Local Malliavin calculus for Lévy processes and applications

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.

Malliavin calculus and its applications

Chapter Vi - the Malliavin Calculus and Applications

Malliavin Calculus and Skorohod Integration for Quantum Stochastic Processes

A derivation operator and a divergence operator are defined on the algebra of bounded operators on the symmetric Fock space over the complexification of a real Hilbert space h and it is shown that they satisfy similar properties as the derivation and divergence operator on the Wiener space over h. The derivation operator is then used to give sufficient conditions for the existence of smooth Wig...

Concentration inequalities via Malliavin calculus with applications

We use the Malliavin calculus to prove a new abstract concentration inequality result for zero mean, Malliavin differentiable random variables which admit densities. We demonstrate the applicability of the result by deriving two new concrete concentration inequalities, one relating to an integral functional of a fractional Brownian motion process, and the other relating to the centered maximum ...