Optimal bankruptcy time and consumption/investment policies on an infinite horizon with a continuous debt repayment until bankruptcy

• 成果类型: Article
• 署名作者: Jeanblanc, M; Lakner, P; Kadam, A
• 署名单位: Universite Paris Saclay; New York University; University of Michigan System; University of Michigan
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1030.0084
• 发表日期: 2004
• 页码: 649-671
• 关键词: subsistence consumption; Personal bankruptcy; Explicit solution; INVESTMENT

摘要

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.