Stochastic Dominance: The Quantile
In Chapter 3 the various stochastic dominance rules were stated in terms of cumulative distributions denoted by F and G. In this chapter FSD, SSD, TSD, and nth order stochastic dominance are restated in terms of distribution quantiles. Both methods yield the same partition of the feasible set into efficient and inefficient sets. The formulas and the stochastic dominance rules based on distribution quantiles are more difficult to grasp intuitively but, as will be shown in this chapter, they are more easily extended to the case of diversification between risky asset and riskless assets. They are also more easily extended to the analysis of stochastic dominance among specific distributions of rates of return (e.g., lognormal distributions). Such extensions are quite difficult in the cumulative distribution framework.
KeywordsCumulative Distribution Risky Asset Strict Inequality Stochastic Dominance Quantile Function
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