论文标题
在波动不确定性下的广义Feynman-kac公式
Generalized Feynman-Kac Formula under volatility uncertainty
论文作者
论文摘要
在本文中，我们通过在PDE中有线性术语在折扣处的线性术语的情况下对Feynmac-kac公式进行了概括。我们在不同的假设下对Hu，Ji，Peng和Song给出的推导（比较定理，Feynman-Kac比较，Feynman-kac公式和Girsanov的比较，对BSDE的g-brownian运动，随机过程及其应用及其应用，124（2））的BSDES，在某些函数上不需要的是，该设置不需要某些函数的consection continction。特别是，我们表明，折扣收益的$ G $ - 条件期望是非线性PDE的粘度解决方案。在应用程序中，这允许以计算有效的方式计算这种透明的期望。
In this paper we provide a generalization of a Feynmac-Kac formula under volatility uncertainty in presence of a linear term in the PDE due to discounting. We state our result under different hypothesis with respect to the derivation given by Hu, Ji, Peng and Song (Comparison theorem, Feynman-Kac formula and Girsanov transformation for BSDEs driven by G-Brownian motion, Stochastic Processes and their Application, 124 (2)), where the Lipschitz continuity of some functionals is assumed which is not necessarily satisfied in our setting. In particular, we show that the $G$-conditional expectation of a discounted payoff is a viscosity solution of a nonlinear PDE. In applications, this permits to calculate such a sublinear expectation in a computationally efficient way.
