Sensitivity of Optimal Retirement Problem to Liquidity Constraints

TL;DR

This paper analytically solves an optimal retirement model considering liquidity constraints, revealing how such constraints influence investment, consumption, and leisure choices through sensitivity analysis.

Contribution

It introduces an analytical solution to a retirement optimization problem with time-varying liquidity constraints using duality methods.

Findings

Liquidity constraints significantly affect optimal investment and consumption strategies.

Sensitivity analysis shows the impact of constraint timing on retirement planning.

The duality approach effectively handles complex constraints in retirement models.

Abstract

In this work we analytically solve an optimal retirement problem, in which the agent optimally allocates the risky investment, consumption and leisure rate to maximise a gain function characterised by a power utility function of consumption and leisure, through the duality method. We impose different liquidity constraints over different time spans and conduct a sensitivity analysis to discover the effect of this kind of constraint.