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Optimal Consumption-Portfolio Policies With Habit Formation


  • Jerome B. Detemple
  • Fernando Zapatero


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.

Suggested Citation

  • Jerome B. Detemple & Fernando Zapatero, 1992. "Optimal Consumption-Portfolio Policies With Habit Formation," Mathematical Finance, Wiley Blackwell, vol. 2(4), pages 251-274.
  • Handle: RePEc:bla:mathfi:v:2:y:1992:i:4:p:251-274

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    Cited by:

    1. 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.
    2. Xiang Yu, 2011. "An Explicit Example Of Optimal Portfolio-Consumption Choices With Habit Formation And Partial Observations," Papers 1112.2939,, revised Aug 2014.
    3. Xiang Yu, 2011. "Utility maximization with addictive consumption habit formation in incomplete semimartingale markets," Papers 1112.2940,, revised May 2015.
    4. repec:eee:eneeco:v:64:y:2017:i:c:p:1-12 is not listed on IDEAS
    5. 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.
    6. Guasoni, Paolo & Huberman, Gur & Ren, Dan, 2014. "Shortfall Aversion," CEPR Discussion Papers 10064, C.E.P.R. Discussion Papers.
    7. Curatola, Giuliano, 2016. "Optimal consumption and portfolio choice with loss aversion," SAFE Working Paper Series 130, Research Center SAFE - Sustainable Architecture for Finance in Europe, Goethe University Frankfurt.
    8. repec:eee:quaeco:v:66:y:2017:i:c:p:345-358 is not listed on IDEAS
    9. 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.
    10. repec:dau:papers:123456789/5374 is not listed on IDEAS
    11. Roman Muraviev, 2011. "Additive habits with power utility: Estimates, asymptotics and equilibrium," Papers 1108.2889,
    12. Arjen Siegmann, 2003. "Shortfall allowed: loss aversion and habit formation," WO Research Memoranda (discontinued) 741, Netherlands Central Bank, Research Department.
    13. Detemple, Jerome B. & Giannikos, Christos I., 1996. "Asset and commodity prices with multi-attribute durable goods," Journal of Economic Dynamics and Control, Elsevier, vol. 20(8), pages 1451-1504, August.
    14. 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.
    15. Xiang Yu, 2014. "Optimal Consumption under Habit Formation In Markets with Transaction Costs and Random Endowments," Papers 1408.1382,, revised Jul 2016.

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