A Quasi-Sure Approach to the Control of Non-Markovian Stochastic Differential Equations
- Working 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. Show more
Journal / seriesarXiv
Pages / Article No.
Organisational unit03844 - Soner, Mete (emeritus) / Soner, Mete (emeritus)
03658 - Schweizer, Martin / Schweizer, Martin
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