Optimal portfolio choice under kinked power utility

We extend the kinked power utility function by allowing a different risk aversion level in the two parts contained in the utility function. We maximize the expected utility of the replacement ratio at retirement that is wealth at retirement to a stochastic benchmark, for plan members in a defined contribution pension plan in a complete market. We derive closed-form optimal solutions under risk aversion and loss aversion implied by the kinked power utility. We find that plan members under kinked power utility tend to de-risk around the reference level, which could lead to a great proportion of the replacement ratio at retirement being on the reference level, while a small variation in the proportion of the replacement ratio at retirement ending up in the left tail. When the reference level is set at 100%, and the market price for future pension premiums (the value of initial capital) is lower than that for the benchmark, a lower risk aversion level when the replacement ratio falls below the reference level, could lead to a significant increase in the proportion of the replacement ratio at retirement being not below the reference level.