Risk management technology applied to high dimensional portfolios needs simple and fast methods for calculation of Value-at-Risk (VaR). The multivariate normal framework provides a simple off-the-shelf methodology but lacks the heavy tailed distributional properties that are observed in data. A...

Over recent years, study on risk management has been prompted by the Basel committee for regular banking supervisory. There are however limitations of some widely-used risk management methods that either calculate risk measures under the Gaussian distributional assumption or involve numerical...

We propose a method of adaptive estimation of a regression function and which is near optimal in the classical sense of the mean integrated error. At the same time, the estimator is shown to be very sensitive to discontinuities or change-points of the underlying function f or its derivatives....

The paper is concerned with the problem of variance estimation for a high-dimensional regression model. The results show that the accuracy n -1/2 of variance estimation can be achieved only under some restrictions on smoothness properties of the regression function and on the dimensionality of...

The paper aims at reconsidering the famous Le Cam LAN theory. The main features of the approach which make it different from the classical one are: (1) the study is non-asymptotic, that is, the sample size is fixed and does not tend to infinity; (2) the parametric assumption is possibly...