Pricing Life Insurance: Combining Economic, Financial, and Actuarial Approaches

This paper examines the pricing of term life insurance based on the economic approach of profit maximization, and incorporating the financial approach of stochastic interest rates, investment returns, and the insolvency option, while also including actuarial modeling of mortality risk. Optimal price (premium) is obtained by optimizing a stochastic objective function based on maximizing the expected net present value (NPV) of insurer profit. Expected claim payments are calculated on the basis of the Cox, Ingersoll, Ross (1985) financial valuation model. Our work analyzes numerically the influence of various parameters on optimal price, optimal expected NPV of insurer profit, and the insolvency put option value. We examine several parameters including the speed of adjustment in the mean reverting prices, the initial value of the short run equilibrium interest rate, the volatility of interest rate, the volatility of asset portfolio, the long run equilibrium interest rate, and the age of the insured. Findings demonstrate that optimal prices generally are most sensitive to changes in the long run equilibrium interest rate. Factors that have a strong influence on the price of the insolvency option include the age of the insured, volatility of interest rate, and volatility of the asset portfolio, especially at larger values of these parameters.