A Unified Approach to Retirement and Consumption-Portfolio Choice

TL;DR

This paper develops a comprehensive model for optimal retirement, consumption, and investment decisions, integrating pre- and post-retirement choices and introducing a novel utility value of lifetime labor through a variational inequality approach.

Contribution

It presents a unified framework that encompasses various models, solving for optimal policies by establishing a duality and identifying the utility value of lifetime labor.

Findings

Unified model of retirement and consumption-portfolio choice.

Utility value of lifetime labor identified as an option.

Methodology using variational inequality to solve for utility value.

Abstract

In this study we propose a unified model of optimal retirement, consumption and portfolio choice of an individual agent, which encompasses a large class of the models in the literature and provide a general methodology to solve the model. Different from the traditional approach, we consider the problems before and after retirement simultaneously and identify the difference in the dual value functions as the utility value of lifetime labor. The utility value has an option nature, namely, it is the maximized value of choosing the retirement time optimally and we discover it by solving a variational inequality. Then, we discover the dual value functions by using the utility value. We discover the value function and optimal policies by establishing a duality between the value function and the dual value function.