A Quasi-Sure Approach to the Control of Non-Markovian Stochastic Differential Equations

Details A Quasi-Sure Approach to the Control of Non-Markovian Stochastic Differential Equations A Quasi-Sure Approach to the Control of Non-Markovian Stochastic Differential Equations

2011-06-16

arxiv.org/abs/1106.3273v1

Mathematics

Probability

27 pages

Scientific paper

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.

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