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A greedy algorithm for habit formation under multiplicative utility

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  • Snezhana Kirusheva
  • Thomas S. Salisbury

Abstract

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 behaviour of the greedy solution, and explore what parameter values make the greedy solution a good approximation to the optimal one.

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  • Snezhana Kirusheva & Thomas S. Salisbury, 2023. "A greedy algorithm for habit formation under multiplicative utility," Papers 2305.04748, arXiv.org.
    • Handle: RePEc:arx:papers:2305.04748
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    References listed on IDEAS

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