Characterization of left-monotone risk aversion in the RDEU model

We extend the characterization of the left-monotone risk aversion developed by Ryan (2006) to the case of unbounded random variables. The notion of weak convergence is insufficient for such an extension. It requires the solution of a host of delicate convergence problems. To this end, some further intrinsic properties of the location independent risk order are investigated. The characterization of the right-monotone risk aversion for unbounded random variables is also mentioned. Moreover, we remove the gap in the proof of the main result in Ryan (2006).