Multifractal random walks with fractional Brownian motion via Malliavin   calculus
  We introduce a Multifractal Random Walk (MRW) defined as a stochastic integral of an infinitely divisible noise with respect to a dependent fractional Brownian motion. Using the techniques of the Malliavin calculus, we study the existence of this object and its properties. We then propose a continuous time model in finance that captures the main properties observed in the empirical data, including the leverage effect. We illustrate our result by numerical simulations. 
Alexis Fauth (SAMM), Ciprian Tudor (LPP)
math.PR