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Additive habit formation: Consumption in incomplete markets with random endowments

Roman Muraviev

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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 (1936).

Date: 2011-06, Revised 2011-09
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Published in Mathematics and Financial Economics 5(2), 67--99, 2011

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