The Annals of Applied Probability

Dual formulation of second order target problems

H. Mete Soner, Nizar Touzi, and Jianfeng Zhang

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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.

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Ann. Appl. Probab., Volume 23, Number 1 (2013), 308-347.

First available in Project Euclid: 25 January 2013

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Primary: 60H10: Stochastic ordinary differential equations [See also 34F05] 60H30: Applications of stochastic analysis (to PDE, etc.)

Stochastic target problem mutually singular probability measures backward SDEs duality


Soner, H. Mete; Touzi, Nizar; Zhang, Jianfeng. Dual formulation of second order target problems. Ann. Appl. Probab. 23 (2013), no. 1, 308--347. doi:10.1214/12-AAP844.

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