Paradoxes with Optimal Investment Rules

Assuming risk aversion, the Second degree Stochastic Dominance (SSD) criterion is employed for prospect ranking. However, in some cases the optimal SSD rule cannot distinguish between two alternative prospects when it is obvious that one prospect is preferred by practically all risk averters-a paradoxical result. The optimal Almost SSD (ASSD) rule which aims to avoid such paradoxical results also fails to do so. We suggest a new rule, the General ASSD rule (GASSD) to replace the ASSD rule, which in turn, solves the SSD as well the ASSD existing and potential paradoxes. The GASSD rule, unlike the SSD and ASSD rules, takes into account the magnitude of the mean return difference of the two prospects under consideration. The ASSD and the GASSD rules coincide only when these two means are equal