Measuring risk is a crucial aspect of the portfolio optimization problem in finance, and of capital adequacy assessment in risk management. Expected Shortfall (ES) has been proposed as a coherent risk measure, by contrast with Value-at-Risk (VaR) and the standard-deviation-type of measures....

Expected Shortfall (ES) has been widely accepted as a risk measure that is conceptually superior to Value-at-Risk (VaR). At the same time, however, it has been criticized for issues relating to backtesting. In particular, ES has been found not to be elicitable which means that backtesting for ES...

The core of risk aggregation in the Solvency II Standard Formula is the so-called square root formula. We argue that it should be seen as a means for the aggregation of different risks to an overall risk rather than being associated with variance-covariance based risk analysis. Considering the...