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Additive habit formation: consumption in incomplete markets with random endowments

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Abstract

We provide a detailed characterization of the optimal consumption stream for the additive habit-forming utility maximization problem, in a framework of general discrete-time incomplete markets and random endowments. This characterization allows us to derive the monotonicity and concavity of the optimal consumption as a function of wealth, for several important classes of incomplete markets and preferences. These results yield a deeper understanding of the fine structure of the optimal consumption and provide a further theoretical support for the classical conjectures of Keynes (The general theory of employment, interest and money. Cambridge University Press, Cambridge, 1936).

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  1. Department of Mathematics and RiskLab, ETH Zurich, Rämistrasse 101, 8092, Zurich, Switzerland

    Roman Muraviev

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  1. Roman Muraviev
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Correspondence to Roman Muraviev.

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Muraviev, R. Additive habit formation: consumption in incomplete markets with random endowments. Math Finan Econ 5, 67–99 (2011). https://doi.org/10.1007/s11579-011-0049-y

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