Backward stochastic differential equations with constraints on the gains-process

Jakša Cvitanić, Ioannis Karatzas, H. Mete Soner

Research output: Contribution to journalArticlepeer-review

37 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)1522-1551
Number of pages30
JournalAnnals of Probability
Volume26
Issue number4
StatePublished - Oct 1 1998
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Backward SDEs
  • Convex constraints
  • Stochastic control

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