Optimal Consumption and Portfolio Selection for Retirees Under Inflation and Pension Default Risk

The optimal investment-consumption analysis under insurer default risk and inflation risk for retirees who receive defined benefit pension payments is conducted. To enhance applicability, the minimum welfare guarantee and bequest motives are considered. Using the dynamic programming principle and the convex-duality method, we obtain the implicit solution of optimal consumption and investment strategies for retirees with a standard constant relative risk aversion utility. Certain implications consistent with financial advice are obtained by numerical analysis. As pension default risk increases, the rich prefer inflation-indexed bonds for hedging motive and the poor invest more in stocks for compensation motive. Despite of the presence of default risk, negative inflation risk premium leads to short positions in inflation-indexed bonds. The life portfolios of the rich tend to be more stable than those of the poor