Optimal Bankruptcy Time and Consumption/Investment Policies on an Infinite Horizon with a Continuous Debt Repayment Until Bankruptcy

Mathematics of Operations Research, Vol. 29, No. 3, pp. 649-671, August 2004

Cass Business School Research Paper

Posted: 9 Aug 2005

See all articles by Monique Jeanblanc

Monique Jeanblanc

Université d'Évry - Departement de Mathematiques

Peter Lakner

New York University (NYU) - Department of Information, Operations, and Management Sciences

Ashay Kadam

IIM Udaipur

Abstract

In this paper we consider the optimization problem of an agent who wants to maximize the total expected discounted utility from consumption over an infinite horizon. The agent is under obligation to pay a debt at a fixed rate until he/she declares bankruptcy. At that point, after paying a fixed cost, the agent will be able to keep a certain fraction of the present wealth, and the debt will be forgiven. The selection of the bankruptcy time is taken to be at the discretion of the agent. The novelty of this paper is that at the time of bankruptcy the wealth process has a discontinuity, and that the agent continues to invest and consume after bankruptcy. We show that the solution of a free boundary problem satisfying some additional conditions is the value function of the above optimization problem. Particular examples such as the logarithmic and the power utility functions will be provided, and in these cases explicit forms will be given for the optimal bankruptcy time, investment and consumption processes.

Keywords: Bankruptcy, Optimal Stopping

Suggested Citation

Jeanblanc, Monique and Lakner, Peter and Kadam, Ashay, Optimal Bankruptcy Time and Consumption/Investment Policies on an Infinite Horizon with a Continuous Debt Repayment Until Bankruptcy. Mathematics of Operations Research, Vol. 29, No. 3, pp. 649-671, August 2004, Cass Business School Research Paper, Available at SSRN: https://ssrn.com/abstract=770824

Monique Jeanblanc (Contact Author)

Université d'Évry - Departement de Mathematiques ( email )

rue du pere Jarlan
F-91025 Evry Cedex
France
33 (0) 1 69 47 02 05/ 02 01 (Phone)
33 (0) 1 69 47 02 18 (Fax)

Peter Lakner

New York University (NYU) - Department of Information, Operations, and Management Sciences ( email )

44 West Fourth Street
New York, NY 10012
United States
212-998-0476 (Phone)

Ashay Kadam

IIM Udaipur ( email )

Mohanlal Sukhadia University Campus
Udaipur, Rajasthan 313001
India

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