Title :

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

Author(s) :

Braouezec, Yann [Auteur]
Lille économie management - UMR 9221 [LEM]
IÉSEG School Of Management [Puteaux]
Cagnol, John [Auteur]
Université Paris-Saclay
Fédération de Mathématiques de l'Ecole Centrale Paris [FR3487]
Mathématiques et Informatique pour la Complexité et les Systèmes [MICS]

HAL domain(s) :

Mathématiques [math]/Probabilités [math.PR]
Économie et finance quantitative [q-fin]/Gestion des risques [q-fin.RM]
Sciences de l'Homme et Société/Economies et finances

English abstract : [en]

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 ...
Show more >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.Show less >

Language :

Anglais

Collections :

• Lille Économie Management (LEM) - UMR 9221

Source :

Harvested from HAL