A lattice approach to the Beta distribution ...
Document type :
Article dans une revue scientifique
Title :
A lattice approach to the Beta distribution induced by stochastic dominance: Theory and applications
Author(s) :
Braouezec, Yann [Auteur]
IÉSEG School Of Management [Puteaux]
Lille économie management - UMR 9221 [LEM]
Cagnol, John [Auteur]
Mathématiques et Informatique pour la Complexité et les Systèmes [MICS]
Fédération de Mathématiques de CentraleSupélec
Université Paris-Saclay
IÉSEG School Of Management [Puteaux]
Lille économie management - UMR 9221 [LEM]
Cagnol, John [Auteur]
Mathématiques et Informatique pour la Complexité et les Systèmes [MICS]
Fédération de Mathématiques de CentraleSupélec
Université Paris-Saclay
Journal title :
Journal of the Operational Research Society
Pages :
1424-1442
Publisher :
Palgrave Macmillan
Publication date :
2023-06-03
ISSN :
0160-5682
HAL domain(s) :
Mathématiques [math]/Probabilités [math.PR]
Sciences de l'Homme et Société/Economies et finances
Économie et finance quantitative [q-fin]/Gestion des risques [q-fin.RM]
Sciences de l'Homme et Société/Economies et finances
Économie et finance quantitative [q-fin]/Gestion des risques [q-fin.RM]
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 >
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
Peer reviewed article :
Oui
Audience :
Internationale
Popular science :
Non
Collections :
Source :
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- http://arxiv.org/pdf/2104.01412
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- 2104.01412
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