Dual Formulation of Second Order Target Problems

Details Dual Formulation of Second Order Target Problems Dual Formulation of Second Order Target Problems

2010-03-31

arxiv.org/abs/1003.6050v2

Mathematics

Probability

36 pages

Scientific paper

This paper provides a new formulation of second order stochastic target problems 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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