In recent years there has been a significant increase of
interest in continuous-time Principal-Agent models, or contract
theory, and their applications. Continuous-time models provide a
powerful and elegant framework for solving stochastic optimization
problems of finding the optimal contracts between two parties,
under various assumptions on the information they have access to,
and the effect they have on the underlying "profit/loss" values.
This monograph surveys recent results of the theory in a systematic
way, using the approach of the so-called Stochastic Maximum
Principle, in models driven by Brownian Motion.
Optimal contracts are characterized via a system of
Forward-Backward Stochastic Differential Equations. In a number of
interesting special cases these can be solved explicitly, enabling
derivation of many qualitative economic conclusions.
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