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

TL;DR

This paper derives explicit solutions for an optimal portfolio, consumption, and life insurance problem considering shortfall aversion and drawdown constraints, providing insights into their effects on financial decision-making.

Contribution

It introduces a novel analytical framework for solving a complex life-cycle consumption and insurance problem with shortfall aversion and drawdown constraints.

Findings

Explicit piecewise solutions for optimal controls

Thresholds for wealth variables identified

Quantitative analysis of parameter impacts

Abstract

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.