In this article, we give a brief informal introduction to Malliavin Calculus for newcomers. We apply these ideas to the simulation of Greeks in Finance. First to European-type options where formulas can be computed explicitly and therefore can serve as testing ground. Later we study the case of Asian options where close formulas are not available, and we also open the view for including more ex...

A well-known problem in Malliavin calculus concerns the relation between the determinant of the Malliavin matrix of a random vector and the determinant of its covariance matrix. We give an explicit relation between these two determinants for couples of random vectors of multiple integrals. In particular, if the multiple integrals are of the same order and this order is at most 4, we prove that ...

This paper deals with the study of the Malliavin calculus of Euclidean motions on Wiener space, (i.e. transformations induced by general measure preserving transformations, called 'rotations', and H-valued shifts) and the associated flows on abstract Wiener spaces.

In the framework of risk management, for the study of the sensitivity of pricing and hedging in stochastic financial models to changes of parameters and to perturbations of the stock prices, we propose an error calculus which is an extension of the Malliavin calculus based on Dirichlet forms. Although useful also in physics, this error calculus is well adapted to stochastic analysis and seems t...

We show that integration by parts formulas based on Malliavin-Skorohod calculus techniques for additive processes help us to compute quantities like ${\E}(L_T h(L_T))$ different suitable functions $h$ and models the cumulative loss process $L_T$. These are important in Insurance Finance. For example they appear computing expected shortfall risk measures or stop-loss contracts. The given present...

We obtain a maximum principle for stochastic control problem of general controlled stochastic differential systems driven by fractional Brownian motions (of Hurst parameter H > 1/2). This maximum principle specifies a system of equations that the optimal control must satisfy (necessary condition for the optimal control). This system of equations consists of a backward stochastic differential eq...

We provide a detailed analysis of the Gelfand integral on Fréchet spaces, showing among other things Vitali theorem, dominated convergence and Fubini result. Furthermore, commutes with linear operators. The Skorohod is conveniently expressed in terms Hida distribution space, which forms our prime motivation example. extend several results integrals to general class pathwise integrals. For examp...