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Consumption and Portfolio Choice under Internal Multiplicative Habit Formation

Published online by Cambridge University Press:  27 September 2019

Servaas van Bilsen
van Bilsen,, University of Amsterdam Department of Quantitative Economics
A. Lans Bovenberg
Bovenberg,, Tilburg University Department of Economics
Roger J. A. Laeven*
Laeven,, University of Amsterdam Department of Quantitative Economics
Laeven (corresponding author),


This paper explores the optimal consumption and investment behavior of an individual who derives utility from the ratio between his consumption and an endogenous habit. We obtain closed-form policies under general utility functionals and stochastic investment opportunities by developing a nontrivial linearization to the budget constraint. This enables us to explicitly characterize how habit formation affects the marginal propensity to consume and optimal stock–bond investments. We also show that in a setting that combines habit formation with Epstein–Zin utility, consumption no longer grows at unrealistically high rates at high ages and investments in risky assets decrease.

Research Article
Copyright © Michael G. Foster School of Business, University of Washington 2019

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We are very grateful to Hendrik Bessembinder (the editor) and Mark Schroder (the referee) for comments and suggestions that have significantly improved the paper. We are also grateful to Yacine Aït-Sahalia, Markus Fels (discussant), Glenn Harrison, Gur Huberman, Frank de Jong, Torsten Kleinow (discussant), Olivia Mitchell, Theo Nijman, Antoon Pelsser (discussant), Hato Schmeiser (discussant), and seminar and conference participants at the Australian Research Council (ARC) Centre of Excellence in Population Ageing Research (CEPAR) in Sydney, the Australasian Finance and Banking Conference, the Center for Economic Analysis of Risk (CEAR)/Munich Risk and Insurance Center (MRIC) Behavioral Insurance Workshop, the European Group of Risk and Insurance Economists (EGRIE) Annual Meeting, the Netspar International Pension Workshop, Oxford University, the Quantitative Methods in Finance Conference, Tilburg University, Tinbergen Institute, the University of Amsterdam, the University of Liverpool, the University of Pennsylvania Wharton School, and the Winter School on Mathematical Finance for their helpful comments and suggestions. An earlier version of this paper was circulated under the title “How to Invest and Spend Wealth in Retirement? A Utility-Based Analysis.” This research was supported in part by the Netherlands Organization for Scientific Research (NWO) under grant NWO VIDI 2009 (van Bilsen, Laeven) and by the European Commission under the seventh framework program (EU-MOPACT; van Bilsen, Bovenberg).


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