B0766
Title: Asymptotic expansion formulas for diffusion processes based on the perturbation method
Authors: Emanuele Guidotti - University of Neuchatel (Switzerland) [presenting]
Nakahiro Yoshida - University of Tokyo (Japan)
Abstract: Diffusion processes are a class of models that plays a prominent role in describing the time-continuous evolution of phenomena in the natural and social sciences. However, only in very few cases, the stochastic differential equation driving the process can be analytically solved. Based on the perturbation method, we present asymptotic expansion formulas to generate accurate approximations to the solution of arbitrary diffusions. In particular, we expand the characteristic function of the process. Then, the approximated expectation and moments are computed by differentiation, and the approximated transition density is written in terms of Hermite polynomials by applying Fourier transform. The computational efficiency, accuracy, and flexibility of the method are assessed via experiments conducted against closed-form solutions and Monte Carlo simulations in tasks involving density approximation, expectations, moments, filtering, and functionals of generic diffusion processes.
