Despite the availability of more sophisticated methods, a popular way to estimate a Pareto exponent is still to run an OLS regression: log(Rank) = <italic>a</italic> - <italic>b</italic> log(Size), and take <italic>b</italic> as an estimate of the Pareto exponent. The reason for this popularity is arguably the simplicity and robustness of this...

Despite the availability of more sophisticated methods, a popular way to estimate a Pareto exponent is still to run an OLS regression: log(Rank)=a-b log(Size), and take b as an estimate of the Pareto exponent. The reason for this popularity is arguably the simplicity and robustness of this...

A popular way to estimate a Pareto exponent is to run an OLS regression: log (Rank) = c - blog (Size), and take b as an estimate of the Pareto exponent. Unfortunately, this procedure is strongly biased in small samples. We provide a simple practical remedy for this bias, and argue that, if one...

This paper presents an analysis of diversification and portfolio value at risk for heavy-tailed dependent risks in models with multiple common shocks. We show that, in the framework of value at risk comparisons, diversification is optimal for moderately heavy-tailed dependent risks with common...

This paper focuses on the analysis of portfolio diversification for a wide class of nonlinear transformations of heavy-tailed risks. We show that diversification of a portfolio of nonlinear transformations of thick-tailed risks increases riskiness if expectations of these functions are infinite....

Recent results in value at risk analysis show that, for extremely heavy-tailed risks with unbounded distribution support, diversification may increase value at risk, and that, generally, it is difficult to construct an appropriate risk measure for such distributions. We further analyze the...

The present paper introduces new sign tests for testing for conditionally symmetric martingale-difference assumptions as well as for testing that conditional distributions of two (arbitrary) martingale-difference sequences are the same. Our analysis is based on the results that demonstrate that...