Discussion Paper WP2005

Simple Explicit Formula for Near-Optimal Stochastic Lifestyling
Ales Cerny and Igor Melichercik
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 life-cycle 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:
finance, optimal investment, stochastic lifestyling, Samuelson paradigm, power utility. 2010 MSC: 90C20, 90C39, 35K55, 49J20  

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