.1007\/978-1-4684-0302-2"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1080\/17442500008834257"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012998346323"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2007.8.261"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160370408"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012901369041"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1137\/0322005"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/080734856","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:32:38Z","timestamp":1787319158000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/080734856"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":20,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1137\/080734856"],"URL":"https:\/\/doi.org\/10.1137\/080734856","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1]]}}}