A Parametric Approach to Stochastic Dominance: The Lognormal Case

Mixing the risky asset with the riskless asset. Levy and Kroll have developed stochastic dominance rules with borrowing and lending (SDR). These rules can be easily applied to discrete distributions (e.g., ex-post data). However, an infinite number of comparisons is involved when the distributions under consideration are continuous. This study suggests a method for applying the SDR criteria to continuous distributions where, in general, a small number of comparisons is involved. For some distributions (e.g., lognormal) the SDR relationship is stated in terms of the distributions' parameters, and hence only one comparison is required. These SDR relationships enable us to establish the lognormal efficient frontier.