Optimal Investment, Consumption and Leisure with an Option to File for Bankruptcy

Abstract

This paper investigates the optimal personal bankruptcy decision of a debtor who participates in the labor market. This paper is based on a mathematical finance model that assumes a Black-Scholes financial market and describes a decision problem as an expected discounted utility maximization problem. Our optimization problem can be cast into a mixed optimal stopping and control problem, and has a symmetry feature with a voluntary retirement decision problem in characterizing the stopping times. To obtain value function and optimal strategies, we use dynamic programming method and transform the relevant nonlinear Bellman equation into a linear equation. Numerical illustrations from our explicit expressions for the optimal strategies reveal how an opportunity to file for bankruptcy affects debtor’s consumption, leisure, and portfolio decisions.

Keywords

• portfolio selection
• dynamic programming method
• consumption/leisure
• Cobb-Douglas utility
• personal bankruptcy