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Title:Foundations of continuous-time recrusive utility: Differentiability and normalization of certainty equivalents PDF Logo
Authors:Kraft, Holger
Seifried, Frank Thomas
Issue Date:2009
Series/Report no.:Working paper series // Johann-Wolfgang-Goethe-Universität Frankfurt am Main, Fachbereich Wirtschaftswissenschaften Finance & accounting 196
Abstract: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 Lévy 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.
Subjects:recursive utility
stochastic differential utility
Lévy framework
certainty equivalents
dynamic programming
Document Type:Working Paper
Appears in Collections:Working Paper Series: Finance and Accounting, Universität Frankfurt a. M.

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