This paper surveys the most important developments in multivariate ARCH-type modelling. It reviews the model specifications, the inference methods, and the main areas of application of these models in financial econometrics.

We propose a dynamic portfolio selection model that maximizes expected returns subject to a Value-at-Risk constraint. The model allows for time varying skewness and kurtosis of portfolio distributions estimating the model parameters by weighted maximum likelihood in a increasing window setup. We...