## A Martingale Approach for Fractional Brownian Motions and Related Path Dependent PDEs

2017-07-17

A Martingale Approach for Fractional Brownian Motions and Related Path            Dependent PDEs

(University of Southern California)

Abstract

Empirical studies show that the volatilities could be rough, which typically go beyond the semimartinagle framework and the fractional Brownian Motion (fBM) becomes a natural tool. Compared with BM, fBM has two features: (i) non-Markoivan; (ii) non-semimar- tingale (when the Hurst parameter $H< {1\over 2}$). We shall show that the recent development of path dependent PDEs provides a convenient tool to extend the standard literature of pricing/hedging derivatives to an fBM fram- work. The talk is based on a joint work with Frederi Viens.