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

作者：Nutz Marcel^*

来源：Electronic Journal of Probability, 2012, 17: 1-23.

DOI：10.1214/EJP.v17-1892

• Stochastic optimal control
• non-Markovian SDE
• second order BSDE
• G-expectation
• random G-expectation
• volatility uncertainty
• risk measure

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.

• 出版日期2012-3-19