Probabilistic Solutions for a Class of Path-Dependent Hamilton-Jacobi-Bellman Equations |
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Authors: | Yuhong Xu |
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Affiliation: | 1. Institute of Mathematics , Shandong University , Jinan , P. R. China yuhong.xu@hotmail.com |
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Abstract: | This article shows that the solution of a backward stochastic differential equation under G-expectation provides a probabilistic interpretation for the viscosity solution of a type of path-dependent Hamilton-Jacobi-Bellman equation. Particularly, a G-martingale can be considered as a nonlinear path-dependent partial differential equation (PDE). We also show that certain class of path-dependent PDEs can be transformed into classical multiple state-dependent PDEs. As an application, the path-dependent uncertain volatility model can be described directly by path-dependent Black-Scholes-Barrenblett equations. |
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Keywords: | Backward stochastic differential equation Feynman-Kac formula Functional Itô calculus G-expectation G-martingale Hamilton-Jacobi-Bellman equation Path-dependent partial differential equation Uncertainty volatility model |
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