Contracting in Continuous Time: Time-Multiplicative Preferences

Jaeyoung Sung
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Jaeyoung Sung: Ajou University

Chapter Chapter 5 in Contract Theory: Discrete- and Continuous-Time Models, 2023, pp 65-98 from Springer

Abstract: 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.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-99-5487-2_5

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DOI: 10.1007/978-981-99-5487-2_5

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