Malliavin calculus and its applications

Chapter Vi - the Malliavin Calculus and Applications

Perturbation Analysis and Malliavin Calculus

Using the Malliavin calculus, we give a uniied treatment of the so-called perturbation analysis of dynamic systems. Several applications are also given.

Malliavin calculus and asymptotic expansion for martingales

We present an asymptotic expansion of the distribution of a random variable which admits a stochastic expansion around a continuous martingale. The emphasis is put on the use of the Malliavin calculus; the uniform nondegeneracy of the Malliavin covariance under certain truncation plays an essential role as the Crame r condition did in the case of independent observations. Applications to stati...

Stochastic Differential Games in Insider Markets via Malliavin Calculus

In this paper we use techniques of Malliavin calculus and forward integration to present a general stochastic maximum principle for anticipating stochastic differential equations driven by a Lévy type of noise. We apply our result to study a general stochastic differential game problem of an insider. MSC2010 : 60G51, 60H40, 60H10, 60HXX, 93E20

On Lévy processes, Malliavin calculus and market models with jumps

Recent work by Nualart and Schoutens (2000), where a kind of chaotic property for Lévy processes has been proved, has enabled us to develop a Malliavin calculus for Lévy processes. For simple Lévy processes some useful formulas for computing Malliavin derivatives are deduced. Applications for option hedging in a jump–diffusion model are given.