In this chapter, we discuss several stochastic dominance (SD) investment criteria, of which some are quite old and well known and some are relatively new and therefore not as widely known. As we see later in this book, we employ some of these SD investment criteria in the analysis of the Capital Asset Pricing Model (CAPM) in the Prospect Theory (PT) framework.
We discuss First-degree SD (FSD), Second-degree SD (SSD), Prospect SD (PSD), and Markowitz's SD (MSD). All these SD rules are derived in the expected utility framework. The FSD criterion is a cornerstone also in the Cumulative Prospect Theory (CPT) framework and is, in fact, imperative to all the relevant competing investment decision paradigms. Actually, to derive the FSD rule, one needs only to assume monotonicity: the more wealth one has, the better off one is. This is a reasonable assumption, and almost all economic models of decision making assume monotonicity. In terms of the utility function, this assumption implies that U′ is non-negative. Indeed, in some of the proofs of expected utility theory (EUT), the FSD requirement replaces the monotonicity axiom.