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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
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
Contact details of provider:
Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Nutz, Marcel & van Handel, Ramon, 2013. "Constructing sublinear expectations on path space," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3100-3121.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators).
If references are entirely missing, you can add them using this form.