A greedy algorithm for habit formation under multiplicative utility
Portfolio Management
2023-05-09 v1
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.
Keywords
Cite
@article{arxiv.2305.04748,
title = {A greedy algorithm for habit formation under multiplicative utility},
author = {Snezhana Kirusheva and Thomas S. Salisbury},
journal= {arXiv preprint arXiv:2305.04748},
year = {2023}
}