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...

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...

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...