In this paper a series representation of the joint density and the joint distribution of a quadratic form and a linear form in normal variables is developed. The expansion makes use of Laguerre polynomials. As an example the calculation of the joint distribution of the mean and the sample...

Abstract In this paper we consider a general control scheme. The control statistic Z t is equal to an arbitrary weighted sum of the past observations X t ,..., X 1 . This approach covers most of the applied control schemes like for instance moving average, EWMA and ARMA(1,1) charts. The process...

Abstract In this paper we consider the portfolio weights obtained by maximizing the expected quadratic utility function. The unknown parameters of the return process, the mean vector and the covariance matrix, are estimated by their sample counterparts. Assuming independent and multivariate...

Abstract In this paper, we consider the sample estimators for the expected return, the variance, the value-at-risk (VaR), and the conditional VaR (CVaR) of the minimum VaR and the minimum CVaR portfolio. Their exact distributions are derived. These expressions are used for studying the...

Abstract In this paper we analyse the properties of hierarchical Archimedean copulas. This class is a generalisation of the Archimedean copulas and allows for general non-exchangeable dependency structures. We show that the structure of the copula can be uniquely recovered from all bivariate...

The exact density of linear combinations of global minimum variance portfolio weights is derived. The exact finite-sample statistical procedure to test general linear restrictions of portfolio weights is obtained. The results are generalized to elliptically contoured distributions, which extends...

In this paper the sequential procedures for monitoring efficiency of the global minimum variance portfolio are proposed. The proposed control schemes can be applied to rather large class of portfolio asset returns distributions, namely, elliptically contoured distributions. Our approach has...

The purpose of this paper is to jointly monitor the mean vector and the covariance matrix of multivariate nonlinear times series. The underlying target process is assumed to be a constant conditional correlation process Bollerslev (Rev Econ Stat 72:498–505, <CitationRef CitationID="CR5">1990</CitationRef>) or a dynamic conditional...</citationref>