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

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  • Grochulskiy, 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 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.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 36539.

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Date of creation: 22 Jul 2011
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Handle: RePEc:pra:mprapa:36539

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Keywords: Limited commitment; Borrowing constraints;

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Cited by:
  1. Yuzhe Zhang & Borys Grochulski, 2013. "Market-based incentives," 2013 Meeting Papers 1180, Society for Economic Dynamics.
  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.
  3. Borys Grochulski & Yuzhe Zhang, 2013. "Market-based incentives," Working Paper 13-05, Federal Reserve Bank of Richmond.

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