In this note we show that the measure of intensity of downside risk aversion proposed recently by Crainich and Eeckhoudt (2007) cannot be guaranteed to exist. We do this by means of an example in which the existence of the measure depends upon the values of the parameters in the problem.

Based on Jewitt (1986) we try to find a characterization of comparative downside risk aversion and love. The desired characterizations involve the decomposition of the dual of the intersection of two convexity cones. The decomposition holds in the case of downside risk love, but not in the case...

In this paper, we analyse the investment allocation and the downside risk faced by the retiring member of a defined contribution pension scheme, where optimal investment strategies (derived from a dynamic programming approach) have been adopted. The behaviour of the optimal investment strategy...