Longevity risk management for individual investors in the retirement stage using SDDP algorithm

Abstract

Increasing life expectancy requires preplanned financial asset management for life after retirement. However, individuals do not fully acknowledge the potential financial shortage arising from longevity risk, which is associated with uncertainty of living longer than expected. In this study, we solve an optimal asset allocation for individuals after retirement using Stochastic Dual Dynamic Programming (SDDP). Uncertainty in life expectancy is incorporated in our model by applying survival probability at each age in base year 1900 to 2100. We utilize SDDP algorithm to reduce the dimensionality problem when solving the optimal financial decision for the planning horizon of 40 years. Total of $100^{40}$ scenario trees are considered in the problem. Our case study shows that as life expectancy increases, more investment is made in risky assets at early stages to prepare for longevity risk. Furthermore, we introduce $\lambda$ to represent the sensitivity of financial decision with respect to basic consumption in order to understand the tradeoff between saving and spending in the presence of longevity risk.