  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.
