Generalized stochastic target problems and related PDEs
by
Bruno Bouchard
PMA, University Paris 6

The general formalism of a stochastic target problem is the following: given a process Z^{z, n} with initial condition z and depending on some control n, find the set G of initial conditions z such that there exists an admissible n for which Z^{z, n}_T belongs a.s. to a prescribed fixed Borel set, called the target. We first relate such problems to semilinear PDEs with gradient constraint and Dirichlet boundary conditions. We then provide a link between a particular class of stochastic target problems and the "second order" BSDEs introduced by Touzi and Soner. We conclude with an interpretation in terms of fully nonlinear parabolic PDEs.

Date received: July 3, 2007

Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cavj-82.