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Optimal Compensation with Hidden Action and Lump-Sum Payment in a Continuous-Time Model

Cvitanić, Jakša and Wan, Xuhu and Zhang, Jianfeng (2009) Optimal Compensation with Hidden Action and Lump-Sum Payment in a Continuous-Time Model. Applied Mathematics and Optiumization, 59 (1). pp. 99-146. ISSN 0095-4616. doi:10.1007/s00245-008-9050-0.

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We consider a problem of finding optimal contracts in continuous time, when the agent’s actions are unobservable by the principal, who pays the agent with a one-time payoff at the end of the contract. We fully solve the case of quadratic cost and separable utility, for general utility functions. The optimal contract is, in general, a nonlinear function of the final outcome only, while in the previously solved cases, for exponential and linear utility functions, the optimal contract is linear in the final output value. In a specific example we compute, the first-best principal’s utility is infinite, while it becomes finite with hidden action, which is increasing in value of the output. In the second part of the paper we formulate a general mathematical theory for the problem. We apply the stochastic maximum principle to give necessary conditions for optimal contracts. Sufficient conditions are hard to establish, but we suggest a way to check sufficiency using non-convex optimization.

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Cvitanić, Jakša0000-0001-6651-3552
Additional Information:© 2009 Springer. Received: 27 July 2005; Accepted: 7 May 2008; Published online: 6 June 2008.
Subject Keywords:Hidden action - Moral hazard - Second-best optimal contracts and incentives - Principal-agent problems - Stochastic maximum principle - Forward-backward SDEs
Issue or Number:1
Record Number:CaltechAUTHORS:CVIamo09
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Official Citation:Cvitanić, J., Wan, X. & Zhang, J. Appl Math Optim (2009) 59: 99.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:13068
Deposited By: Archive Administrator
Deposited On:16 Jan 2009 19:43
Last Modified:08 Nov 2021 22:35

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