Stochastic Optimal Bequest and Consumption Strategy for Retirees: A Monte Carlo Based Dynamic Programming Approach
Samuel Essamuah Assabil
*
Department of Statistics, University of Cape Coast, Cape Coast, Ghana.
Ali Abubakar
Department of Mathematics, University of Cape Coast, Cape Coast, Ghana.
*Author to whom correspondence should be addressed.
Abstract
Determining optimal consumption and bequest policies is complex but essential aspect of retirement planning. It can balance the immediate need for consumption with the desire to leave a legacy, managing risks and economic activities more sustainably and efficiently. One of the key challenges for such optimal retirement planning is the stochasticity in the retiree’s income, which can include uncertain pension payments, fluctuating investment returns, or unexpected windfalls or losses. This paper proposes a robust Monte Carlo-based-dynamic programming technique to approximate the deterministic equivalent of the intractable stochastic utility bequest-consumption problem. The utility function is modelled using constant relative risk aversion (CRRA), and a weighting function modulates the bequest utility. This stochastic approach allows for a more realistic representation of the uncertainties faced by retirees. The dynamic programming approach involves recursive value functions that consider the maximum expected utility from the current period to the end of the planning horizon, given the state variables of wealth and income. This paper contributes to retirement planning by offering a sophisticated tool for optimizing consumption and bequest strategies in uncertain future income and survival probabilities.
Keywords: Monte-Carlo simulation, bequest planning, optimal consumption, survival probability, stochastic income, dynamic programming model