What is Coherent Risk Measures

A risk measure is coherent, if it possesses the following four desirable properties, with economic interpretations in brackets according to McNeil et al. (2005) , p. 240: (1) translation invariance (the consequence of an increase/ a decrease with a constant of a position, to which corresponds a loss quantity L, leads to a modification of the risk requirements with exactly the same amount); (2) positive homogeneity (no diversifying or netting of losses in a portfolio); (3) monotonicity (more risk capital must be allocated to positions, associated with higher losses); (4) subadditivity (diversification decreases risk).

Estimating Risk with Copulas

Iva Mihaylova (University of St. Gallen, Switzerland)