2010/06/01 by IMRE KONDOR, Imre Kondor, ISTVÁN VARGA-HASZONITS +1 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #Risk and Portfolio Optimization #Stochastic processes and financial applications #Insurance, Mortality, Demography, Risk Management
paper · doi:10.1142/s0219525910002591
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 that sample, and the risk measure diverges to minus infinity. This instability was first discovered in the special example of Expected Shortfall which is used here both as an illustration and as a springboard for generalization.