Research on the optimal consumption and portfolio of assets based on constant absolute risk aversion utility function

Abstract

In this paper, Merton’s typical consumption-saving and investment portfolio selection problem was expanded to the having-time inconformity preference of object, so individual needs to consider to change his/her personal preference when making a decision. By using the simpler method, the HJB equations under different circumstances of limited time and unlimited time were respectively obtained. Besides, the analytical solution of the consumption & investment portfolio selection of the utility function for constant absolute risk aversion was obtained. Compared the study result of Merton with that of this paper, the consumption and wealth were founded to have a linear relationship; however their percentage was not a constant any more, and the percentage of the investment on risky assets was not a constant either, but the total value of the investment on risky assets remained unchanged. Such conclusion has an important guiding significance to the optimization of the cross-period consumption and investment portfolio of investor.