This paper analyses and develops insights to systematic risk and diversification when random, imperfectly dependent, losses are aggregated. Systematic risk and diversification are shown to vary across layers of component losses according to local dependence and volatility structures. Systematic...

This article discusses the determination of risk capital based on quot;aversionquot; functions. Aversion functions weigh different outcomes according to perceived severity or likelihood. Many risk measures are usefully viewed in terms of aversion functions including those arising from distortion...

The bootstrap is, at heart, a way to obtain an approximate sampling distribution for a statistic (and hence, if required, produce a confidence interval). Where that statistic is a suitable estimator for a population parameter of interest, the bootstrap enables inferences about that parameter. In...

We compare the short- to medium-term accuracy of five variants or extensions of the Lee-Carter method for mortality forecasting. These include the original Lee-Carter, the Lee-Miller and Booth-Maindonald-Smith variants, and the more flexible Hyndman-Ullah and De Jong-Tickle extensions. These...

We compare the short- to medium-term accuracy of five variants or extensions of the Lee-Carter method for mortality forecasting. These include the original Lee-Carter, the Lee-Miller and Booth-Maindonald-Smith variants, and the more flexible Hyndman-Ullah and De Jong-Tickle extensions. These...

SRISK methodology recently proposed in the literature is refined and extended. The refinement is to define systemic risk using a formalised stress testing framework including a stress function. Baseline risk and the stress risk are in terms of the ordinary and stressed expectation. Stressed...

A new measure of local dependence called "layer dependence" is proposed and analysed. Layer dependence measures the dependence between two random variables at different percentiles in their joint distribution. Layer dependence satisfies coherence properties similar to Spearman's correlation,...

This paper proposes a framework to analyze mean and distortion risk across layers forming a random loss. Layers are standard insurance and financial constructs representing insurance coverage, capital shortfall, derivative payouts and debt tranches. Layers are expressed using percentiles or...

A critical problem in risk analysis involving financial variables is the calculation of risk margins. When there are a number of risks, the total risk margin is often reduced to reflect "diversification benefits." How large should the diversification benefit be? And how should the benefit be...