Optimal risk sharing and borrowing constraints in a continuous-time model with limited commitment

• 成果类型: Article
• 署名作者: Grochulski, Borys; Zhang, Yuzhe
• 署名单位: University of Iowa; Federal Reserve System - USA; Federal Reserve Bank - Richmond
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2011.10.007
• 发表日期: 2011
• 页码: 2356-2388
• 关键词: Risk sharing; limited commitment; borrowing constraints

摘要

We study a continuous-time version of the optimal risk-sharing problem with one-sided commitment. In the optimal contract, the agent's consumption is a time-invariant, strictly increasing function of a single state variable: the maximal level of the agent's income realized to date. We characterize this function in terms of the agent's outside option value function and the discounted amount of time in which the agent's income process is expected to reach a new to-date maximum. Under constant relative risk aversion we solve the model in closed-form: optimal consumption of the agent equals a constant fraction of his maximal income realized to date. In the complete-markets implementation of the optimal contract, the Alvarez-Jermann solvency constraints take the form of a simple borrowing constraint familiar from the Bewley-Aiyagari incomplete-markets models. (C) 2011 Elsevier Inc. All rights reserved.