The aim of this paper is to analyze the sensitivity of Value at Risk (VaR) with respect to portfolio allocation. We derive analytical expressions for the first and second derivatives of the Value at Risk, and explain how they can be used to simplify statistical inference and to perform a local...

This paper derives conditions under which the generalized method of moments (GMM) estimator is as efficient as the maximum likelihood estimator (MLE). The data are supposed to be drawn from a parametric family and to be stationary Markov. We study the efficiency of GMM in a general framework...

In many circumstances, the likelihood function does not have a simple tractable expression. The main examples discussed in the paper are the convolution and the mixture of distributions. Finite mixture models are commonly used to model data from a population composed of a finite number of...