Coherent measures of risk

In this paper we study both market risks and nonmarket risks, without compl ete markets assumption, and discuss methods of measurement of these risks. We present and justify a set of four desirable properties for measures of r isk, and call the measures satisfying these properties "coherent." We exami ne the measures of risk provided and the related actions required by SPAN, by the SEC/NASD rules, and by quantile-based methods. We demonstrate the un iversality of scenario-based methods for providing coherent measures. We of fer suggestions concerning the SEC method. We also suggest a method to repa ir the failure of subadditivity of quantile-based methods.