We develop explicit asymptotic expansions of the portfolio Value-at-Risk (VaR) and portfolio Expected Shortfall (ES) for a large family of multivariate elliptical distributions. The family includes distributions of exponential type such as Kotz distributions, and power type such as the...

The past decade has witnessed the rapid growing of the world palladium market. Thus, it is even more important to develop effective quantitative tools for risk management of palladium assets at this moment. In this paper, we investigate five different types of widely-used statistical...

In this paper portfolio problems with linear loss functions and multivariate elliptical distributed returns are studied. We consider two risk measures, Value-at-Risk and Conditional-Value-at-Risk, and two types of decision makers, risk neutral and risk averse. For Value-at-Risk, we show that the...

The paper develops a tail risk forecasting model that incorporates the wealth of economic and financial information available to risk managers. The approach can be viewed as a regularized extension of the two-stage GARCH-EVT model of McNeil and Frey (2000) where we permit a time-varying...