Impact Of Income And Leisure On Optimal Portfolio, Consumption, Retirement Decisions Under Exponential Utility

TL;DR

This paper models an optimal control problem for investment, consumption, and retirement decisions under exponential utility, revealing how income and leisure influence financial and lifestyle choices over an infinite horizon.

Contribution

It introduces a dual approach to derive implicit solutions for optimal strategies, characterizing conditions for no retirement and analyzing income and leisure effects.

Findings

No retirement occurs below a specific income threshold.

Income and leisure significantly impact optimal portfolio and consumption.

The model provides insights into financial and lifestyle decision interplay.

Abstract

We study an optimal control problem encompassing investment, consumption, and retirement decisions under exponential (CARA-type) utility. The financial market comprises a bond with constant drift and a stock following geometric Brownian motion. The agent receives continuous income, consumes over time, and has the option to retire irreversibly, gaining increased leisure post-retirement compared to pre-retirement. The objective is to maximize the expected exponential utility of weighted consumption and leisure over an infinite horizon. Using a martingale approach and dual value function, we derive implicit solutions for the optimal portfolio, consumption, and retirement time. The analysis highlights key contributions: first, the equivalent condition for no retirement is characterized by a specific income threshold; second, the influence of income and leisure levels on optimal portfolio, consumption, and retirement decisions is thoroughly examined. These results provide valuable insights into the interplay between financial and lifestyle choices in retirement planning.