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

Xun Li, Xiang Yu, Qinyi Zhang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

2 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)25-45
Number of pages21
JournalInsurance: Mathematics and Economics
Publication statusPublished - Jan 2023


  • Consumption drawdown constraint
  • Life insurance
  • Optimal consumption
  • Piecewise feedback control
  • Shortfall aversion

ASJC Scopus subject areas

  • Statistics and Probability
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty


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