, Volume 1, Issue 1, pp 21-55
Date: 16 Mar 2007

Optimal compensation with adverse selection and dynamic actions

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We consider continuous-time models in which the agent is paid at the end of the time horizon by the principal, who does not know the agent’s type. The agent dynamically affects either the drift of the underlying output process, or its volatility. The principal’s problem reduces to a calculus of variation problem for the agent’s level of utility. The optimal ratio of marginal utilities is random, via dependence on the underlying output process. When the agent affects the drift only, in the risk- neutral case lower volatility corresponds to the more incentive optimal contract for the smaller range of agents who get rent above the reservation utility. If only the volatility is affected, the optimal contract is necessarily non-incentive, unlike in the first-best case. We also suggest a procedure for finding simple and reasonable contracts, which, however, are not necessarily optimal.

Research supported in part by NSF grants DMS 04-03575 and 06-31298. We would like to express our gratitude to participants of the following seminars and conferences for useful comments and suggestions: UCLA (Econ Theory), Caltech (Econ Theory), Columbia (Probability), Princeton (Fin. Engineering), U. Texas at Austin (Math Finance), Banff Workshop on Optim. Problems in Fin. Econ, Kyoto U. (Economics), UC Irvine (Probability), Cornell (Fin. Engineering), Bachelier Seminar. Moreover, we are very grateful to the anonymous referee for helpful suggestions. The remaining errors are the authors’ sole responsibility.