Optimal Investment Considerations for a Single Cohort Life Insurance Portfolio

This study examines the portfolio optimization problem of an insurance company that issues an annuity, receives the associated premiums as a lump sum, and invests in a financial market. The insurer’s objective is to determine an investment strategy that minimizes the likelihood of defaulting on annuity payments before ceasing operations, where default occurs if the portfolio value, net of the annuity liability, becomes negative. Unlike the previous work, here the mortality intensity is stochastic and follows a Cox–Ingersoll–Ross (CIR) process. Dynamic programming is employed, and the value function is characterized by a Hamilton–Jacobi–Bellman (HJB) equation, and the former is linearized through the Legendre transform. Numerical results show that default probability declines with higher initial wealth and mortality intensity, while stochastic mortality volatility has little impact—though slightly higher volatility marginally reduces default risk. Optimal stock investment falls with increasing wealth and mortality intensity, and is nearly constant for low wealth levels. Mortality volatility has minimal influence, but a higher Sharpe ratio raises optimal investment, underscoring the role of risk-adjusted returns.