We analyze the performance of RiskMetrics, a widely used methodology for measuring market risk. Based on the assumption of normally distributed returns, the RiskMetrics model completely ignores the presence of fat tails in the distribution function, which is an important feature of financial...

Correlations of returns on various assets play a central role in financial theory and also in many practical applications. From a theoretical point of view, the main interest lies in the proper description of the structure and dynamics of correlations, whereas for the practitioner the emphasis...

We address the problem of portfolio optimization under the simplest coherent risk measure, i.e. the expected shortfall. As is well known, one can map this problem into a linear programming setting. For some values of the external parameters, when the available time series is too short, portfolio...

A statistical analysis of the Budapest Stock Index (BUX) is presented. The high time resolution (5 s sampling) makes it possible to extract information on market functioning which does not emerge from daily data. The main results are as follows: from a statistical point of view the large drop in...

Correlations and other collective phenomena are considered in a schematic model of pairwise interacting, competing and collaborating agents facing a binary choice and situated at the nodes of the complete graph and a 2-dimensional regular lattice, respectively. The agents may be subjected to an...

We consider the problem of portfolio optimization in the presence of market impact, and derive optimal liquidation strategies. We discuss in detail the problem of finding the optimal portfolio under expected shortfall (ES) in the case of linear market impact. We show that, once market impact is...

It is shown that the axioms for coherent risk measures imply that whenever there is a pair of portfolios such that one of them dominates the other in a given sample (which happens with finite probability even for large samples), then there is no optimal portfolio under any coherent measure on...