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Simple Explicit Formula for Near-Optimal Stochastic Lifestyling

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  • Alev{s} v{C}ern'y
  • Igor Melicherv{c}'ik

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.

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  • Alev{s} v{C}ern'y & Igor Melicherv{c}'ik, 2018. "Simple Explicit Formula for Near-Optimal Stochastic Lifestyling," Papers 1801.00980, arXiv.org, revised Dec 2019.
    • Handle: RePEc:arx:papers:1801.00980
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    1. Gerrard, Russell & Kyriakou, Ioannis & Nielsen, Jens Perch & Vodička, Peter, 2023. "On optimal constrained investment strategies for long-term savers in stochastic environments and probability hedging," European Journal of Operational Research, Elsevier, vol. 307(2), pages 948-962.

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