Optimal Investment Strategy of Defined Contribution Pension Based on Bequest Motivation and Loss Aversion

Under the S-shaped utility of loss aversion, this paper considers the bequest motivation of pension plan participants, random salary income before retirement and the substitution rate between receiving pension benefits after retirement and wages before retirement, and studies the optimal investment strategy of defined contribution (DC) pension. Assuming that pension funds can invest in a financial market consisting of three assets (risk-free asset cash, rolling bonds and stocks), inflation is considered by discount. Under the S-shaped utility, the Lagrange method is used to find the terminal optimal surplus of pensions in retirement, so as to find the terminal optimal wealth, and then the martingale method is used to find the optimal wealth process and investment strategy. Finally, a sensitivity analysis is carried out on the the influence of bequest motivation and loss aversion on the optimal investment strategy of DC pension.