In the present paper, we propose an exact test on the structure of the covariance matrix. In its development the properties of the Wishart distribution are used. Unlike the classical likelihood-ratio type tests and the tests based on the empirical distance, whose statistics depend on the total...

In the paper, a finite sample test is suggested for detecting changes in the composition of the global minimum variance portfolio. The exact density of the test statistic is calculated. It appears that under the null hypothesis of no change, it is independent of the parameters of the asset...

The efficient frontier is a parabola in the mean-variance space which is uniquely determined by three characteristics. Assuming that the portfolio asset returns are independent and multivariate normally distributed, we derive tests and confidence sets for all possible arrangements of these...

A methodology which allows applying the standard monitoring techniques for the mean behaviour of Gaussian processes in the detection of shifts in the covariance matrix is developed. Moreover, the proposed methodology allows the use of an estimator of the covariance matrix based on a single...

In this paper, we derive the Stein-Haff identity for the multivariate elliptically contoured matrix distributions. Our results generalize the results of the papers by [Stein, C., 1977. Personal communication. Unpublished notes on estimating the covariance matrix] and [Haff, L.R., 1979a. An...

In this paper, a new measure of dependence is proposed. Our approach is based on transforming univariate data to the space where the marginal distributions are normally distributed and then, using the inverse transformation to obtain the distribution function in the original space. The...

In this paper we discuss the distributions and independency properties of several generalizations of the Wishart distribution. First, an analog to Muirhead [R.J. Muirhead, Aspects of Multivariate Statistical Theory, Wiley, New York, 1982] Theorem 3.2.10 for the partitioned matrix is...

In this paper we derive the exact solution of the multi-period portfolio choice problem for an exponential utility function under return predictability. It is assumed that the asset returns depend on predictable variables and that the joint random process of the asset returns and the predictable...