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...

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...

Measuring the risk of a financial portfolio involves two steps: estimating the loss distribution of the portfolio from available observations and computing a ``risk measure" which summarizes the risk of the portfolio. We define the notion of ``risk measurement procedure", which includes both of...

This paper investigates Value at Risk and Expected Shortfall for CAC 40, S&P 500, Wheat and Crude Oil indexes during the 2008 financial crisis. We show an underestimation of the risk of loss for the unconditional VaR models as compared with the conditional models. This underestimation is...

Basel II and Solvency 2 both use the Value-at Risk (VaR) as the risk measure to compute the Capital Requirements. In practice, to calibrate the VaR, a normal approximation is often chosen for the unknown distribution of the yearly log returns of financial assets. This is usually justified by the...

Systematic and multifactor risk models are revisited via methods which were already successfully developed in signal processing and in automatic control. The results, which bypass the usual criticisms on those risk modeling, are illustrated by several successful computer experiments.

European market deregulation is destabilizing the economic environment of French farmers leading to an increase in market risks. In the dairy sector, the 2003 CAP reform has lead to major changes (removal of export subsidies and increase in the European milk quota). The dairy supply chain is now...

Regulation and Risk management in banks depend on underlying risk measures. In general this is the only purpose that is seen for risk measures. In this paper, we suggest that the reporting of risk measures can be used to determine the loss distribution function for a financial entity. We...

Starting from the requirement that risk measures of financial portfolios should be based on their losses, not their gains, we define the notion of loss-based risk measure and study the properties of this class of risk measures. We characterize loss-based risk measures by a representation theorem...

The banking systems that deal with risk management depend on underlying risk measures. Following the recommendation of the Basel II accord, most banks have developed internal models to determine their capital requirement. The Value at Risk measure plays an important role in computing this...