Optimal retirement in presence of stochastic labor income: a free boundary approach in an incomplete market

TL;DR

This paper investigates the optimal retirement decision considering stochastic wages in an incomplete market, formulating it as a free boundary problem to determine the optimal retirement boundary.

Contribution

It introduces a novel free boundary approach to solve the retirement problem with stochastic income in an incomplete market setting.

Findings

Derived a free boundary model for retirement timing

Characterized the optimal retirement boundary under market incompleteness

Provided analytical insights into the impact of stochastic wages on retirement decisions

Abstract

In this work, we address the optimal retirement problem in the presence of a stochastic wage, formulated as a free boundary problem. Specifically, we explore an incomplete market setting where the wage cannot be perfectly hedged through investments in the risk-free and risky assets that characterize the financial market.