Dynamic Principal Agent Models: A Continuous Time Approach Introduction

Dynamic Principal Agent Models: A Continuous Time Approach

Introduction

Florian Ho¤mann Sebastian Pfeil

Stockholm April 2012

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Organizational Issues

I Ph.D. "Mini-Course".

I Schedule: Mon - Thu 10:15-12:00 and 14:15-17:00.

I Contact: fho¤mann(at)…nance.uni-frankfurt.de and pfeil(at)…nance.uni-frankfurt.de.

I Course webpage: www.sebastianpfeil.de/teaching/dynamicsse.

I Course requirements:

I Class participation,

I Referee report on a paper from reading list and/or problem set.

What is it about?

I Course covers new continuous time methods to study dynamic incentive problems.

I Focus on selective topics rather than an exhaustive overview of the dynamic contracting literature.

I The goal is to

I learn new methods,

I get to know some recent applications of these methods with a focus on corporate …nance,

I be able to do own research in this …eld.

Dynamic Agency Models

I "Standard" dynamic agency models:

I Agent takes hidden action in time periods 1, 2, 3, ... or continuously.

I Output depends on agent’s hidden action.

I Principal observes output and can commit to a contract that speci…es payments to the agent as a function of output history.

I Alternatively: Agent privately observes output and can divert part of it for consumption. Payments then depend on history of reported output.

I Problem: Find contract maximizing principal’s pro…t subject to giving agent a desired level of utility.

I Advantages of continuous time approach:

I clean, computationally simple characterization (also easily solved on

Dynamic Agency Models

I The continuous time methods studied in this course (and closely related ones) have found important applications in various …elds:

I corporate …nance (e.g. executive compensation, capital structure and security design, corporate investment, mortgage lending),

I personnel economics (e.g. labor contracts),

I health economics,

I macroeconomics (e.g. economic growth/development, macro-…nance, …rm dynamics),

I repeated games and reputation.

I We focus on corporate …nance applications.

Dynamic Financial Contracting

I Large fraction of corporate …nance literature focusses on con‡icts of interests arising between investors and managers/entrepreneurs.

I Financial Contracting literature characterizes optimal contracts designed to mitigate these agency con‡icts.

I So far, most of these corporate …nance models are framed in static frameworks.

I However, …nancial contracting is inherently dynamic:

!Need for dynamic …nancial contracting models.

The Need for Dynamic Financial Contracting Models

I Corporate …nance data usually dynamic:

I Time series of cash ‡ows, balance sheet variables, history of dividend payments, security issuance,...

I Dynamic models are needed to confront theory with this data.

I How robust are predictions of static models in a dynamic setting?

I What restrictions do dynamic models put on time-series data?

The Need for Dynamic Financial Contracting Models

I Corporate Finance studies design and issuance of securities:

I So far mostly using static models.

I Asset pricing is concerned with the dynamics of their valuations:

I Generally dynamic and mostly in continuous time.

I How do agency con‡icts a¤ect both security design and pricing?

Overview of the Course

I Lecture 1:

I Refresher of discrete time dynamic moral hazard.

I Introduce basic continuous time principal agent model.

I Standard hidden action model with risk averse agent.

I Overview results from stochastic calculus needed to solve continuous time incentive problems.

I Based on Sannikov (2008).

I Lecture 2:

I Introduce the workhorse model for …nancial contracting.

I Cash ‡ow diversion model with risk neutral agent protected by limited liability.

I Derive optimal contract, provide capital structure implementation, discuss asset pricing implications and show how to do comparative statics.

I Based on DeMarzo and Sannikov (2006) and Biais et al. (2007).

Overview of the Course

I Lecture 3:

I Show relation of workhorse model to discrete time approaches.

I Solve for optimal contract in static and discrete time model and discuss its properties.

I Show convergence of optimal contract in the continuous time limit.

I Based on Biais et al. (2007) and Biais et al. (2011).

I Remaining Time: Extensions and Applications

I Managerial compensation: He (2009), Ho¤mann and Pfeil (2010),

I Investment: DeMarzo et al. (2011), Ho¤mann and Pfeil (2012),

I Corporate Governance/ monitoring: Piskorski and Wester…eld (2011),