Considering the economic situation, we investigate the optimal asset allocation of defined contribution pension funds with random payouts after retirement under a modified criterion of quadratic loss. The HJB equation is derived adhering to the dynamic programming principle, and the time-consistent optimal investment strategy is designed based on the calculus theory. Finally, under two different risk attitudes, namely surplus preference and risk aversion, the impact of key parameters on the optimal investment strategy and the function of minimum loss at the initial moment is compared and analyzed, the economic significance is demonstrated, and the rationality of the model is verified.

In this paper, by enhancing the penalty coefficient, the general square loss criterion was modified into a novel criterion to more precisely identify risks and returns. Then, under this criterion, the ideal asset allocation for pension fund participants was investigated considering wealth management fees before retirement. Then, the Hamilton-Jacobi-Bellman (HJB) equation was formulated through the dynamic programming approach, and both the optimal investment strategy and minimum loss function were determined using calculus methods. Finally, how important parameters affect the initial optimal investment strategy and minimum loss function was analyzed, their economic implications were explained, the rationality of the model was validated, and several recommendations for management were provided.