Nonrecursive separation of risk and time preferences

Matthias Albrecht Fahrenwaldt, Ninna Reitzel Jensen, Mogens Steffensen

Research output: Contribution to journalArticle

Abstract

Recursive utility disentangles preferences with respect to time and risk by recursively building up a value function of local increments. This involves certainty equivalents of indirect utility. Instead we disentangle preferences with respect to time and risk by building up a value function as a non-linear aggregation of certainty equivalents of direct utility of consumption. This entails time-consistency issues which are dealt with by looking for an equilibrium control and an equilibrium value function rather than a classical optimal control and a classical optimal value function. We characterize the solution in a general diffusive incomplete market model and find that, in certain special cases of utmost interest, the characterization coincides with what would arise from a recursive utility approach. But also importantly, in other cases, it does not: The two approaches are fundamentally different but match, exclusively but importantly, in the mathematically special case of homogeneity of the value function.

Original languageEnglish
Pages (from-to)95-108
Number of pages14
JournalJournal of Mathematical Economics
Volume90
Early online date16 Jul 2020
DOIs
Publication statusPublished - Oct 2020

Keywords

  • Certainty equivalents
  • Equilibrium strategies
  • Generalized Hamilton–Jacobi–Bellman equation
  • Recursive utility
  • Time-consistency
  • Time-global preferences

ASJC Scopus subject areas

  • Economics and Econometrics
  • Applied Mathematics

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