Theoretical Economics 10 (2015), 1–9 1555-7561/20150001 The Foster–Hartmeasure of riskiness for general gambles

Foster and Hart propose a measure of riskiness for discrete random variables. Their defining equation has no solution for many common continuous distribu-tions. We show how to extend consistently the definition of riskiness to continu-ous random variables. For many continuous random variables, the risk measure is equal to the worst-case risk measure, i.e., the maximal possible loss incurred by that gamble. For many discrete gambles with a large number of values, the Foster– Hart riskiness is close to the maximal loss. We give a simple characterization of gambles whose riskiness is or is close to the maximal loss