A lattice approach to the Beta distribution induced by stochastic dominance: Theory and applications

We provide a comprehensive analysis of the two-parameter Beta distributions seen from perspective second-order stochastic dominance. By changing its parameters through bijective mapping, we work with bounded subset D instead an unbounded plane. show that mean-preserving spread is equivalent to increase variance, which means higher moments are irrelevant compare riskiness distributions. then derive lattice structure induced by dominance, feasible thanks topological closure D. Finally, consider standard (expected-utility based) portfolio optimization problem in inputs distribution. explicitly characterize for optimal solution consists investing 100% wealth risky asset and exhaustive numerical this (color-coded) graphs.