MALLIAVIN CALCULUS AND ANTICIPATIVE ITÔ FORMULAE FOR LÉVY PROCESSES

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.

Pricing formulae for derivatives in insurance using the Malliavin calculus *

In this paper we provide a valuation formula for different classes of actuarial and financial contracts which depend on a general loss process, by using the Malliavin calculus. In analogy with the celebrated Black-Scholes formula, we aim at expressing the expected cash flow in terms of a building block. The former is related to the loss process which is a cumulated sum indexed by a doubly stoch...

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...

Sensitivity analysis using Itô-Malliavin calculus and application to stochastic optimal control

Malliavin Greeks without Malliavin Calculus

We derive and analyze Monte Carlo estimators of price sensitivities (“Greeks”) for contingent claims priced in a diffusion model. There have traditionally been two categories of methods for estimating sensitivities: methods that differentiate paths and methods that differentiate densities. A more recent line of work derives estimators through Malliavin calculus. The purpose of this article is t...