{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:47:23Z","timestamp":1787320043145,"version":"build-2736575974"},"reference-count":26,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2009,1]]},"abstract":"<jats:p>This paper concerns continuous-time optimal investment and the consumption decision of a constant relative risk aversion (CRRA) investor who faces proportional transaction costs and a finite time horizon. In the no-consumption case, it has been studied by Liu and Loewenstein [Review of Financial Studies, 15 (2002), pp. 805\u2013835] and Dai and Yi [J. Differential Equations, 246 (2009), pp. 1445\u20131469]. Mathematically, it is a singular stochastic control problem whose value function satisfies a parabolic variational inequality with gradient constraints. The problem gives rise to two free boundaries which stand for the optimal buying and selling strategies, respectively. We present an analytical approach to analyze the behaviors of free boundaries. The regularity of the value function is studied as well. Our approach is essentially based on the connection between singular control and optimal stopping, which is first revealed in the present problem.<\/jats:p>","DOI":"10.1137\/070703685","type":"journal-article","created":{"date-parts":[[2009,3,11]],"date-time":"2009-03-11T21:31:17Z","timestamp":1236807077000},"page":"1134-1154","source":"Crossref","is-referenced-by-count":63,"title":["Finite Horizon Optimal Investment and Consumption with Transaction Costs"],"prefix":"10.1137","volume":"48","author":[{"given":"Min","family":"Dai","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lishang","family":"Jiang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peifan","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fahuai","family":"Yi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2009,3,11]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012993247159"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9965.1996.tb00075.x"},{"key":"R3","doi-asserted-by":"crossref","unstructured":"M. Dai, Z. Q. Xu, and X. Y. Zhou (2007),\n                      Continuous-Time Mean-Variance Portfolio Selection with Proportional Transaction Costs\n                      , Working paper, National University of Singapore, Singapore.","DOI":"10.2139\/ssrn.1210105"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2008.11.003"},{"key":"R5","doi-asserted-by":"crossref","unstructured":"M. Dai and Y. F. Zhong (2008),\n                      Penalty Methods for Continuous-Time Portfolio Selection with Proportional Transaction Costs\n                      , Working paper, National University of Singapore, Singapore.","DOI":"10.2139\/ssrn.1210105"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1287\/moor.15.4.676"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1137\/0331022"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1080\/03605307908820103"},{"key":"R9","unstructured":"W. H. Fleming and H. M. Soner (2006),\n                      Controlled Markov Processes and Viscosity Solutions\n                      , 2nd ed., Springer-Verlag, New York."},{"key":"R10","unstructured":"A. Friedman (1982),\n                      Variational Principles and Free-Boundary Problems\n                      , Wiley, New York."},{"key":"R11","first-page":"78","volume":"5","author":"Hu B.","year":"1986","journal-title":"Beijing Daxue Xuebao"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1080\/03605308308820271"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1007\/s00780-003-0113-4"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1137\/0322054"},{"key":"R15","doi-asserted-by":"crossref","unstructured":"I. Karatzas and S. E. Shreve (1998),\n                      Methods of Mathematical Finance\n                      , Springer-Verlag, New York.","DOI":"10.1007\/b98840"},{"key":"R16","doi-asserted-by":"crossref","unstructured":"T. L. Lai and T. W. Lim (2003),\n                      Singular stochastic control in optimal investment and hedging in the presence of transaction costs\n                      , in Probability, Statistics, and Their Applications, IMS Lecture Notes Monogr. Ser. 41, Inst. Math. Statist., Beachwood, OH, pp. 209\u2013227.","DOI":"10.1214\/lnms\/1215091666"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1093\/rfs\/15.3.805"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0531(76)90019-3"},{"key":"R19","first-page":"77","volume":"7","author":"Markowitz H. M.","year":"1952","journal-title":"J. Finance","ISSN":"https:\/\/id.crossref.org\/issn\/0022-1082","issn-type":"print"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.2307\/1926560"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0531(71)90038-X"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1214\/aoap\/1177004966"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1080\/03605309108820763"},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1080\/03605308108820181"},{"key":"R25","unstructured":"J. M. Yong and X. Y. Zhou (1999),\n                      Stochastic Controls: Hamiltonian Systems and HJB Equations\n                      , Springer-Verlag, New York."},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1007\/BF01182322"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/070703685","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:54:54Z","timestamp":1787316894000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/070703685"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,1]]},"references-count":26,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2009,1]]}},"alternative-id":["10.1137\/070703685"],"URL":"https:\/\/doi.org\/10.1137\/070703685","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,1]]}}}