Cvitanić, Jakša and Karatzas, Ioannis and Soner, H. Mete (1998) Backward stochastic differential equations with constraints on the gains-process. Annals of Probability, 26 (4). pp. 1522-1551. ISSN 0091-1798. http://resolver.caltech.edu/CaltechAUTHORS:20111220-131043977
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We consider backward stochastic differential equations with convex constraints on the gains (or intensity-of-noise) process. Existence and uniqueness of a minimal solution are established in the case of a drift coefficient which is Lipschitz continuous in the state and gains processes and convex in the gains process. It is also shown that the minimal solution can be characterized as the unique solution of a functional stochastic control-type equation. This representation is related to the penalization method for constructing solutions of stochastic differential equations, involves change of measure techniques, and employs notions and results from convex analysis, such as the support function of the convex set of constraints and its various properties.
|Additional Information:||© 1998 Institute of Mathematical Statistics. Received October 1997; revised April 1998. Supported in part by U.S. Army Research Office Grant DAAH 04-95-1-0528. Supported in part by U.S. Army Research Grant DAAH-04-95-1-0226.|
|Subject Keywords:||backward SDEs; convex constraints; stochastic control|
|Other Numbering System:|
|Classification Code:||AMS 1991 subject classifications: Primary 60H10, 93E20; secondary 60G40|
|Official Citation:||Backward Stochastic Differential Equations with Constraints on the Gains-Process Jaksa Cvitanic, Ioannis Karatzas and H. Mete Soner The Annals of Probability , Vol. 26, No. 4 (Oct., 1998), pp. 1522-1551 Published by: Institute of Mathematical Statistics Article Stable URL: http://www.jstor.org/stable/2652779|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Tony Diaz|
|Deposited On:||20 Dec 2011 22:12|
|Last Modified:||26 Dec 2012 14:38|
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