## Jianfeng Zhang, University of Southern California

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

Joint with Frederi Viens

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-semimartingale (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 framework.