Optimal annuitization post-retirement with labor income

TL;DR

This paper investigates the optimal timing of annuitization after retirement considering ongoing labor income, using advanced stochastic control methods to derive explicit solutions and analyze the influence of wages and labor rates.

Contribution

It introduces a novel actuarial model incorporating post-retirement labor income into optimal annuitization, providing explicit solutions and insights into labor income effects.

Findings

Optimal annuitization time is linearly related to initial wealth.

Wage and labor rates can have opposing effects on annuitization decisions.

Labor income influences the leverage ratio, affecting annuitization timing.

Abstract

Evidence shows that the labor participation rate of retirement age cohorts is non-negligible, and it is a widespread phenomenon globally. In the United States, the labor force participation rate for workers age 75 and older is projected to be over 10 percent by 2026 as reported by the Bureau of Labor Statistics. The prevalence of post-retirement work changes existing considerations of optimal annuitization, a research question further complicated by novel factors such as post-retirement labor rates, wage rates, and capacity or willingness to work. To our knowledge, this poses a practical and theoretical problem not previously investigated in actuarial literature. In this paper, we study the problem of post-retirement annuitization with extra labor income in the framework of stochastic control, optimal stopping, and expected utility maximization. The utility functions are of the Cobb-Douglas type. The martingale methodology and duality techniques are employed to obtain closed-form solutions for the dual and primal problems. The effect of labor income is investigated by exploiting the explicit solutions and Monte-Carlo simulation. The latter reveals that the optimal annuitization time is strongly linear with respect to the initial wealth, with or without labor income. When it comes to optimal annuitization, we find that the wage and labor rates may play opposite roles. However, their impact is mediated by the leverage ratio.