The theory of random utility maximization for a finite set of alternatives is generalized to alternatives which are elements of a compact metric space $T$. We model the random utility of these alternatives ranging over a continuum as a random process $\{Y_t, t \in T\}$ with upper semicontinuous (usc) sample paths. The alternatives which achieve the maximum utility levels constitute a random closed, compact set $M$. We specialize to a model where the random utility is a max-stable process with a.s. usc paths. Further path properties of these processes are derived and explicit formulas are calculated for the hitting and containment functionals of $M$. The hitting functional corresponds to the choice probabilities.
Publié le : 1991-05-14
Classification:
Choice theory,
extreme values,
extremal processes,
random closed sets,
random upper semicontinuous functions,
max-stable processes,
60K10,
60J20
@article{1177005937,
author = {Resnick, Sidney I. and Roy, Rishin},
title = {Random USC Functions, Max-Stable Processes and Continuous Choice},
journal = {Ann. Appl. Probab.},
volume = {1},
number = {4},
year = {1991},
pages = { 267-292},
language = {en},
url = {http://dml.mathdoc.fr/item/1177005937}
}
Resnick, Sidney I.; Roy, Rishin. Random USC Functions, Max-Stable Processes and Continuous Choice. Ann. Appl. Probab., Tome 1 (1991) no. 4, pp. 267-292. http://gdmltest.u-ga.fr/item/1177005937/