A Variational Approach to Contracting under Imperfect Observations | Zendy

Agostino Capponi | Zendy; Jakša Cvitanić | Zendy; Türkay Yolcu | Zendy

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A Variational Approach to Contracting under Imperfect Observations

Author(s) -

Agostino Capponi,

Jakša Cvitanić,

Türkay Yolcu

Publication year - 2012

Publication title -

siam journal on financial mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.251

H-Index - 33

ISSN - 1945-497X

DOI - 10.1137/110859075

Subject(s) - comparative statics , imperfect , sensitivity (control systems) , compensation (psychology) , action (physics) , shareholder , mathematical optimization , process (computing) , statics , value (mathematics) , computer science , outcome (game theory) , noise (video) , lévy process , mathematical economics , economics , mathematics , microeconomics , finance , physics , engineering , artificial intelligence , psychoanalysis , image (mathematics) , philosophy , electronic engineering , linguistics , operating system , psychology , corporate governance , classical mechanics , quantum mechanics , machine learning

We consider a continuous-time model of the project value process that can be observed only 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 problem, 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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