Optimal Compensation with Hidden Action and Lump-Sum Payment in a Continuous-Time Model
- Caltech, M/C 228-77 (United States)
- HKUST Business School, Department of Information and Systems Management (Hong Kong)
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.
- OSTI ID:
- 21241901
- Journal Information:
- Applied Mathematics and Optimization, Vol. 59, Issue 1; Other Information: DOI: 10.1007/s00245-008-9050-0; Copyright (c) 2009 Springer Science+Business Media, LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
- Country of Publication:
- United States
- Language:
- English
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