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Robust portfolio choice with learning in the framework of regret / Andrew E. B. Lim in Management science, Vol 58 N°9 (Septembre 2012) 

Public ISBD [article]  in Management science > Vol 58 N°9 (Septembre 2012) . - pp.1732-1746 Titre : Robust portfolio choice with learning in the framework of regret : Single - period case Type de document : texte imprimé Auteurs : Andrew E. B. Lim, Auteur ; J. George Shanthikumar, Auteur ; Gah-Yi Vahn, Auteur Année de publication : 2012 Article en page(s) : pp.1732-1746 Note générale : Management Langues : Anglais (eng) Mots-clés : Parameter  uncertainty  Ambiguity  Model  uncertainty  Learning  Regret  Relative  regret  Competitive  analysis  Portfolio  selection  Bayesian  methods  Objective-based  loss  functions  Convex  duality Résumé : In this paper, we formulate a single-period portfolio choice problem with parameter uncertainty in the framework of relative regret. Relative regret evaluates a portfolio by comparing its return to a family of benchmarks, where the benchmarks are the wealths of fictitious investors who invest optimally given knowledge of the model parameters, and is a natural objective when there is concern about parameter uncertainty or model ambiguity. The optimal relative regret portfolio is the one that performs well in relation to all the benchmarks over the family of possible parameter values. We analyze this problem using convex duality and show that it is equivalent to a Bayesian problem, where the Lagrange multipliers play the role of the prior distribution, and the learning model involves Bayesian updating of these Lagrange multipliers/prior. This Bayesian problem is unusual in that the prior distribution is endogenously chosen by solving the dual optimization problem for the Lagrange multipliers, and the objective function involves the family of benchmarks from the relative regret problem. These results show that regret is a natural means by which robust decision making and learning can be combined. ISSN : 0025-1909 En ligne : http://mansci.highwire.org/content/early/2012/07/18/mnsc.1120.1518.short?rss=1&s [...] [article] Robust portfolio choice with learning in the framework of regret : Single - period case [texte imprimé] / Andrew E. B. Lim, Auteur ; J. George Shanthikumar, Auteur ; Gah-Yi Vahn, Auteur . - 2012 . - pp.1732-1746. Management Langues : Anglais (eng) in Management science > Vol 58 N°9 (Septembre 2012) . - pp.1732-1746 Mots-clés : Parameter  uncertainty  Ambiguity  Model  uncertainty  Learning  Regret  Relative  regret  Competitive  analysis  Portfolio  selection  Bayesian  methods  Objective-based  loss  functions  Convex  duality Résumé : In this paper, we formulate a single-period portfolio choice problem with parameter uncertainty in the framework of relative regret. Relative regret evaluates a portfolio by comparing its return to a family of benchmarks, where the benchmarks are the wealths of fictitious investors who invest optimally given knowledge of the model parameters, and is a natural objective when there is concern about parameter uncertainty or model ambiguity. The optimal relative regret portfolio is the one that performs well in relation to all the benchmarks over the family of possible parameter values. We analyze this problem using convex duality and show that it is equivalent to a Bayesian problem, where the Lagrange multipliers play the role of the prior distribution, and the learning model involves Bayesian updating of these Lagrange multipliers/prior. This Bayesian problem is unusual in that the prior distribution is endogenously chosen by solving the dual optimization problem for the Lagrange multipliers, and the objective function involves the family of benchmarks from the relative regret problem. These results show that regret is a natural means by which robust decision making and learning can be combined. ISSN : 0025-1909 En ligne : http://mansci.highwire.org/content/early/2012/07/18/mnsc.1120.1518.short?rss=1&s [...]