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

Yann Braouezec (1, 2) , John Cagnol (3, 4)

1 LEM - Lille économie management - UMR 9221
2 IÉSEG School Of Management [Puteaux]
3 Fédération de Mathématiques de CentraleSupélec
4 MICS - Mathématiques et Informatique pour la Complexité et les Systèmes

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

Mots clés: Beta distribution; secondorder stochastic dominance; topological closure; lattice structure and Hasse diagram; portfolio choices and exhaustive numerical analysis; Risk analysis; Beta distribution

Domaines: Probabilités [math.PR]; Economies et finances; Gestion des risques [q-fin.RM]

Yann Braouezec, John Cagnol. A lattice approach to the Beta distribution induced by stochastic dominance: Theory and applications. Journal of the Operational Research Society, 2023, 74 (6), pp.1424-1442. ⟨10.1080/01605682.2022.2096500⟩. ⟨hal-04373020⟩