Additive habits with power utility: Estimates, asymptotics and equilibrium
AbstractWe consider a power utility maximization problem with additive habits in a framework of discrete-time markets and random endowments. For certain classes of incomplete markets, we establish estimates for the optimal consumption stream in terms of the aggregate state price density, investigate the asymptotic behaviour of the propensity to consume (ratio of the consumption to the wealth), as the initial endowment tends to infinity, and show that the limit is the corresponding quantity in an artificial market. For complete markets, we concentrate on proving the existence of an Arrow-Debreu equilibrium in an economy inhabited by heterogeneous individuals who differ with respect to their risk-aversion coefficient, impatience rate and endowments stream, but possess the same degree of habit-formation. Finally, in a representative agent equilibrium, we compute explicitly the price of a zero coupon bond and the Lucas tree equity, and study its dependence on the habit-formation parameter.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1108.2889.
Date of creation: Aug 2011
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-08-22 (All new papers)
- NEP-DGE-2011-08-22 (Dynamic General Equilibrium)
- NEP-UPT-2011-08-22 (Utility Models & Prospect Theory)
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