{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:20:17Z","timestamp":1787322017839,"version":"build-2736575974"},"reference-count":20,"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":[[2015,1]]},"abstract":"<jats:p>We study a problem of stochastic control in mathematical finance, with the goal of maximizing expected utility of investment and consumption over a finite trading horizon. The asset prices are modeled by It\u00f4 processes, for which the market parameters are subject to regime switching in the sense of being adapted to the joint filtration of the driving Brownian motion and a finite-state Markov chain which models \u201cregime states\u201d of the market. The vector of portfolios is constrained to a specified closed and convex set, and margin payments are levied on the investor, resulting in a wealth equation which is nonlinear in the portfolio. We proceed by the method of conjugate duality to construct a dual optimization problem together with optimality relations between putative solutions of the given (i.e., \u201cprimal'') optimization problem and the dual optimization problem. These optimality relations are then used to address the specific cases of power-type and logarithmic utility functions, with convex cone portfolio constraints, and a higher rate of interest for borrowing than for lending. We get completely explicit optimal portfolios and characterize the optimal consumption rate as the solution of a backward stochastic differential equation (BSDE) \u201cdriven\u201d by the canonical martingales of the regime-state Markov chain. For the power utility function this is a rather unconventional BSDE, to which standard existence results do not apply, and accordingly we establish existence and uniqueness of solutions for this BSDE.<\/jats:p>","DOI":"10.1137\/130951245","type":"journal-article","created":{"date-parts":[[2015,8,27]],"date-time":"2015-08-27T12:46:31Z","timestamp":1440679591000},"page":"2608-2656","source":"Crossref","is-referenced-by-count":7,"title":["Utility Maximization in a Regime Switching Model with Convex Portfolio Constraints and Margin Requirements: Optimality Relations and Explicit Solutions"],"prefix":"10.1137","volume":"53","author":[{"given":"Andrew J.","family":"Heunis","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2015,8,27]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(73)90066-8"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9965.00099"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1214\/aoap\/1177005576"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1137\/100809271"},{"key":"atypb5","doi-asserted-by":"crossref","unstructured":"J. B. Hiriart-Urruty and C. Lemare\u0301chal,\n                      Fundamentals of Convex Analysis\n                      , Springer-Verlag, Berlin, 2001.","DOI":"10.1007\/978-3-642-56468-0"},{"key":"atypb6","unstructured":"J. M. Holtzman,\n                      Nonlinear System Theory-A Functional Analysis Approach\n                      , Prentice-Hall, Englewood Cliffs, NJ, 1970."},{"key":"atypb7","doi-asserted-by":"crossref","unstructured":"J. Jacod and A. N. Shiryayev,\n                      Limit Theorems for Stochastic Processes\n                      , Springer-Verlag, Berlin, 1987.","DOI":"10.1007\/978-3-662-02514-7"},{"key":"atypb8","doi-asserted-by":"crossref","unstructured":"O. Kallenberg,\n                      Foundations of Modern Probability\n                      , 2nd ed., Springer-Verlag, New York, 2002.","DOI":"10.1007\/978-1-4757-4015-8"},{"key":"atypb9","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":"atypb10","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9965.2006.00301.x"},{"key":"atypb11","unstructured":"A. N. Kolmogorov and S. V. Fomin,\n                      Introductory Real Analysis\n                      , Dover, Mineola, NY, 1975."},{"key":"atypb12","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1080\/17442500802525401","volume":"81","author":"Labbe\u0301 C.","year":"2009","journal-title":"Stochastics"},{"key":"atypb13","doi-asserted-by":"crossref","unstructured":"R. Sh. Liptser and A. N. Shiryayev,\n                      Theory of Martingales\n                      , Kluwer, Dordrecht, Netherlands, 1989.","DOI":"10.1007\/978-94-009-2438-3"},{"key":"atypb14","doi-asserted-by":"crossref","unstructured":"P. E. Protter,\n                      Stochastic Integration and Differential Equations\n                      , Springer-Verlag, Berlin, 2004.","DOI":"10.1007\/978-3-662-10061-5"},{"key":"atypb15","unstructured":"D. Revuz and M. Yor,\n                      Continuous Martingales and Brownian Motion\n                      , Springer-Verlag, Berlin, 1994."},{"key":"atypb16","doi-asserted-by":"crossref","unstructured":"L. C. G. Rogers and D. Williams,\n                      Diffusions, Markov Processes and Martingales, Volume II, Ito Calculus\n                      , 2nd ed., Cambridge University Press, Cambridge, UK, 2000.","DOI":"10.1017\/CBO9780511805141"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9965.2009.00366.x"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1214\/aoap\/1177005772"},{"key":"atypb19","unstructured":"J. Yong and X. Y. Zhou,\n                      Stochastic Controls: Hamiltonian Systems and HJB Equations\n                      , Springer-Verlag, New York, 1999."},{"key":"atypb20","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\/130951245","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:17:09Z","timestamp":1787318229000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/130951245"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,1]]},"references-count":20,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2015,1]]}},"alternative-id":["10.1137\/130951245"],"URL":"https:\/\/doi.org\/10.1137\/130951245","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,1]]}}}