June 27 to July 12, 2023
This intensive online summer school brings students to the frontier of modern continuous time modeling techniques at the intersection between macroeconomics, monetary economics, and (international) finance. The aim of this course is to develop and teach advanced tools and includes a step-by-step solution procedure that students can apply to a variety of economic problems.
The course is designed for Ph.D students in economics, finance, and related fields. The course is suitable for first year PhD students.
Participating students must be nominated by their Ph.D. advisor. However, this course is no longer taking nominations.
Flipped classroom setting:
- Students watch online lectures at their preferred time.
- Review sessions are held simultaneously for all participants at 11 a.m. (Eastern Time), 17:00 (European Time).
- Participating students are expected to solve and submit problem sets. They are also allowed to do it in small groups.
- Students that perform well on problem sets are eligible to attend the Princeton Initiative 2023 in Princeton from September 8-10.
- Receive a certificate of participation from Markus
Outline, Timing and Links:
1. Why Continuous Time Modeling
2. Continuous Time Stochastic Optimization (Consumption, Portfolio)
3. A Simple Macro-Finance Model with Heterogeneous Agents
4. Endogenous Risk Dynamics with Log utility
5. Monetary Models with one Sector
- 10video_b_constant idiosyncratic risk
- 10video_c_FTPL_stochastic idiosyncratic risk (optional)
- Problem Set with Idiosyncratic Risk and Money
- Review Session: Friday Jul 7, 2023
6. Numerical Methods and Value Function Iteration
Videos by Yuliy Sannikov
- Introduction: General Class of Equations
- Example: Valuation Equation and HJB
- Forward and Backward Equations: HJB, KFE
- Finite Difference Schemes: Key Principles
- Finite Difference Operator and sign of Matrix M
- Explicit Scheme
- Implicit Scheme
- Stationary Value Function in a Single Step
- KFE using Matrix M
- General Class of HJB in One Dimension
- Solving HJB
Videos by Andrey Alexandrov
 This is not an official degree from Princeton University.