Target Benefit Pension with Longevity Risk and Stochastic Interest Rate

This paper introduces a target benefit pension (TBP) model that incorporates longevity risk and stochastic interest rate. Previous models have not considered the dynamic nature of remaining lifetime, and this paper proposes an Ornstein-Uhlenbeck (OU) process to simulate average remaining lifetime. Additionally, the paper evaluates the annuity with stochastic interest rate and establishes an approximation of the overall profit of the pension fund. From the perspective of the pension fund, the paper allows for investment in both risk-free and risky assets and establishes a stochastic control problem. The control variables are the risky investment amount and the overall adjustment, and explicit expressions for the problem are obtained using Hamilton-Jacobi-Bellman methods. The study highlights the importance of the adjustment term in fighting inflation and shows the significant impact of longevity risk on pension funds. This study contributes to the TBP model by increasing its potential in intergenerational risk sharing and compensating for the disadvantage of fixed annuity that its real value declines due to inflation.