Optimal Consumption and Life Insurance under Shortfall Aversion and a Drawdown Constraint

This paper studies a life-cycle optimal portfolio-consumption problem when the consumption performance is measured by a shortfall aversion preference under an additional drawdown constraint on consumption rate. Meanwhile, the agent also dynamically chooses her life insurance premium to maximize the expected bequest at the death time. By using dynamic programming arguments and the dual transform, we solve the HJB variational inequality explicitly in a piecewise form across different regions and derive some thresholds of the wealth variable for the piecewise optimal feedback controls. Taking advantage of our analytical results, we are able to numerically illustrate some quantitative impacts on optimal consumption and life insurance by model parameters and discuss their financial implications.