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

See all articles by Aleš Černý

Aleš Černý

Business School, City, University of London

Igor Melichercik

Comenius University - Faculty of Mathematics, Physics and Informatics; Department of Applied Mathematics and Statistics

Date Written: January 2, 2018

Abstract

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

Černý, Aleš and Melichercik, Igor, Simple Explicit Formula for Near-Optimal Stochastic Lifestyling (January 2, 2018). Cass Business School Research Paper; final version available in European Journal of Operational Research (2020, doi:10.1016/j.ejor.2019.12.032), Available at SSRN: https://ssrn.com/abstract=3095887 or http://dx.doi.org/10.2139/ssrn.3095887

Aleš Černý (Contact Author)

Business School, City, University of London ( email )

106 Bunhill Row
London, EC1Y 8TZ
United Kingdom

Igor Melichercik

Comenius University - Faculty of Mathematics, Physics and Informatics; Department of Applied Mathematics and Statistics ( email )

Mlynská dolina
SK-842 48 Bratislava, 842 48
Slovakia

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