A Quasi-Sure Approach to the Control of Non-Markovian Stochastic Differential Equations
We study stochastic differential equations (SDEs) whose drift and diffusion coefficients are path-dependent and controlled. We construct a value process on the canonical path space, considered simultaneously under a family of singular measures, rather than the usual family of processes indexed by the controls. This value process is characterized by a second order backward SDE, which can be seen as a non-Markovian analogue of the Hamilton-Jacobi-Bellman partial differential equation. Moreover, our value process yields a generalization of the G-expectation to the context of SDEs.
|Date of creation:||Jun 2011|
|Date of revision:||May 2012|
|Publication status:||Published in Electronic Journal of Probability, Vol. 17, No. 23, pp. 1-23, 2012|
|Contact details of provider:|| Web page: http://arxiv.org/|