A closed-form solution to the continuous-time consumption model with endogenous labor income

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A closed-form solution to the continuous-time consumption model with endogenous labor income

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Aihua Zhang

Abstract

In this paper, we study an intertemporal maximization problem of an infinitely-lived individual who faces both labor income and asset return uncertainty. Given the growth rate of wage, the uncertainty of labor income is caused by the stochastic labor supply which is to be determined upon the available market information. Closed forms of consumption, labor supply and portfolio are obtained analytically by means of the martingale method. The Euler equation under uncertainty is established.

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Paper provided by Centre for Research into Industry, Enterprise, Finance and the Firm in its series CRIEFF Discussion Papers with number 0710.

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Date of creation: Sep 2007
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Handle: RePEc:san:crieff:0710

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Find related papers by JEL classification:
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis
C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
G1 - Financial Economics - - General Financial Markets
J22 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Time Allocation and Labor Supply

This paper has been announced in the following NEP Reports:

NEP-ALL-2007-10-13 (All new papers)
NEP-DGE-2007-10-13 (Dynamic General Equilibrium)

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Pitchford, John, 1991. "Optimum responses of the current account when income is uncertain," Journal of Economic Dynamics and Control, Elsevier, vol. 15(2), pages 285-296, April. [Downloadable!] (restricted)
Toche, Patrick, 2005. "A tractable model of precautionary saving in continuous time," Economics Letters, Elsevier, vol. 87(2), pages 267-272, May. [Downloadable!] (restricted)
Mason, Robin & Wright, Stephen, 2001. "The effects of uncertainty on optimal consumption," Journal of Economic Dynamics and Control, Elsevier, vol. 25(1-2), pages 185-212, January. [Downloadable!] (restricted)
Other versions:
- Mason, R. & Wright, S., 1999. "The Effects of Uncertainty on Optimal Consumption," Discussion Paper Series In Economics And Econometrics 9907, Economics Division, School of Social Sciences, University of Southampton.

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