The Annals of Probability

Backward stochastic differential equations with constraints on the gains-process

Jak{\v{s}}a Cvitani{\'c}, Ioannis Karatzas, and H. Mete Soner

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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.

Article information

Source
Ann. Probab. Volume 26, Number 4 (1998), 1522-1551.

Dates
First available in Project Euclid: 31 May 2002

Permanent link to this document
http://projecteuclid.org/euclid.aop/1022855872

Mathematical Reviews number (MathSciNet)
MR1675035

Digital Object Identifier
doi:10.1214/aop/1022855872

Zentralblatt MATH identifier
0935.60039

Subjects
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05] 93E20: Optimal stochastic control
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]

Keywords
Backward SDEs convex constraints stochastic control

Citation

Cvitani{\'c}, Jak{\v{s}}a; Karatzas, Ioannis; Soner, H. Mete. Backward stochastic differential equations with constraints on the gains-process. The Annals of Probability 26 (1998), no. 4, 1522--1551. doi:10.1214/aop/1022855872. http://projecteuclid.org/euclid.aop/1022855872.


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