Work

Optimal Consumption, Leisure, and Investment with Partial Borrowing Constraints over a Finite Horizon

Year: 2025

Type: article

Abstract: We study an optimal consumption, leisure, and investment problem over a finite horizon in a continuous-time financial market with partial borrowing constraints. The agent derives utility from consumption and leisure, with preferences represented by a Cobb–Douglas utility function. The agent allocates time between work and leisure, earning wage income based on working hours. A key feature of our model is a partial borrowing constraint that limits the agent’s debt capacity to a fraction of the present value of their maximum future labor income. We employ the dual-martingale approach to derive the optimal consumption, leisure, and investment strategies. The problem reduces to solving a variational inequality with a free boundary, which we analyze using analytical and numerical methods. We provide an integral equation representation of the free boundary and solve it numerically via a recursive integration method. Our results highlight the impact of the borrowing constraint on the agent’s optimal decisions and the interplay between labor supply, consumption, and portfolio choice.

Source: Mathematics

DOI: 10.3390/math13060989

Authors: Geonwoo Kim, Junkee Jeon

Institutions: Seoul National University of Science and Technology, Kyung Hee University

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

SDG: Decent work and economic growth

Open Access status: gold

Estimated APC paid: $3,137