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

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  • Marcel Nutz
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    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.

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    File URL: http://arxiv.org/pdf/1106.3273
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1106.3273.

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    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
    Handle: RePEc:arx:papers:1106.3273

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    Web page: http://arxiv.org/

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    Cited by:
    1. 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.
    2. 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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