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

Borys Grochulski and Yuzhe Zhang ()

Journal of Economic Theory, 2011, vol. 146, issue 6, 2356-2388

Abstract: We study a continuous-time version of the optimal risk-sharing problem with one-sided commitment. In the optimal contract, the agentʼs consumption is a time-invariant, strictly increasing function of a single state variable: the maximal level of the agentʼs income realized to date. We characterize this function in terms of the agentʼs outside option value function and the discounted amount of time in which the agentʼs 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: Risk sharing; Limited commitment; Borrowing constraints (search for similar items in EconPapers)
JEL-codes: C61 D86 (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (30)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:jetheo:v:146:y:2011:i:6:p:2356-2388

DOI: 10.1016/j.jet.2011.10.007

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