We propose a measure for systemic risk: CoVaR, the value at risk (VaR) of financial institutions conditional on other … institutions being in distress. We define an institution's (marginal) contribution to systemic risk as the difference between CoVaR … systemic risk contribution. We argue for macro-prudential regulation based on the degree to which such characteristics forecast …

We study the implications of the value at risk concept for the bank's optimum amount of equity capital under credit … risk. The market value of loans is risky and lognormally distributed. We show that the required equity capital depends upon …

is plugged in a fairly general distribution-invariant risk measure. We focus on the rate of the convergence of the error … means of a numerical example. Regarding the risk measure, we take into account distortion risk measures as well as … distribution-invariant coherent risk measures. …

In this paper we provide a review of copula theory with applications to finance. We illustrate the idea on the … allocation problems, Value-at-Risk and time series models. The paper is complemented with an extensive simulation study and an …

A strategically minded CFO will realize that strategic corporate risk management is about finding the right balance … between risk prevention and proactive value generation. Efficient risk and performance management requires adequate assessment … of risk and risk exposures on the one hand and performance on the other. Properly designed, a risk measure should provide …

Linear optimization problems are investigated whose parameters are uncertain. We apply coherent distortion risk …, principally, for the mean-risk portfolio selection problem. Each risk constraint induces an uncertainty set of coefficients, which …

The current subprime crisis has prompted us to look again into the nature of risk at the tail of the distribution. In … particular, we investigate the risk contribution of an asset, which has infrequent but huge losses, to a portfolio using two risk … measures, namely Value-at-Risk (VaR) and Expected Shortfall (ES). While ES is found to measure the tail risk contribution …

Value at risk (VaR) has become a standard measure of portfolio risk over the last decade. It even became one of the … increase risk. This finding is of relevance not only for investors, but even more so for bank regulation authorities. …

The paper provides an axiomatic characterization of dynamic risk measures for multi-period financial positions. For the … special case of a terminal cash flow, we require that risk depends on its conditional distribution only. We prove a … representation theorem for dynamic risk measures and investigate their relation to static risk measures. Two notions of dynamic …

downside risk and recognizes the heavytail feature of the asset return distributions. Then we show that optimal portfolio sizes …