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A Variational Approach to Contracting under Imperfect Observations

We consider a continuous time model of the project value process that can only be observed with noise, and we allow for the possibility that the manager in charge of the project can misrepresent the observed value. The manager is compensated by the shareholders, based on the filtering estimate of the project outcome. By means of a variational calculus methodology, novel for this kind of problems, we are able to compute in closed form the optimal pay-per-performance sensitivity of the compensation and the optimal misreporting action. We illustrate our theoretical predictions through a detailed comparative statics analysis, which indicates that the shareholders induce the manager to increase the amount of misreporting over time.

Author(s) :

Agostino Capponi, Jakša Cvitanic, Türkay Yolcu

Summary :

We consider a continuous time model of the project value process that can only be observed with noise, and we allow for the possibility that the manager in charge of the project can misrepresent the observed value. The manager is compensated by the shareholders, based on the filtering estimate of the project outcome. By means of a variational calculus methodology, novel for this kind of problems, we are able to compute in closed form the optimal pay-per-performance sensitivity of the compensation and the optimal misreporting action. We illustrate our theoretical predictions through a detailed comparative statics analysis, which indicates that the shareholders induce the manager to increase the amount of misreporting over time.

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Type : Working paper
Date : 12/05/2011
Keywords :

Asset Pricing