Contract Theory in Continuous-Time Models

  • Jakša Cvitanić
  • Jianfeng Zhang

Part of the Springer Finance book series (FINANCE)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Introduction

    1. Front Matter
      Pages 1-1
    2. Jakša Cvitanić, Jianfeng Zhang
      Pages 3-6
    3. Jakša Cvitanić, Jianfeng Zhang
      Pages 7-14
  3. First Best: Risk Sharing Under Full Information

    1. Front Matter
      Pages 15-15
    2. Jakša Cvitanić, Jianfeng Zhang
      Pages 17-24
    3. Jakša Cvitanić, Jianfeng Zhang
      Pages 25-43
  4. Second Best: Contracting Under Hidden Action—The Case of Moral Hazard

    1. Front Matter
      Pages 45-45
    2. Jakša Cvitanić, Jianfeng Zhang
      Pages 47-84
    3. Jakša Cvitanić, Jianfeng Zhang
      Pages 85-113
  5. Third Best: Contracting Under Hidden Action and Hidden Type—The Case of Moral Hazard and Adverse Selection

    1. Front Matter
      Pages 135-135
    2. Jakša Cvitanić, Jianfeng Zhang
      Pages 137-153
  6. Backward SDEs and Forward-Backward SDEs

    1. Front Matter
      Pages 155-155
    2. Jakša Cvitanić, Jianfeng Zhang
      Pages 157-182
    3. Jakša Cvitanić, Jianfeng Zhang
      Pages 183-227
    4. Jakša Cvitanić, Jianfeng Zhang
      Pages 229-248
  7. Back Matter
    Pages 249-255

About this book


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.


91G80, 93E20 forward-backward SDEs optimal contracts principal-agent problems quantitative finance stochastic maximum principle

Authors and affiliations

  • Jakša Cvitanić
    • 1
  • Jianfeng Zhang
    • 2
  1. 1.Div. of the Humanities, Social ScienceCalifornia Institute of TechnologyPasadenaUSA
  2. 2.Department of MathematicsUniversity of Southern CaliforniaLos AngelesUSA

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2013
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-14199-7
  • Online ISBN 978-3-642-14200-0
  • Series Print ISSN 1616-0533
  • Series Online ISSN 2195-0687
  • Buy this book on publisher's site
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Finance, Business & Banking