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An Isomorphism Between Asset Pricing Models With and Without Linear Habit Formation

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  • Mark Schroder
  • Costis Skiadas

Abstract

We show an isomorphism between optimal portfolio selection or competitive equilibrium models with utilities incorporating linear habit formation, and corresponding models without habit formation. The isomorphism can be used to mechanically transform known solutions not involving habit formation to corresponding solutions with habit formation. For example, the Constantinides (1990) and Ingersoll (1992) solutions are mechanically obtained from the familiar Merton solutions for the additive utility case, without recourse to a Bellman equation or first-order conditions. More generally, recent solutions to portfolio selection problems with recursive utility and a stochastic investment opportunity set are readily transformed to novel solutions of corresponding problems with utility that combines recursivity with habit formation. The methodology also applies in the context of Hindy--Huang--Kreps (1992) preferences, where our isomorphism shows that the solution obtained by Hindy and Huang (1993) can be mechanically transformed to Dybvig's (1995) solution to the optimal consumption-investment problem with consumption ratcheting. Copyright 2002, Oxford University Press.

Suggested Citation

  • Mark Schroder & Costis Skiadas, 2002. "An Isomorphism Between Asset Pricing Models With and Without Linear Habit Formation," Review of Financial Studies, Society for Financial Studies, vol. 15(4), pages 1189-1221.
  • Handle: RePEc:oup:rfinst:v:15:y:2002:i:4:p:1189-1221
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    Cited by:

    1. 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.
    2. Zhou, Y., 2014. "Essays on habit formation and inflation hedging," Other publications TiSEM 4886da12-1b84-4fd9-aa07-3, Tilburg University, School of Economics and Management.
    3. Xiang Yu, 2011. "Utility maximization with addictive consumption habit formation in incomplete semimartingale markets," Papers 1112.2940, arXiv.org, revised May 2015.
    4. 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.
    5. Schroder, Mark & Skiadas, Costis, 2003. "Optimal lifetime consumption-portfolio strategies under trading constraints and generalized recursive preferences," Stochastic Processes and their Applications, Elsevier, vol. 108(2), pages 155-202, December.
    6. 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.
    7. Qian Lin & Frank Riedel, 2014. "Optimal consumption and portfolio choice with ambiguity," Papers 1401.1639, arXiv.org.
    8. Pascal St-Amour, 2005. "Direct Preference Wealth in Aggregate Household Portfolios," FAME Research Paper Series rp136, International Center for Financial Asset Management and Engineering.
    9. Xiang Yu, 2014. "Optimal Consumption under Habit Formation In Markets with Transaction Costs and Random Endowments," Papers 1408.1382, arXiv.org, revised Jul 2016.
    10. Liu, Xuan & Yang, Fang & Cai, Zongwu, 2016. "Does relative risk aversion vary with wealth? Evidence from households׳ portfolio choice data," Journal of Economic Dynamics and Control, Elsevier, vol. 69(C), pages 229-248.
    11. Ricardo M. Sousa, 2007. "Wealth Shocks and Risk Aversion," NIPE Working Papers 28/2007, NIPE - Universidade do Minho.
    12. Watson, John G. & Scott, Jason S., 2014. "Ratchet consumption over finite and infinite planning horizons," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 84-96.
    13. Schroder, Mark & Skiadas, Costis, 2005. "Lifetime consumption-portfolio choice under trading constraints, recursive preferences, and nontradeable income," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 1-30, January.
    14. Xianzhe Chen & Weidong Tian, 2014. "Optimal portfolio choice and consistent performance," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 37(2), pages 453-474, October.
    15. Pascal St-Amour, 2005. "Direct Preference for Wealth in Aggregate Household Portfolio," Cahiers de Recherches Economiques du Département d'Econométrie et d'Economie politique (DEEP) 05.04, Université de Lausanne, Faculté des HEC, DEEP.
    16. Zvi Bodie & Jérôme Detemple & Marcel Rindisbacher, 2009. "Life-Cycle Finance and the Design of Pension Plans," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 249-286, November.
    17. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance,in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742 Elsevier.

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