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  • 1
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    Frankfurt a. M.: Johann Wolfgang Goethe-Universität Frankfurt am Main, Fachbereich Wirtschaftswissenschaften
    Publication Date: 2017-03-15
    Description: 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.
    Keywords: D81 ; D91 ; C61 ; ddc:330 ; recursive utility ; stochastic differential utility ; Lévy framework ; certainty equivalents ; normalization ; dynamic programming ; Zeitpräferenz ; Stochastischer Prozess ; Erwartungsnutzen ; Dynamische Optimierung ; Theorie
    Repository Name: EconStor: OA server of the German National Library of Economics - Leibniz Information Centre for Economics
    Language: English
    Type: doc-type:workingPaper
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  • 2
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    Frankfurt a. M.: Goethe University Frankfurt, SAFE - Sustainable Architecture for Finance in Europe
    Publication Date: 2019-01-15
    Description: 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 Duffie and Epstein (1992), in the continuous-time limit of vanishing grid size.
    Keywords: D81 ; D91 ; ddc:330 ; Stochastic differential utility ; recursive utility ; convergence ; backward stochastic differential equation
    Repository Name: EconStor: OA server of the German National Library of Economics - Leibniz Information Centre for Economics
    Language: English
    Type: doc-type:workingPaper
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  • 3
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    Frankfurt a. M.: Goethe University Frankfurt, SAFE - Sustainable Architecture for Finance in Europe
    Publication Date: 2019-01-15
    Description: 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.
    Keywords: D91 ; D11 ; D14 ; ddc:330 ; Consumption hump ; life-cycle utility maximization ; habit formation ; impatience
    Repository Name: EconStor: OA server of the German National Library of Economics - Leibniz Information Centre for Economics
    Language: English
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  • 4
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    Frankfurt a. M.: Goethe University Frankfurt, SAFE - Sustainable Architecture for Finance in Europe
    Publication Date: 2019-09-05
    Description: The observed hump-shaped life-cycle pattern in individuals' consumption cannot be explained by the classical consumption-savings model. We explicitly solve a model with utility of both consumption and leisure and with educational decisions affecting future wages. We show optimal consumption is hump shaped and determine the peak age. The hump results from consumption and leisure being substitutes and from the implicit price of leisure being decreasing over time; more leisure means less education, which lowers future wages, and the present value of foregone wages decreases with age. Consumption is hump shaped whether the wage is hump shaped or increasing over life.
    Keywords: D11 ; D14 ; D91 ; I21 ; J24 ; ddc:330 ; education ; leisure ; consumption hump ; wage hump
    Repository Name: EconStor: OA server of the German National Library of Economics - Leibniz Information Centre for Economics
    Language: English
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  • 5
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    Frankfurt a. M.: Goethe University Frankfurt, SAFE - Sustainable Architecture for Finance in Europe
    Publication Date: 2019-09-17
    Description: We study continuous-time optimal consumption and investment with Epstein-Zin recursive preferences in incomplete markets. We develop a novel approach that rigorously constructs the solution of the associated Hamilton-Jacobi-Bellman equation by a fixed point argument and makes it possible to compute both indirect utility and, more importantly, optimal strategies. Based on these results, we also establish a fast and accurate method for numerical computations. Our setting is not restricted to affine asset price dynamics; we only require boundedness of the underlying model coefficients.
    Description: This version: May 31, 2016
    Keywords: G11 ; G12 ; D52 ; D91 ; C61 ; C68 ; ddc:330 ; consumption-portfolio choice ; asset pricing ; stochastic di erential utility ; incomplete markets ; fixed point approach ; FBSDE
    Repository Name: EconStor: OA server of the German National Library of Economics - Leibniz Information Centre for Economics
    Language: English
    Type: doc-type:workingPaper
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