This paper considers the portfolio problem for high dimensional data when the dimension and size are both large.We analyze the traditional Markowitz mean-variance (MV) portfolio by large dimension matrix theory, and find the spectral distribution of the sample covariance is the main factor to...

The paper examines the performance of four multivariate volatility models, namely CCC, VARMA-GARCH, DCC and BEKK, for the crude oil spot and futures returns of two major benchmark international crude oil markets, Brent and WTI, to calculate optimal portfolio weights and optimal hedge ratios, and...