Dual formulation of second order target problems

H. Mete Soner, Nizar Touzi, Jianfeng Zhang

Research output: Contribution to journalArticle

58 Scopus citations

Abstract

This paper provides a new formulation of second order stochastic target problems introduced in [SIAM J. Control Optim. 48 (2009) 2344-2365] by modifying the reference probability so as to allow for different scales. This new ingredient enables us to prove a dual formulation of the target problem as the supremum of the solutions of standard backward stochastic differential equations. In particular, in the Markov case, the dual problem is known to be connected to a fully nonlinear, parabolic partial differential equation and this connection can be viewed as a stochastic representation for all nonlinear, scalar, second order, parabolic equations with a convex Hessian dependence.

Original languageEnglish (US)
Pages (from-to)308-347
Number of pages40
JournalAnnals of Applied Probability
Volume23
Issue number1
DOIs
StatePublished - Feb 1 2013
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Backward SDEs
  • Duality
  • Mutually singular probability measures
  • Stochastic target problem

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