Indexing Gamble Desirability by Extending Proportional Stochastic Dominance

We axiomatically characterise two new orders of desirability of gambles (risky assets) that are natural extensions of the proportional stochastic dominance order to complete orders. These orders are represented by indices with parallels to the recently introduced Aumann-Serrano index of riskiness and the Foster-Hart measure of riskiness. The new indices are shown to be related to the concept of coherent measures of risk and to the Sharpe ratio.