Value-at-Risk (VaR) is a simple, but useful measure in risk management. When some volatility model is employed, conditional VaR is of importance. As autoregressive conditional heteroscedastic (ARCH) and generalized ARCH (GARCH) models are widely used in modelling volatilities, in this article,...

Fan and Yao (1998) proposed an efficient method to estimate the conditional variance of heteroskedastic regression models. Chen, Cheng, and Peng (2009) applied variance reduction techniques to the estimator of Fan and Yao (1998) and proposed a new estimator for conditional variance to account...

In quantitative risk management, it is important and challenging to find sharp bounds for the distribution of the sum of dependent risks with given marginal distributions, but an unspecified dependence structure. These bounds are directly related to the problem of obtaining the worst...

For the estimation of the mean of a heavy tailed distribution with tail index -[alpha]<-1, the asymptotic distribution of the sample mean is not normal as [alpha]<2. In this paper we propose an alternative estimator whose limiting distribution, under a second order condition, is normal for any [alpha]>1.

For samples of random variables with a regularly varying tail estimating the tail index has received much attention recently. For the proof of asymptotic normality of the tail index estimator second-order regular variation is needed. In this paper we first supplement earlier results on...