Almost Stochastic Dominance (ASD)

13.6 Summary

FSD, SSD and M-V investment criteria may reveal no dominance between two options when experimentally or empirically there is an ultimate preference for one of these options — hence paradoxes are created. The paradoxes are induced by the fact that the investment criteria correspond to all preferences (in a given class) including preferences which do not conform with any investor’s behavior. We suggest in this chapter decision rules called Almost SD (ASD), which correspond to all preferences, excluding those preferences which mathematically are accepted but do not conform with any investor’s behavior. These specific preference: which are excluded can be considered as pathological, unreasonable or simply irrelevant preferences. Thus, Almost FSD replaces FSD, Almost SSD replace SSD, and Almost M-V replaces M-V rule. The investment criteria AFSD and ASSD allow the establishment of preference despite the fact that there is no FSD or SSD, hence the paradoxes are avoided.

We have the following relationship:

$$ \begin{array}{*{20}c} {FSD \Rightarrow } \\ \Downarrow \\ {SSD \Rightarrow } \\ \end{array} \begin{array}{*{20}c} {AFSD(or FSD*)} \\ \Downarrow \\ {ASSD(or FSD*)} \\ \end{array} $$