A Quasi-Sure Approach to the Control of Non-Markovian Stochastic Differential Equations
AbstractWe 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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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1106.3273.
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
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- Epstein, Larry G. & Ji, Shaolin, 2014. "Ambiguous volatility, possibility and utility in continuous time," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 269-282.
- Nutz, Marcel & van Handel, Ramon, 2013. "Constructing sublinear expectations on path space," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3100-3121.
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