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AN ITERATIVITY CONDITION FOR THE MEAN-VALUE PRINCIPLE UNDER CUMULATIVE PROSPECT THEORY

Published online by Cambridge University Press:  29 April 2013

Marek Kaluszka  and
Michał Krzeszowiec
Marek Kaluszka
Affiliation:
Institute of Mathematics, Ł ódź University of Technology, U1. Wólczańska 215, 90-924 Ł ódź, Poland E-mail: kaluszka@p.lodz.pl
Michał Krzeszowiec*
Affiliation:
Institute of Mathematics of the Polish Academy of Sciences, Śniadeckich 8, P.O. Box 21, 00-956 Warszawa, Poland
*
Institute of Mathematics, Ł ódźUniversity of Technology, U1. Wólczańska 215, 90-924 Ł ódź, Poland E-mail: michalkrzeszowiec@gmail.com
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Abstract

In this paper, we present the full characterization of the iterativity condition for the mean-value principle under the cumulative prospect theory. It turns out that the premium principle is iterative for exactly six pairs of probability distortion functions. Some of the corresponding premium principles are the classical mean-value principle, essential infimum or essential supremum of the random loss. Moreover, from the proof of the main theorem of this paper, it follows that the iterativity of the mean-value principle is equivalent to the iterativity of the generalized Choquet integral.

Keywords

Cumulative Prospect TheoryGeneralized Choquet Integraliterativitypremium principlesmean-value principledistorted probability
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 43 , Issue 1 , January 2013 , pp. 61 - 71
Copyright
Copyright © ASTIN Bulletin 2013

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