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Backward stochastic differential equations with constraints on the gains-process

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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Abstract

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://projecteuclid.org/euclid.aop/1022855872PublisherUNSPECIFIED
http://www.jstor.org/stable/2652779PublisherUNSPECIFIED
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.
Funders:
Funding AgencyGrant Number
Army Research Office (ARO)DAAH 04-95-1-0528
Army Research Office (ARO)DAAH-04-95-1-0226
Subject Keywords:backward SDEs; convex constraints; stochastic control
Other Numbering System:
Other Numbering System NameOther Numbering System ID
Mathematical Reviews number (MathSciNet)MR1675035
Zentralblatt MATH identifier0935.60039
Classification Code:AMS 1991 subject classifications: Primary 60H10, 93E20; secondary 60G40
Record Number:CaltechAUTHORS:20111220-131043977
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20111220-131043977
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.
ID Code:28538
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:20 Dec 2011 22:12
Last Modified:26 Dec 2012 14:38

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