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

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  • Grochulski, Borys
  • Zhang, Yuzhe

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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 146 (2011)
Issue (Month): 6 ()
Pages: 2356-2388

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Handle: RePEc:eee:jetheo:v:146:y:2011:i:6:p:2356-2388

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Web page: http://www.elsevier.com/locate/inca/622869

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Keywords: Risk sharing; Limited commitment; Borrowing constraints;

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Cited by:
  1. Grochulski, Borys & Zhang, Yuzhe, 2013. "Market-based incentives," MPRA Paper 45576, University Library of Munich, Germany.
  2. Zhang, Yuzhe, 2013. "Characterization of a risk sharing contract with one-sided commitment," Journal of Economic Dynamics and Control, Elsevier, vol. 37(4), pages 794-809.

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