Grochulskiy, Borys and Zhang, Yuzhe (2011): Optimal risk sharing and borrowing constraints in a continuoustime model with limited commitment. Published in: Journal of Economic Theory , Vol. 146, (2011): pp. 23562388.

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Abstract
We study a continuoustime version of the optimal risksharing problem with onesided commitment. In the optimal contract, the agent's consumption is a timeinvariant, 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 todate maximum. Under constant relative risk aversion we solve the model in closedform: optimal consumption of the agent equals a constant fraction of his maximal income realized to date. In the completemarkets implementation of the optimal contract, the AlvarezJermann solvency constraints take the form of a simple borrowing constraint familiar from the BewleyAiyagari incompletemarkets models.
Item Type:  MPRA Paper 

Original Title:  Optimal risk sharing and borrowing constraints in a continuoustime model with limited commitment 
Language:  English 
Keywords:  Limited commitment; Borrowing constraints 
Subjects:  D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D86  Economics of Contract: Theory C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C61  Optimization Techniques; Programming Models; Dynamic Analysis 
Item ID:  36539 
Depositing User:  Yuzhe Zhang 
Date Deposited:  09. Feb 2012 14:05 
Last Modified:  13. Feb 2013 15:10 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/36539 