Contract Theory: Discrete- and Continuous-Time Models

✍ Scribed by Jaeyoung Sung

• Publisher: Springer
• Year: 2023
• Tongue: English
• Leaves: 348
• Category: Library

✦ Synopsis

This book provides a self-contained introduction to discrete-time and continuous-time models in contracting theory to advanced undergraduate and graduate students in economics and finance and researchers focusing on closed-form solutions and their economic implications. Discrete-time models are introduced to highlight important elements in both economics and mathematics of contracting problems and to serve as a bridge for continuous-time models and their applications. The book serves as a bridge between the currently two almost separate strands of textbooks on discrete- and continuous-time contracting models

This book is written in a manner that makes complex mathematical concepts more accessible to economists. However, it would also be an invaluable tool for applied mathematicians who are looking to learn about possible economic applications of various control methods.

✦ Table of Contents

Introduction
References
Contents
Part I General Elements in Modelling Contracting Problems
1 Incentive Problems
1.1 Main Issues in Contracting
1.2 Principal's Problem
1.3 Agency Problems in Corporate Finance
1.4 Empirical Evidences on Managerial Compensation
References
2 Basic Structures of Contracting Problems
2.1 First Best
2.1.1 Certainty Case
2.1.2 Uncertainty Case
2.2 Second Best
2.3 Exercises
References
3 Discrete-Time Formulation I
3.1 First Best
3.1.1 Positive Effort
3.1.2 Zero Effort
3.1.3 Condition for Positive Effort
3.2 Second Best with a Risk-Neutral Agent
3.2.1 Positive Effort
3.2.2 Zero Effort
3.2.3 Condition for Positive Effort
3.3 Second Best with a Risk-Averse Agent
3.3.1 Positive Effort
3.3.2 Condition for Positive Effort
3.4 Remarks on the Discrete-Time Binomial-Outcome Model
3.5 Notes
3.6 Exercises
References
4 Discrete-Time Formulation II
4.1 First Best
4.2 Second Best
4.2.1 The First-Order Approach
4.2.2 Shape of Second-Best Contract
4.2.3 Value of Informative Signal in Contracting
4.2.4 Summary
4.3 Validity of First-Order Approach
4.3.1 First-Order Approach with a Normally Distributed Outcome
4.3.2 Normally Distributed Outcome
4.4 Notes
4.5 Exercises
References
Part II Contracting Under Risk Uncertainties: Continuous-Time Models
5 Contracting in Continuous Time: Time-Multiplicative Preferences
5.1 The Model
5.2 Representation of Admissible Contracts
5.3 First Best
5.3.1 First Best with a General Outcome Process
5.4 Second Best
5.4.1 Agent's Problem
5.4.2 Principal's Problem
5.4.3 Second Best with a General Non-Markovian Outcome Process
5.5 Application to Managerial Compensation
5.6 Notes
5.7 Exercises
References
6 Optimal Performance Metrics
6.1 Structure of the Optimal Performance Metric
6.2 Value of a Signal
6.3 Relative Performance Evaluation (RPE)
6.3.1 RPE in the Presence of Financial Markets
6.4 Notes
6.5 Exercises
References
7 Contracting Under Incomplete Information
7.1 Case I: dθt = 0
7.2 Case II: a(t) = a and b(t) = b
7.3 Notes
7.4 Exercises
References
8 Career Concerns in Competitive Executive Job Markets
8.1 The Model
8.2 Agent's Problem and Market Expectation
8.3 Principal's Problem
8.4 Notes
8.5 Exercises
References
9 Agency Problem in Weak Formulation
9.1 Agent's Problem
9.2 Principal's Problem
9.2.1 Markovian Outcome
9.3 Notes
References
10 Contracting with a Mean-Volatility Controlled Outcome
10.1 Agent's Mean-Volatility Control Problem
10.2 Principal's Problem: Observable Volatility
10.2.1 Markovian Outcome
10.2.2 Observable Project Selection
10.3 Principal's Problem: Unobservable Volatility
10.3.1 Unobservable-Project Selection
10.4 Comparing Observable- and Unobservable-Project Decisions
10.5 Unobservable-Volatility Case II
10.6 Notes
10.7 Exercises
References
11 Hierarchical Contracting: A Mean-Volatility Control Problem
11.1 The Model
11.2 Contracting on Individual Effort Outcomes
11.3 Contracting on Optimal Performance Metrics
11.3.1 Middle Managerial Contracts
11.3.2 Top Managerial Contract
11.3.3 A Numerical Example
11.4 Notes
11.5 Exercises
References
12 Contracting in Continuous Time: Time-Additive Preferences
12.1 The Model
12.2 First Best
12.3 Second Best
12.4 Notes
12.5 Exercises
References
Part III Contracting Under Ambiguity Uncertainties
13 Contracting Under Ambiguity: Introduction
13.1 Additional Remarks on Risk and Ambiguity
13.1.1 True Versus Perceived Distributions
13.1.2 A Submartingale Property
13.1.3 Learning from Each Other
13.2 A Discrete-Time Model
13.3 Structure of Optimal Contracts
13.4 First Best
13.5 Second Best
13.6 Notes
13.7 Exercises
References
14 Contracting Under Ambiguity in Continuous Time
14.1 The Principal-Agent Problems
14.2 Representation of Admissible Contracts
14.2.1 Why the K Process and the Submartingale Property?: A Digression
14.3 First-Best Contracting
14.4 Second-Best Contracting
14.4.1 Incentive Compatibility
14.4.2 Principal's Problem
14.5 The Linear-Quadratic Case
14.6 Notes
14.7 Exercises
References
Part IV Contracting in the Presence of Information Asymmetry
15 Information Asymmetry: Hidden Information
15.1 The Model
15.2 Hidden Effort and Project Decisions Under Hidden Information
15.2.1 The Principal's Problem
15.2.2 Numerical Simulation
15.3 Notes
15.4 Exercises
References
16 Information Asymmetry: Adverse Selection
16.1 The Model: Pure Adverse Selection
16.2 The Two-Type Case
16.2.1 First Best
16.2.2 Second Best
16.2.3 Intuition
16.3 Continuum of Types
16.4 Notes
References
17 Information Asymmetry: Adverse Selection and Moral Hazard
17.1 A Discrete-Time Model
17.1.1 Project Selection
17.2 A Continuous-Time Model
17.3 Principal's Problem
17.4 Notes
References
Appendix A Review on Some Stochastic Control Methods
A.1 A Brief Review on Stochastic Calculus
A.2 Dynamic Programming Equation with Exponential Utility
A.3 Martingale Method
A.3.1 Integral Objective
A.3.2 Exponential Objective
A.3.2.1 Volatility Control Under Strong Formulation
A.4 Mean-Volatility Control Problem in Weak Formulation
A.4.1 Admissible Probability Measures
A.4.2 The Mean-Volatility Control Problem
References
Author Index
Subject Index