Contract Theory in Continuous-Time Models


Book 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.




On Sannikov's Continuous-Time Principal-Agent Problem


Book Description

The principal-agent problem is a classic problem in economics, in which the principal seeks an optimal way to delegate a task to an agent that has private information or hidden action. A general continuous-time stochastic control problem based on the moral hazard problem in Sannikov (2008) is considered, with more general retirement cost and structure. In the problem, a risk-neutral principal tries to determine an optimal contract to compensate a risk-averse agent for exerting costly and hidden effort over an infinite time horizon. The compensation is based on observable output, which has a drift component equal to the hidden effort and a noise component driven by a Brownian motion. In this thesis, a rigorous mathematical formulation is posed for the problem, which is modeled as a combined optimal stopping and control problem. Conditions are given on how a solution to the control problem could be implemented as a contract in the principal-agent framework with moral hazard. Our formulation allows for general continuous retirement profit functions, subject to an upper bound by the first-best profit. The optimal profit function is studied and proved to be concave and continuous. It is shown that the optimal profit function is the unique viscosity solution of the Hamilton-Jacobi-Bellman (HJB) equation.




Contract Theory in Continuous-Time Models


Book 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.




Principal-Agent Analysis in Continuous-Time


Book Description

The principal-agent problems in continuous-time with general utilities are analyzed. We show that, when the agent's utility function is separable over income and action, the principal-agent problems can be converted to standard dynamic optimization ones over a space of controlled processes, which again can be further reduced to solving static optimization problems over the space of probability measures via the Martingale approach. The optimal contract is explicitly characterized and is shown to be a nonlinear function of some linear aggregates when the underlying cost function of probability measure is separable. Comparative statics analysis is performed and various applications are given in specific situations. In terms of model tractability, the analysis of the paper can be best understood as the nonlinear analogue of Holmstrom and Milgrom (1987).




Contract Theory in Continuous-Time Models


Book 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.




Optimal Contracts Under Moral Hazard and Adverse Selection


Book Description

In spite of the importance of optimal contracting problems under moral hazard and adverse selection, current literature offers no optimal solutions to contracting problems under moral hazard and adverse selection with risk averse agents. The agent's risk aversion, however, appears to be critical for understanding managerial compensation problems. We present a continuous-time agency model with a risk-averse agent and a risk-neutral principal to show that moral hazard and adverse selection can be optimally resolved with a menu of linear contracts. In application, we discuss a few managerial compensation problems involving managerial project selection and capital budgeting decisions, and show that a flat-wage contract is sometimes optimal.




The Theory of Incentives


Book Description

Economics has much to do with incentives--not least, incentives to work hard, to produce quality products, to study, to invest, and to save. Although Adam Smith amply confirmed this more than two hundred years ago in his analysis of sharecropping contracts, only in recent decades has a theory begun to emerge to place the topic at the heart of economic thinking. In this book, Jean-Jacques Laffont and David Martimort present the most thorough yet accessible introduction to incentives theory to date. Central to this theory is a simple question as pivotal to modern-day management as it is to economics research: What makes people act in a particular way in an economic or business situation? In seeking an answer, the authors provide the methodological tools to design institutions that can ensure good incentives for economic agents. This book focuses on the principal-agent model, the "simple" situation where a principal, or company, delegates a task to a single agent through a contract--the essence of management and contract theory. How does the owner or manager of a firm align the objectives of its various members to maximize profits? Following a brief historical overview showing how the problem of incentives has come to the fore in the past two centuries, the authors devote the bulk of their work to exploring principal-agent models and various extensions thereof in light of three types of information problems: adverse selection, moral hazard, and non-verifiability. Offering an unprecedented look at a subject vital to industrial organization, labor economics, and behavioral economics, this book is set to become the definitive resource for students, researchers, and others who might find themselves pondering what contracts, and the incentives they embody, are really all about.







Optimal Contracts Under Adverse Selection and Moral Hazard


Book Description

This article presents a continuous-time agency model in the presence of adverse selection and moral hazard with a risk-averse agent and a risk-neutral principal. Under the model setup, we show that the optimal controls are constant over time, and thus the optimal menu consists of contracts that are linear in the final outcome. We also show that when a moral hazard problem adds to an adverse selection problem, the monotonicity condition well known in the pure adverse selection literature needs to be modified to ensure the incentive compatibility for information revelation. The model is applied to a few managerial compensation problems involving managerial project selection and capital budgeting decisions. We argue that in the third-best world, the relationship between the volatility of the outcome and the sensitivity of the contract depends on interactions between the managerial cost and the firm`s production functions. Contrary to conventional wisdom, sometimes the higher the volatility, the higher the sensitivity of the contract. The firm receiving good news sometimes chooses safer projects or invests less than it does with bad news. We also examine the effects of the observability of the volatility on corporate investment decisions.