Optimal contracting with effort and misvaluation
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We propose a new continuous-time contracting model, in which the firm value process can only be observed with noise, and there are two sources of moral hazard: the agent’s effort and misvaluation. The principal can induce the agent to alter the perceived fundamental value of the firm through misvaluation, thus changing the market estimate of that value. We consider two cases in detail: the one in which the market correctly anticipates only the effort, and the other in which it correctly anticipates both the effort and the amount of misvaluation. In the first case, we find that it is optimal for the principal to induce the agent to apply a non-zero amount of misvaluation. Using calculus of variation techniques, we find the optimal pay-per-performance sensitivity (PPS) of the contract and optimal effort and misvaluation amount, by means of solving of a second order ordinary differential equation. In the second case, which can be viewed as an extension of the seminal Holmstrom-Milgrom model to the case of noisy observations, we find that the optimal misvaluation value is zero, and we compare the resulting optimal contract to the Holmstrom-Milgrom contract.
KeywordsOptimal contracts Principal-agent problem Variational calculus Stochastic filtering Moral hazard
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- 1.Auzinger, W., Kneisl, G., Koch, O., Weinmuller, E.: SBVP 1.0—A MATLAB Solver for Singular Boundary Value Problems, Technical Report, Vienna University of Technology, 2011Google Scholar
- 6.Capponi, A., Cvitanić, J., Yolcu, T.: A variational approach to contracting under imperfect observations. SIAM J. Financ. Math. (2012)Google Scholar
- 7.Clarke, F.H.: Methods of Dynamics and Nonsmooth Optimization, vol. 57, pp. 30–40. Capital city press, Montpelier, Vermont (1989)Google Scholar
- 12.Ferrarin, G., Giudici, P.: Financial scandals and the role of private enforcement: the Parmalat case. ECGI Law Working Paper 40, 2005Google Scholar
- 13.Gibbons, R.: Lecture Note 1: Agency Theory. Preprint available at http://web.mit.edu/rgibbons/www/903LN1S10.pdf, 2010
- 15.Jensen, M.: Agency costs of overvalued equity. Financ. Manag. 34(1) (2005)Google Scholar
- 16.Liptser R.S., Shiryaev A.N.: Statistics of Random Processes II. Applications. Springer, New York (2000)Google Scholar
- 23.Tonelli, L.: Sur une mithode directe du calcd des variations. Rend. Circ. Mat. Palermo 39 (1915)Google Scholar