The Basel Committee on Banking Supervision (BIS) has recently sanctioned Expected Shortfall (ES) as the market risk … measure to be used for banking regulatory purposes, replacing the well-known Value-at-Risk (VaR). This change is motivated by … the appealing theoretical properties of ES as a measure of risk and the poor ones of VaR. In particular, VaR fails to …

Risk diversification is the basis of insurance and investment. It is thus crucial to study the effects that could limit … it. One of them is the existence of systemic risk that affects all the policies at the same time. We introduce here a … probabilistic approach to examine the consequences of its presence on the risk loading of the premium of a portfolio of insurance …

the estimation and backtesting of ES, it can be considered a good risk measure. In particular, there is no sufficient …Expected Shortfall (ES) has been widely accepted as a risk measure that is conceptually superior to Value-at-Risk (VaR … desirable properties of risk measures like coherence, comonotonic additivity, robustness and elicitability. We check VaR, ES and …

Risk diversification is the basis of insurance and investment. It is thus crucial to study the effects that could limit … it. One of them is the existence of systemic risk that affects all of the policies at the same time. We introduce here a … probabilistic approach to examine the consequences of its presence on the risk loading of the premium of a portfolio of insurance …

Risk diversification is the basis of insurance and investment. It is thus crucial to study the effects that could limit … it. One of them is the existence of systemic risk that affects all the policies at the same time. We introduce here a … probabilistic approach to examine the consequences of its presence on the risk loading of the premium of a portfolio of insurance …

Since Value-at-Risk (VaR) disregards tail losses beyond the VaR boundary, the expected shortfall (ES), which measures … the average loss when a VaR is exceeded, and the tail-risk-of-VaR (TR), which sums the sizes of tail losses, are used to … small sample asymptotic technique to backtest ES and TR. Because the two risk measures are complementary to each other and …

undesirable, the ‘risk’. While these properties are commonly identified with mean and variance of returns, respectively, we test … empirical performance of portfolios selected by optimising risk–reward ratios constructed from these alternative functions. We … the data. The main theme throughout our results is that minimising risk, as opposed to maximising reward, often leads to …