Bayes decision problems require subjective elicitation of the inputs: beliefs and preferences. Sometimes, elicitation methods may not perfectly represent the Decision Maker's judgements. Several foundations propose to overlay this problem using robust approaches. In these models, beliefs are modelled by a class of probability distributions and preferences by a class of loss functions. Thus, the solution concept is the set of non-dominated alternatives. In this paper we focus on the computation of the efficient set when the preferences are modelled by a class of convex loss functions, specifically the quantile loss functions. We illustrate the idea with examples and introduce the use of stochastic dominance in this context.
Keywords. Bayesian Robustness, non-dominated alternatives, Bayes alternatives, quantile loss functions, stochastic orders, quantile class of prior distributions, band probability class .
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Authors addresses:
Javier Hernández
c/ Castillo de Alconchel 11 06006 Badajoz
Jacinto Martín
Dept. Matemáticas
Escuela Politécnica Cáceres
Carretera de Trujillo, s/n
10071 Cáceres
Spain
José Pablo Arias
Escuela Politécnica.
Departamento de Matemáticas.
Universidad de Extremadura.
Avda de la Universidad s.n.
C.P. 10071
Cáceres. Spain
Alfonso Suarez-Llorens
Facultad de Ciecias Económicas
y Empresariales
Universidad de Cádiz
C/ Duque de Nájera 8
C.P; 11002
Cádiz
E-mail addresses:
| Javier Hernández | javierhs@materiales.unex.es |
| Jacinto Martín | jrmartin@unex.es |
| José Pablo Arias | jparias@unex.es |
| Alfonso Suarez-Llorens | alfonso.suarez@uca.es |