The PDEs and Numerical Scheme for Derivatives under Uncertainty Volatility

摘要

We use the stochastic differential equations (SDE) driven by G-Brownian motion to describe the basic assets (such as stocks) price processes with volatility uncertainty. We give the estimation method of the SDE’s parameters. Then, by the nonlinear Feynman-Kac formula, we get the partial differential equations satisfied by the derivatives. At last, we give a numerical scheme to solve the nonlinear partial differential equations.