1. Optimal Compensation with Hidden Action and Lump-Sum Payment in a Continuous-Time Model.
- Author
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Cvitanić, Jakša, Wan, Xuhu, and Zhang, Jianfeng
- Subjects
LUMP sum distributions (Pensions) ,PENSIONS ,MATHEMATICAL functions ,DEFINED contribution pension plans ,MATHEMATICAL optimization ,MATHEMATICS ,DIFFERENTIAL equations ,UTILITY functions ,MATHEMATICAL analysis - Abstract
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. [ABSTRACT FROM AUTHOR]
- Published
- 2009
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