Contract Theory in Continuous Time Models Preface PART I Introduction: 1.The Principal Agent Problem 2.Single Period Examples PART II First Best. Risk Sharing under Full Information: 3.Linear Models with Project Selection and Preview of Results 4.The General Risk Sharing Problem PART III Second Best. Contracting Under Hidden Action The Case of Moral Hazard: 5.The General Moral Hazard Problem 6.DeMarzo and Sannikov (2007) Biais et al (2007) – An Application to Capital Structure Problems: Optimal Financing of a Company PART IV Third Best. Contracting Under Hidden Action and Hidden Type – The Case of Moral Hazard and Adverse Selection: 7.Controlling the Drift 8.Controlling the Volatility Drift Trade Off with the First Best PART IV Appendix: Backward SDEs and Forward Backward SDEs 9.Introduction 10.Backward SDEs 11.Decoupled Forward Backward SDEs 12.Coupled Forward Backward SDEs References Index. 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.