Foundations of continuous-time recursive utility : differentiability and normalization of certainty equivalents

This paper relates recursive utility in continuous time to its discrete-time origins and provides a rigorous and intuitive alternative to a heuristic approach presented in [Duffie, Epstein 1992], who formally define recu
This paper relates recursive utility in continuous time to its discrete-time origins and provides a rigorous and intuitive alternative to a heuristic approach presented in [Duffie, Epstein 1992], who formally define recursive utility in continuous time via backward stochastic differential equations (stochastic differential utility). Furthermore, we show that the notion of Gâteaux differentiability of certainty equivalents used in their paper has to be replaced by a different concept. Our approach allows us to address the important issue of normalization of aggregators in non-Brownian settings. We show that normalization is always feasible if the certainty equivalent of the aggregator is of expected utility type. Conversely, we prove that in general L´evy frameworks this is essentially also necessary, i.e. aggregators that are not of expected utility type cannot be normalized in general. Besides, for these settings we clarify the relationship of our approach to stochastic differential utility and, finally, establish dynamic programming results. JEL Classifications: D81, D91, C61
show moreshow less

Download full text files

Export metadata

  • Export Bibtex
  • Export RIS

Additional Services

    Share in Twitter Search Google Scholar
Metadaten
Author:Holger Kraft, Frank Thomas Seifried
URN:urn:nbn:de:hebis:30-62768
Parent Title (English):Universität Frankfurt am Main. Fachbereich Wirtschaftswissenschaften: [Working paper series / Finance and accounting] Working paper series, Finance & Accounting ; No. 196
Series (Serial Number):Working paper series / Johann-Wolfgang-Goethe-Universität Frankfurt am Main, Fachbereich Wirtschaftswissenschaften : Finance & Accounting (196)
Publisher:Univ., Fachbereich Wirtschaftswiss.
Place of publication:Frankfurt am Main
Document Type:Working Paper
Language:English
Year of Completion:2009
Year of first Publication:2009
Publishing Institution:Univ.-Bibliothek Frankfurt am Main
Release Date:2009/03/13
Tag:L´evy framework; certainty equivalents; dynamic programming; normalization; recursive utility; stochastic differential utility
SWD-Keyword:Nutzen
Pagenumber:36
HeBIS PPN:210577762
Institutes:Wirtschaftswissenschaften
Dewey Decimal Classification:330 Wirtschaft
Sammlungen:Universitätspublikationen
Licence (German):License Logo Veröffentlichungsvertrag für Publikationen

$Rev: 11761 $