This textbook provides a comprehensive and accessible guide to solving heterogeneous agent models in Economics and Finance, building upon representative agent frameworks. Designed for advanced master's students, Ph.D. candidates, and researchers, it systematically introduces the numerical tools and methods required to solve these models, addressing both idiosyncratic and aggregate risk.

The book is structured in two parts, covering both discrete and continuous time frameworks. Part I focuses on discrete time, introducing foundational concepts such as stochastic optimal control theory and numerical dynamic programming. It covers key computational techniques, including value function iteration, the endogenous gridpoint method, and methods for handling inequality constraints. These tools are then extended to heterogeneous agent models, exploring their mechanics, the law of motion of the agents' distribution, stationary equilibria, transition dynamics, and aggregate risk. Notable models, such as Huggett (1993), Aiyagari (1994), and Krusell-Smith (1998), are thoroughly examined and solved with step-by-step numerical algorithms and visualizations.

Part II transitions to continuous time, enabling the incorporation of more sophisticated stochastic processes. Topics include dynamic programming in continuous time, diffusion and jump diffusion processes, and the numerical methodssuch as finite upwind difference schemesneeded to solve these models.

With a step-by-step approach, this textbook bridges the gap between representative and heterogeneous agent models, providing clear visualizations, numerical algorithms, and solution techniques. Readers will gain not only the computational skills to implement these models but also the insight to select the appropriate framework for their research objectives.

Explains how to solve heterogeneous agent models Visualizes numerical algorithms and solution concepts of heterogeneous agent models Covers both discrete and continuous time frameworks

Autorentext

Patrick Brock is a Ph.D. candidate in Finance at Goethe University Frankfurt (Germany). He holds a B.Sc. and M.Sc. in Economics from Humboldt University Berlin, an M.Sc. in Applied Mathematics from the London School of Economics, and an M.Sc. in Quantitative Economics from Goethe University.

Christian Schlag is a professor of Finance at Goethe University Frankfurt (Germany). He earned an M.Sc. in Economics and Business from the University of Augsburg, an M.A. in Economics from Wayne State University, and a Ph.D. in Business from the University of Karlsruhe (now KIT).

Inhalt

Part I. Discrete Time.- Chapter 1. Stochastic Optimal Control Problems.- Chapter 2. Dynamic Programming.- Chapter 3. Discrete State Space Methods.- Chapter 4. Value Function Iteration.- Chapter 5. First-Order Methods.- Chapter 6. Endogenous Gridpoint Method.- Chapter 7. Heterogeneous Agent Models.- Part II. Continuous Time.- Chapter 8. From Discrete to Continuous Time.- Chapter 9. Dynamic Programming Approach.- Chapter 10. Diffusion Process.- Chapter 11. Jump-Diffusion Process.- Chapter 12. Heterogeneous Agents in Continuous Time.- Chapter 13. Finite Differences.