This paper is intended as a guide to building insurance risk (loss) models. A typical model for insurance risk, the so-called collective risk model, treats the aggregate loss as having a compound distribution with two main components: one characterizing the arrival of claims and another...

A large number of exact inferential procedures in statistics and econometrics involve the sampling distribution of ratios of random variables. If the denominator variable is positive, then tail probabilities of the ratio can be expressed as those of a suitably defined difference of random...

The upper tail of the firm size distribution is often assumed to follows a Power Law behavior. Recently, using different estimators and on different data sets, several papers conclude that this distribution follows the Zipf Law, that is that the fraction of firms whose size is above a given...

The upper tail of the firm size distribution is often assumed to follow a Power Law. Several recent papers, using different estimators and different data sets, conclude that the Zipf Law, in particular, provides a good fit, implying that the fraction of firms with size above a given value is...

Zipf's law is a well-known empirical regularity of firm size distribution. To date, it remains a puzzle as to what is the identity of the firms that causes this regularity. We document the multi-plant firm origin of Zipf's law - plants of multi-plant fi rms (exponent close to one) are more...

Granted, it is generally understood that using past performance as the basis for either choosing an investment alternative or for selecting a particular configuration of a given alternative poses the risk of mistaking chance outperformance for something that might endure. But if many of the...

Power law behavior has been recognized to be a pervasive feature of many phenomena in natural and social sciences. While immense research efforts have been devoted to the analysis of behavioural mechanisms responsible for the ubiquity of power-law scaling, the strong theoretical foundation of...

I introduce a novel, hierarchical model of tail dependent asset returns which can be particularly useful for measuring portfolio credit risk within the structural framework. To allow for a stronger dependence within sub-portfolios than between them, I utilise the concept of nested Archimedean...

This paper introduces a multivariate pure-jump Lévy process which allows for skewness and excess kurtosis of single asset returns and for asymptotic tail dependence in the multivariate setting. It is termed Variance Compound Gamma (VCG). The novelty of my approach is that, by applying a...