Investors who optimize their portfolios under any of the coherent risk measures are naturally led to regularized portfolio optimization when they take into account the impact their trades make on the market. We show here that the impact function determines which regularizer is used. We also show...

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 two-dimensional regular lattice, respectively. The agents may be subjected to...

The contour map of estimation error of Expected Shortfall (ES) is constructed. It allows one to quantitatively determine the sample size (the length of the time series) required by the optimization under ES of large institutional portfolios for a given size of the portfolio, at a given...

Using public data (Forbes Global 2000) we show that the asset sizes for the largest global firms follow a Pareto distribution in an intermediate range, that is "interrupted" by a sharp cut-off in its upper tail, where it is totally dominated by financial firms. This flattening of the...

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...

Using public data (Forbes Global 2000) we show that the distribution of asset sizes for the largest global firms follows a Pareto distribution in an intermediate range that is “interrupted” by a sharp cutoff in its upper tail, which is totally dominated by financial firms. This contrasts...

The problem of estimation error in portfolio optimization is discussed, in the limit where the portfolio size N and the sample size T go to infinity such that their ratio is fixed. The estimation error strongly depends on the ratio N/T and diverges for a critical value of this parameter. This...