Book
Vol I. Representative Agent in Asset Pricing
A Continuous-Time General Equilibrium Approach
Origin
This book is part of a research project on heterogeneous agents in asset pricing that I initiated at Arizona State University in 2021. The primary goal is to remove barriers that researchers encounter when delving into this field. To facilitate learning, we divided this research project into two volumes. The first volume, Volume I, is dedicated to the representative agent in asset pricing. It offers a foundation in stochastic calculus, dynamic programming, models involving a representative agent, and a numerical method (finite difference) for solving them. The second volume, Volume II, explores models with heterogeneous agents in asset pricing and the associated numerical methods for solving them.
Philosophy
This book aims to demonstrate how to numerically solve a representative agent model in general equilibrium when time is continuous. Our approach is step-by-step; that is, we carefully illustrate the implementation of the finite difference method and Upwind scheme to solve a dynamic programming problem in asset pricing. In every chapter, when appropriate, we provide Matlab code to replicate the results.
Content
- Chapter 1. Stochastic Processes and Stochastic Calculus. (PDF) (Codes)
- Chapter 2. Dynamic Programming Approach. (PDF) (Codes)
- Chapter 3. Martingale Approach. (PDF) (Codes)
- Chapter 4. Wealth Dynamic. (PDF) (Codes)
- Chapter 5. A General Equilibrium Model With 𝒌 State Variables. (PDF) (Codes)
- Chapter 6. A General Equilibrium Model With CRRA Preferences and 𝒌 State Variables. (PDF) (Codes)
- Chapter 7. A General Equilibrium Model with Log Utility Function and One State Variable. (PDF) (Codes)
- Chapter 8. Solving Numerically the HJB Equation: Foundations. (PDF) (Codes)
- Chapter 9. Solving Numerically the HJB Equation: Examples. (PDF) (Codes)