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This paper studies a life-cycle optimal portfolio-consumption problem whenthe consumption performance is measured by a shortfall aversion preference withan additional drawdown constraint on consumption rate. Meanwhile, the agentalso dynamically chooses her life insurance premium to maximize the expectedbequest at the death time. By using dynamic programming arguments and the dualtransform, we solve the HJB variational inequality explicitly in a piecewiseform across different regions and derive some thresholds of the wealth variablefor the piecewise optimal feedback controls. Taking advantage of our analyticalresults, we are able to numerically illustrate some quantitative impacts onoptimal consumption and life insurance by model parameters and discuss theirfinancial implications.

Optimal consumption and life insurance under shortfall aversion and a drawdown constraint