Multifractal random walks with fractional Brownian motion via Malliavin calculus

Fauth, Alexis; Tudor, Ciprian

Document type :

Compte-rendu et recension critique d'ouvrage

Title :

Multifractal random walks with fractional Brownian motion via Malliavin calculus

Author(s) :

Fauth, Alexis [Auteur]
Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne) [SAMM]
Tudor, Ciprian [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

IEEE Transactions on Information Theory

Pages :

Publisher :

Institute of Electrical and Electronics Engineers

Publication date :

2014

ISSN :

0018-9448

HAL domain(s) :

Mathématiques [math]/Probabilités [math.PR]

English abstract : [en]

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 ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

Collections :