A new characterization of comonotonicity and its application in behavioral finance

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8 Citations (Scopus)

Abstract

It is well-known that an Rn-valued random vector (X1, X2, ⋯, Xn) is comonotonic if and only if (X1, X2, ⋯, Xn) and (Q1(U), Q2(U), ⋯, Qn(U)) coincide in distribution, for any random variable U uniformly distributed on the unit interval (0, 1), where Qk({dot operator}) are the quantile functions of Xk, k=1, 2, ⋯, n. It is natural to ask whether (X1, X2, ⋯, Xn) and (Q1(U), Q2(U), ⋯, Qn(U)) can coincide almost surely for some special U. In this paper, we give a positive answer to this question by construction. We then apply this result to a general behavioral investment model with a law-invariant preference measure and develop a universal framework to link the problem to its quantile formulation. We show that any optimal investment output should be anti-comonotonic with the market pricing kernel. Unlike previous studies, our approach avoids making the assumption that the pricing kernel is atomless, and consequently, we overcome one of the major difficulties encountered when one considers behavioral economic equilibrium models in which the pricing kernel is a yet-to-be-determined unknown random variable. The method is applicable to general models such as risk sharing model.
Original languageEnglish
Pages (from-to)612-625
Number of pages14
JournalJournal of Mathematical Analysis and Applications
Volume418
Issue number2
DOIs
Publication statusPublished - 15 Oct 2014

Keywords

  • Atomless/non-atomic
  • Behavioral finance
  • Comonotonicity
  • Cumulative prospect theory
  • Economic equilibrium model
  • Pricing kernel
  • Quantile formulation
  • Rank-dependent utility theory

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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