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Optimal Consumption-Portfolio Policies With Habit Formation

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  • Jerome B. Detemple
  • Fernando Zapatero
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    Abstract

    This is a companion paper to the authors 'Asset Prices in an Exchange Economy with Habit Formation" in "Econometrica" which focuses on consumption demand and asset pricing when preferences are habit forming. Here we prove existence of optimal consumption-portfolio policies for (i) utility functions for which the marginal cost of consumption (MCC) interacts with the habit formation process and satisfies a recursive integral equation with forward functional Lipschitz integrand and (ii) utilities for which the MCC is independent of the standard of living and satisfies a recursive integral equation with locally Lipschitz integrand. Result (i) is demonstrated here for the first time. Result (ii) is novel and enables us to consider Cobb-Douglas utilities without placing lower bounds on the system of Arrow-Debreu prices. We also review and extend our earlier results in the linear case; in particular, we provide new insights about the structure of optimal portfolios. Additional new features of the model include the possibility of finite marginal utility of consumption at zero and habit formation mechanisms with stochastic coefficients. an extension to a financial market model with general processes is outlined. A byproduct of the analysis is a set of fixed-point theorems for recursive integral equations with forward functional Lipschitz or locally Lipschitz integrands. Copyright 1992 Blackwell Publishers.

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    Bibliographic Info

    Article provided by Wiley Blackwell in its journal Mathematical Finance.

    Volume (Year): 2 (1992)
    Issue (Month): 4 ()
    Pages: 251-274

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    Handle: RePEc:bla:mathfi:v:2:y:1992:i:4:p:251-274

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    Cited by:
    1. Arjen Siegmann, 2003. "Shortfall allowed: loss aversion and habit formation," WO Research Memoranda (discontinued) 741, Netherlands Central Bank, Research Department.
    2. Munk, Claus, 2008. "Portfolio and consumption choice with stochastic investment opportunities and habit formation in preferences," Journal of Economic Dynamics and Control, Elsevier, vol. 32(11), pages 3560-3589, November.
    3. Xiang Yu, 2011. "An Explicit Example Of Optimal Portfolio-Consumption Choices With Habit Formation And Partial Observations," Papers 1112.2939, arXiv.org, revised Aug 2014.
    4. Antonelli, Fabio & Barucci, Emilio & Mancino, Maria Elvira, 2001. "Asset pricing with a forward-backward stochastic differential utility," Economics Letters, Elsevier, vol. 72(2), pages 151-157, August.
    5. Paul Ehling, 2004. "Consumption, Portfolio Policies and Dynamic Equilibrium in the Presence of Preference for Ownership," Econometric Society 2004 North American Winter Meetings 311, Econometric Society.
    6. Roman Muraviev, 2011. "Additive habits with power utility: Estimates, asymptotics and equilibrium," Papers 1108.2889, arXiv.org.
    7. Xiang Yu, 2011. "Utility Maximization with Addictive Consumption Habit Formation in Incomplete Semimartingale Markets," Papers 1112.2940, arXiv.org, revised Apr 2014.
    8. Bodie, Zvi & Detemple, Jerome B. & Otruba, Susanne & Walter, Stephan, 2004. "Optimal consumption-portfolio choices and retirement planning," Journal of Economic Dynamics and Control, Elsevier, vol. 28(6), pages 1115-1148, March.
    9. Jérôme B. Detemple & Christos I. Giannikos, 1995. "Asset and Commodity Prices with Multiattribute Durable Goods," CIRANO Working Papers 95s-47, CIRANO.

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