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Optimal Investment and Consumption under a Habit-Formation Constraint

Bahman Angoshtari, Erhan Bayraktar and Virginia R. Young

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Abstract: We formulate an infinite-horizon optimal investment and consumption problem, in which an individual forms a habit based on the exponentially weighted average of her past consumption rate, and in which she invests in a Black-Scholes market. The individual is constrained to consume at a rate higher than a certain proportion $\alpha$ of her consumption habit. Our habit-formation model allows for both addictive ($\alpha=1$) and nonaddictive ($0

Date: 2021-02, Revised 2021-11
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Published in SIAM J. Financial Math., 13(1), pp. 321-352, 2022

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