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A quasi-sure approach to the control of non-Markovian stochastic differential equations

   
@article{EJP1892,
	author = {Marcel Nutz},
	title = {A quasi-sure approach to the control of non-Markovian stochastic differential equations},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {17},
	year = {2012},
	keywords = {Stochastic optimal control; non-Markovian SDE; second order BSDE; \$G\$-expectation; random \$G\$-expectation; volatility uncertainty; risk measure},
	abstract = {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.},
	pages = {no. 23, 1-23},
	issn = {1083-6489},
	doi = {10.1214/EJP.v17-1892},    
        url = {http://ejp.ejpecp.org/article/view/1892}}