Chapter Vi - the Malliavin Calculus and Applications

Statistical inference and Malliavin calculus∗

The derivative of the log-likelihood function, known as score function, plays a central role in parametric statistical inference. It can be used to study the asymptotic behavior of likelihood and pseudo-likelihood estimators. For instance, one can deduce the local asymptotic normality property which leads to various asymptotic properties of these estimators. In this article we apply Malliavin C...

An Introduction to Malliavin Calculus with Applications to Economics

Preface These are unpolished lecture notes from the course BF 05 " Malliavin calculus with applications to economics " , which I gave at the Norwegian School of Economics and Business Administration (NHH), Bergen, in the Spring semester 1996. The application I had in mind was mainly the use of the Clark-Ocone formula and its generalization to finance, especially portfolio analysis, option prici...

Malliavin calculus and its 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...