OPUS 4 Latest Documents RSS FeedLatest documents
http://publikationen.ub.uni-frankfurt.de/index/index/
Thu, 27 Jun 2013 16:09:30 +0200Thu, 27 Jun 2013 16:09:30 +0200Stochastic differential utility as the continuous-time limit of recursive utility
http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/30570
We establish a convergence theorem that shows that discrete-time recursive utility, as developed by Kreps and Porteus (1978), converges to stochastic differential utility, as introduced by Dufffie and Epstein (1992), in the continuous-time limit of vanishing grid size.Holger Kraft; Frank Thomas Seifriedworkingpaperhttp://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/30570Thu, 27 Jun 2013 16:09:30 +0200Consumption habits and humps
http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/30568
We show that the optimal consumption of an individual over the life cycle can have the hump shape (inverted U-shape) observed empirically if the preferences of the individual exhibit internal habit formation. In the absence of habit formation, an impatient individual would prefer a decreasing consumption path over life. However, because of habit formation, a high initial consumption would lead to high required consumption in the future. To cover the future required consumption, wealth is set aside, but the necessary amount decreases with age which allows consumption to increase in the early part of life. At some age, the impatience outweighs the habit concerns so that consumption starts to decrease. We derive the optimal consumption strategy in closed form, deduce sufficient conditions for the presence of a consumption hump, and characterize the age at which the hump occurs. Numerical examples illustrate our findings. We show that our model calibrates well to U.S. consumption data from the Consumer Expenditure Survey.Holger Kraft; Claus Munk; Frank Thomas Seifried; Sebastian Wagnerworkingpaperhttp://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/30568Thu, 27 Jun 2013 15:22:20 +0200Foundations of continuous-time recursive utility : differentiability and normalization of certainty equivalents
http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/6243
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, C61Holger Kraft; Frank Thomas Seifriedworkingpaperhttp://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/6243Fri, 13 Mar 2009 11:12:36 +0100