Solution of a functional equation arising in an axiomatization of the utility of binary gambles

János Aczél, Gyula Maksa, Zsolt Páles

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

For a new axiomatization, with fewer and weaker assumptions, of binary rank-dependent expected utility of gambles the solution of the functional equation (z/P)γ-1[zγ(p)] = φ-1[φ(z)ψ(p)] (z,p ∈]0,1[) is needed under some monotonicity and surjectivity conditions. We furnish the general such solution and also the solutions under weaker suppositions. In the course of the solution we also determine all sign preserving solutions of the related general equation h(u)[g(u + v)- g(v)} = f(v)g(u + v) (u ∈ ℝ+, v ∈ℝ).

Original languageEnglish
Pages (from-to)483-493
Number of pages11
JournalProceedings of the American Mathematical Society
Volume129
Issue number2
Publication statusPublished - Dec 1 2001

Keywords

  • Binary gamble
  • Convexity
  • Functional equation

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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