  This paper studies a life-cycle optimal portfolio-consumption problem when
the consumption performance is measured by a shortfall aversion preference with
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.
