By assuming that the underlying distribution belongs to the domain of attraction of an extreme value distribution, one can extrapolate the data to a far tail region so that a rare event can be predicted. However, when the distribution is in the domain of attraction of a Gumbel distribution, the...

In financial practice, it is important to understand the dependence structure between the returns of individual assets and the market index. This particularly true under extreme situations. Theoretically, this amounts to regress the dependence relationship against a set of pre-specified...

In general, risk of an extreme outcome in financial markets can be expressed as a function of the tail copula of a high-dimensional vector after standardizing marginals. Hence it is of importance to model and estimate tail copulas. Even for moderate dimension, nonparametrically estimating a tail...

For an AR(1) process with ARCH(1) errors, we propose empirical likelihood tests for testing whether the sequence is strictly stationary but has infinte variance, or the sequence is an ARCH(1) sequence or the sequence is an iid sequence. Moreover, an empirical likelihood based confidence interval...

Recently there has been an increasing interest in applying elliptical distributions to risk management. Under weak conditions, Hult and Lindskog (2002) showed that a random vector with an elliptical distribution is in the domain of attraction of a multivariate extreme value distribution. In this...