36 Session 27: Split Track — Infrastructure Case / Fokker-Planck & Master Equation
| Unit | 5 — Split Track |
| Track 1 source | Class 22 (Infrastructure: The 57% Illusion) |
| Track 2 source | Class 6 (Fokker-Planck Equations) |
36.1 Track 1: Infrastructure Case — “The 57% Illusion”
36.1.1 Track 1 Learning Objectives
By the end of this session, Track 1 students will be able to:
- Apply GE-LAV to a 20+ year infrastructure asset (longest duration in private markets).
- Identify why long-duration assets carry the largest accumulated Jensen bias.
- Compute the “57% illusion” — the gap between DCF and GE-LAV for stressed infrastructure positions.
- Translate GE-LAV findings into pension fund and insurance regulatory language.
- Connect infrastructure valuation errors to systemic financial stability concerns.
36.1.2 Track 1 Pre-Class Assignment
- Read: Book Chapter 22 case (or Class 22 slides if available)
- Optional: Global Infrastructure Hub report on private infrastructure valuation
36.1.3 Track 1 In-Class Outline (75 minutes)
| Time | Segment | Format |
|---|---|---|
| 0:00–0:10 | Why infrastructure is special: duration + cash flow stability | Lecture |
| 0:10–0:25 | The “57% illusion” decomposed | Lecture |
| 0:25–0:55 | Lab: value a real infrastructure asset (Indianapolis Toll Road or comparable) | Group work |
| 0:55–1:15 | Group recommendations + regulatory implications | Presentations |
36.2 Track 2: Fokker-Planck & Master Equation Derivations
36.2.1 Track 2 Learning Objectives
By the end of this session, Track 2 students will be able to:
- Derive the Fokker-Planck equation from the SDE via Chapman-Kolmogorov.
- Prove well-posedness of the GE-LAV Fokker-Planck (Theorem 14.2).
- State and apply the master equation for value functions on Wasserstein space (Theorem 15.1).
- Implement a Fokker-Planck solver for the GE-LAV liquidity state.
- Verify numerical convergence of the FP solution to the analytical stationary distribution.
36.2.2 Track 2 Pre-Class Assignment
- Read: Book Chapters 14, 15 in full (with proofs)
- Pre-read: Pavliotis, Stochastic Processes and Applications, Chapters 4–5; or Risken, The Fokker-Planck Equation, Chapter 4
36.2.3 Track 2 In-Class Outline (75 minutes)
| Time | Segment | Format |
|---|---|---|
| 0:00–0:15 | Derivation of FP from Chapman-Kolmogorov | Lecture + board |
| 0:15–0:35 | Well-posedness (existence + uniqueness): Theorem 14.2 | Lecture |
| 0:35–0:55 | The master equation on Wasserstein space | Lecture |
| 0:55–1:10 | Numerical FP solver | Code walkthrough |
| 1:10–1:15 | Verification: numerical → analytical stationary | Discussion |
36.2.4 Track 2 Discussion Questions
- The FP derivation assumes the transition density is Gaussian at small \(\Delta t\). This holds for Itô SDEs with smooth coefficients. What if there are jumps (Lévy processes)? How does the FP change?
- The master equation is on Wasserstein space — an infinite-dimensional manifold. Numerically, we discretize \(\mu\) on a grid. What’s the discretization error? When does this matter?
- The well-posedness theorem requires nondegeneracy (\(\sigma_L > 0\)). What happens if \(\sigma_L = 0\) (deterministic OU)? Does the framework break down?
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Run your own scenario: Apply the FP-coupled GE-LAV® system to a custom infrastructure asset at liquidityillusion.com.