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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Jakša Cvitanić held positions at Columbia University (Statistics), University of Southern California (Mathematics and Economics), and currently at Caltech (Social Sciences). He has served on the editorial boards of journals in the areas of Financial Mathematics, Applied Probability and Optimization, as well as on the Council of the Bachelier Finance Society. Jianfeng Zhang is currently associate professor at the University of Southern California (Mathematics Department).

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