A greedy algorithm for habit formation under multiplicative utility
A greedy algorithm for habit formation under multiplicative utility ArXiv ID: 2305.04748 “View on arXiv” Authors: Unknown 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. ...