Target benefit pension with longevity risk and stochastic interest rate valuation

This paper introduces a target benefit pension (TBP) model that integrates both longevity risk and stochastic interest rate valuation. The TBP benefit incorporates a fixed target benefit annuity and a dynamic adjustment term, determined through a stochastic control problem. To capture the dynamic nature of average remaining lifespan influenced by longevity risk, we combine a linear function with an Ornstein-Uhlenbeck (OU) process to model the evolving average remaining lifespan. We evaluate the expected discounted value of the target benefit annuity, taking into account stochastic interest rates and the dynamic average remaining lifespan. The pension fund trustee strategically invests in both risk-free and risky assets, framing a stochastic control problem with control variables that include asset allocation and the overall adjustment term. This paper advances pension theory by introducing a novel longevity risk model and enhancing the potential of TBP for intergenerational risk sharing.