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Contracting in Continuous Time: Time-Multiplicative Preferences

In: Contract Theory: Discrete- and Continuous-Time Models

Author

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  • Jaeyoung Sung

    (Ajou University)

Abstract

We study a generalized version of the classical Holmström-Milgrom (1987) continuous-time model which helps overcome main limitations of discrete-time models. We state the general model in strong formulation with the (production) outcome driven by a drift-controlled Brownian Motion. The strong formulation helps us understand, hopefully intuitively, the general structures and issues of the first-best and second-best problems. We study the implementability theorem which justifies the use of the first-order approach to the second-best continuous-time model, and then apply the well-known dynamic programming method to obtain closed-form solutions to the two interesting cases: namely, a stationary case, and a linear-quadratic case. The former and the latter cases help characterize, respectively, static and dynamic aspects of optimal contracts.

Suggested Citation

  • Jaeyoung Sung, 2023. "Contracting in Continuous Time: Time-Multiplicative Preferences," Springer Books, in: Contract Theory: Discrete- and Continuous-Time Models, chapter 0, pages 65-98, Springer.
  • Handle: RePEc:spr:sprchp:978-981-99-5487-2_5
    DOI: 10.1007/978-981-99-5487-2_5
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