Optimal consumption, portfolio, and life insurance policies under interest rate and inflation risks

This paper solves the optimal life insurance, consumption, and portfolio decisions of a wage earner before retirement under interest rate and inflation risks. The wage earner’s preferences are represented by the stochastic differential utility, which separates the coefficient of relative risk aversion from the elasticity of intertemporal substitution (EIS). The wage earner’s life insurance demand is affected by the volatile interest rates and inflation. The optimal life insurance demand decreases with the level of nominal interest rates. Under an assumption of deterministic nominal income, the demand for life insurance would not be affected by the level of inflation. However, if the wage earner’s income is indexed to inflation, the life insurance demand would increase with the level of inflation. Furthermore, under investment opportunities with greater volatilities, wage earners who optimally allocate their wealth to the financial market benefit more from financial investments and cut their demand for life insurance. An analysis of EIS and risk aversion on life insurance demand shows that the demand for life insurance over the planning horizon increases with the measure of relative risk aversion but decreases with EIS. Optimal consumption is affected by the insurance premium load and the direction depends on the size of EIS relative to unity.