Simple Explicit Formula for Near-Optimal Stochastic Lifestyling
Cass Business School Research Paper; final version available in European Journal of Operational Research (2020, doi:10.1016/j.ejor.2019.12.032)
24 Pages Posted: 8 Jan 2018 Last revised: 2 Jan 2020
Date Written: January 2, 2018
In life-cycle economics the Samuelson paradigm (Samuelson, 1969) states that the optimal investment is in constant proportions out of lifetime wealth composed of current savings and the present value of future income. It is well known that in the presence of credit constraints this paradigm no longer applies. Instead, optimal lifecycle investment gives rise to so-called stochastic lifestyling (Cairns et al., 2006), whereby for low levels of accumulated capital it is optimal to invest fully in stocks and then gradually switch to safer assets as the level of savings increases. In stochastic lifestyling not only does the ratio between risky and safe assets change but also the mix of risky assets varies over time. While the existing literature relies on complex numerical algorithms to quantify optimal lifestyling the present paper provides a simple formula that captures the main essence of the lifestyling effect with remarkable accuracy.
Keywords: optimal investment, stochastic lifestyling, Samuelson paradigm, power utility, stochastic optimal control
JEL Classification: C61, G11
Suggested Citation: Suggested Citation