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

Borys Grochulskiy and Yuzhe Zhang ()

MPRA Paper from University Library of Munich, Germany

Abstract: 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.

Keywords: Limited commitment; Borrowing constraints (search for similar items in EconPapers)
JEL-codes: C61 D86 (search for similar items in EconPapers)
Date: 2011-07-22
New Economics Papers: this item is included in nep-dge and nep-mic
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (31)

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Journal Article: Optimal risk sharing and borrowing constraints in a continuous-time model with limited commitment (2011)
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