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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: The utility-maximizing consumption and investment strategy of an individual investor receiving an unspanned labor income stream seems impossible to find in closed form and very difficult to find using numerical solution techniques. We suggest an easy procedure for finding a specific, simple, and admissible consumption and investment strategy, which is near-optimal in the sense that the wealthequivalent loss compared to the unknown optimal strategy is very small. We first explain and implement the strategy in a simple setting with constant interest rates, a single risky asset, and an exogenously given income stream, but we also show that the success of the strategy is robust to changes in parameter values, to the introduction of stochastic interest rates, and to endogenous labor supply decisions.
    Keywords: G11 ; ddc:330 ; Optimal consumption and investment ; labor income ; incomplete markets ; artificially completed markets ; welfare loss ; Kapitalanlage ; Konsumtheorie ; Zeitpräferenz ; Optimaler Konsum ; Lohn ; Finanzmarkt ; Unvollkommener Markt ; Wohlfahrtseffekt ; 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.: Johann Wolfgang Goethe-Universität Frankfurt am Main, Fachbereich Wirtschaftswissenschaften
    Publication Date: 2017-03-15
    Description: We provide explicit solutions to life-cycle utility maximization problems simultaneously involving dynamic decisions on investments in stocks and bonds, consumption of perishable goods, and the rental and the ownership of residential real estate. House prices, stock prices, interest rates, and the labor income of the decision-maker follow correlated stochastic processes. The preferences of the individual are of the Epstein-Zin recursive structure and depend on consumption of both perishable goods and housing services. The explicit consumption and investment strategies are simple and intuitive and are thoroughly discussed and illustrated in the paper. For a calibrated version of the model we find, among other things, that the fairly high correlation between labor income and house prices imply much larger life-cycle variations in the desired exposure to house price risks than in the exposure to the stock and bond markets. We demonstrate that the derived closed-form strategies are still very useful if the housing positions are only reset infrequently and if the investor is restricted from borrowing against future income. Our results suggest that markets for REITs or other financial contracts facilitating the hedging of house price risks will lead to non-negligible but moderate improvements of welfare.
    Keywords: G11 ; D14 ; D91 ; C6 ; ddc:330 ; Housing ; labor income ; portfolio choice ; life-cycle decisions ; recursive utility ; REITs ; Wohneigentum ; Besitzformwahl ; Kapitalanlage ; Konsumtheorie ; Lebensverlauf ; Zeitpräferenz ; Portfolio-Management ; Immobilienfonds ; 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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  • 3
    ISSN: 1573-692X
    Keywords: contingent claims ; dynamic programming ; incomplete markets ; numerical solutions ; reservation prices
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Notes: Abstract With constrained portfolios contingent claims do not generally havea unique price that rules out arbitrage opportunities.Earlier studies have demonstratedthat when there are constraints on the hedge portfolio,a no-arbitrage price interval for any contingent claim exists.I consider the more realistic case where the constraints are imposed on the total portfolio of each investor and define reservation buying and selling prices for contingent claims. I derive propertiesof these prices, show how they can be computed numerically, and study two simple examples in which the reservation prices and the corresponding hedging strategies are compared to the Black–Scholes setting.
    Type of Medium: Electronic Resource
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  • 4
    ISSN: 1573-7144
    Keywords: the term structure of interest rates ; stochastic duration ; multi-factor models ; coupon bond option pricing ; swaption pricing
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Notes: Abstract Generalizing Cox, Ingersoll, and Ross (1979), this paper defines the stochastic duration of a bond in a general multi-factor diffusion model as the time to maturity of the zero-coupon bond with the same relative volatility as the bond. Important general properties of the stochastic duration measure are derived analytically, and the stochastic duration is studied in detail in various well-known models. It is also demonstrated by analytical arguments and numerical examples that the price of a European option on a coupon bond (and, hence, of a European swaption) can be approximated very accurately by a multiple of the price of a European option on a zero-coupon bond with a time to maturity equal to the stochastic duration of the coupon bond.
    Type of Medium: Electronic Resource
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  • 5
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    Frankfurt a. M.: Goethe University Frankfurt, SAFE - Sustainable Architecture for Finance in Europe
    Publication Date: 2019-01-15
    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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  • 6
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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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  • 7
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    Frankfurt a. M.: Goethe University Frankfurt, SAFE - Sustainable Architecture for Finance in Europe
    Publication Date: 2019-09-17
    Description: We solve a rich life-cycle model of household decisions involving consumption of perishable goods and housing services, habit formation for housing consumption, stochastic labor income, stochastic house prices, home renting and owning, stock investments, and portfolio constraints. In line with empirical observations, the optimal decisions involve (i) stock investments that are low or zero for many young agents and then gradually increasing over life, (ii) an age- and wealth-dependent housing expenditure share, (iii) non-housing consumption being significantly more sensitive to wealth and income shocks than housing consumption, and (iv) non-housing consumption being humpshaped over life.
    Description: June 15, 2015
    Keywords: G10 ; D14 ; D91 ; E21 ; R21 ; ddc:330 ; Habit formation ; life-cycle household decisions ; housing expenditureshare ; consumption hump ; stock market participation ; human capital
    Repository Name: EconStor: OA server of the German National Library of Economics - Leibniz Information Centre for Economics
    Language: English
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  • 8
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    Frankfurt a. M.: Goethe University Frankfurt, SAFE - Sustainable Architecture for Finance in Europe
    Publication Date: 2019-09-17
    Description: In a calibrated consumption-portfolio model with stock, housing, and labor income predictability, we disentangle the welfare effects of skill and luck. Skilled investors are able to take advantage of all sources of predictability, whereas unskilled investors ignore predictability. Lucky investors enter the market at a favorable time. For an unskilled investor the certainty equivalent of wealth is 0.3-6.8% lower than for a skilled investor, depending on the market entry date. Across market entry dates, skilled but unlucky investors can lose up to 15.4% compared to unskilled but lucky investors. Simulation studies confirm the relative importance of luck and document that, if anything, housing predictability is more important than stock predictability.
    Description: Current version: February 6, 2017
    Keywords: G11 ; D91 ; D14 ; ddc:330 ; Return predictability ; scenarios ; welfare ; performance ; housing
    Repository Name: EconStor: OA server of the German National Library of Economics - Leibniz Information Centre for Economics
    Language: English
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