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arXiv · 2305.04748

A greedy algorithm for habit formation under multiplicative utility

Snezhana Kirusheva·Thomas S. Salisbury
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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. 2023-05-08. A greedy algorithm for habit formation under multiplicative utility. https://arxiv.org/abs/2305.04748

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