A popular risk measure, conditional value-at-risk (CVaR), is called expected shortfall (ES) in financial applications … for the analysis is established with the quadrangle theory of risk functions. We derived relationships between elements of … CVaR quadrangle and mixed-quantile quadrangle for discrete distributions with equally probable atoms. The deviation in the …

risk aggregation. The so-called "square-root formula" uses correlation parameters between, for example, market risk, non …-life insurance risk and default risk to determine the company's aggregate capital requirement. To support decision-making, companies … will allocate the required capital back to business segments and risk drivers. We demonstrate that capital allocations …

The Pareto model is very popular in risk management, since simple analytical formulas can be derived for financial … downside risk measures (value-at-risk, expected shortfall) or reinsurance premiums and related quantities (large claim index …