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October 1998 Backward stochastic differential equations with constraints on the gains-process
Jak{\v{s}}a Cvitani{\'c}, Ioannis Karatzas, H. Mete Soner
Ann. Probab. 26(4): 1522-1551 (October 1998). DOI: 10.1214/aop/1022855872


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.


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Jak{\v{s}}a Cvitani{\'c}. Ioannis Karatzas. H. Mete Soner. "Backward stochastic differential equations with constraints on the gains-process." Ann. Probab. 26 (4) 1522 - 1551, October 1998.


Published: October 1998
First available in Project Euclid: 31 May 2002

zbMATH: 0935.60039
MathSciNet: MR1675035
Digital Object Identifier: 10.1214/aop/1022855872

Primary: 60H10 , 93E20
Secondary: 60G40

Keywords: Backward SDEs , convex constraints , Stochastic control

Rights: Copyright © 1998 Institute of Mathematical Statistics

Vol.26 • No. 4 • October 1998
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