A GREEDY ALGORITHM FOR HABIT FORMATION UNDER MULTIPLICATIVE UTILITY

Snezhana Kirusheva () and Thomas S. Salisbury
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Snezhana Kirusheva: Department of Mathematical and Computational Sciences, University of Toronto Mississauga, 3359 Mississauga Road, Mississauga, Ontario, Canada L5L 1C6, Canada
Thomas S. Salisbury: Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario, Canada M3J 1P3, Canada

International Journal of Theoretical and Applied Finance (IJTAF), 2024, vol. 27, issue 03n04, 1-20

Abstract: In this paper, we consider the problem of optimizing lifetime consumption under a habit formation model, both with and without an exogenous pension. Unlike much of the existing literature, we apply a power utility to the ratio of consumption to habit, rather than to their difference. The martingale/duality method becomes intractable in this setting, so we develop a greedy version of this method that is solvable using Monte Carlo simulation. We investigate the behavior of the greedy solution, and explore what parameter values make the greedy solution a good approximation to the optimal one.

Keywords: Optimal consumption; multiplicative habit formation; greedy algorithm (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0219024923500279

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