Contract Theory in Continuous-Time Models
Published in October 2012
Book
Hardback
XII, 255 pages
978-3-642-14199-7 (ISBN)
Description
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.
Reviews / Votes
"The book under review provides a complete treatment of the principal-agent problem that covers all cases treated in economic literature ... . It is the first of its kind in that it provides a fully developed mathematical framework addressing the principal-agent problem with complete proofs and explanations of all mathematical tools used therein. ... The introduction of this book is accessible to a general audience." (Olympia Hadjiliadis, Bulletin of the American Mathematical Society, Vol. 52 (3), July, 2015)"The present book presents a nice exposition of the theory of the stochastic maximum principle, starting with BSDEs, and of its applications to contract theory. ... I recommend it to anyone working on or teaching the mathematical aspects of contract theory and/or stochastic control." (Etienne Pardoux, SIAM Review, Vol. 57 (2), June, 2015)
"This book considers contract theory in continuous time. ... This book is a good reference book for researchers and graduate students in economic theory, finance and mathematical economics. Continuous-time contract theory is particularly useful in finance. This book provides a basic methodological framework, which can be used to develop further advances, both in applications and in theory." (Susheng Wang, Mathematical Reviews, August, 2013)
More details
Product info
Book
Series
Edition
2013
Language
English
Place of publication
Heidelberg
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
XII, 256 p.
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 21 mm
Weight
571 gr
ISBN-13
978-3-642-14199-7 (9783642141997)
DOI
10.1007/978-3-642-14200-0
Schweitzer Classification
Other editions
Additional editions
Jaksa Cvitanic | Jianfeng Zhang
Contract Theory in Continuous-Time Models
Book
10/2014
Springer
€106.99
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Jaksa Cvitanic | Jianfeng Zhang
Contract Theory in Continuous-Time Models
E-Book
09/2012
1st Edition
Springer
€96.29
Available for download
Persons
JakSa Cvitanic 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).
Content
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.