35  Session 26: Split Track — VC & Secondaries / McKean-Vlasov MFG Proofs

Unit 5 — Split Track
Track 1 source Class 27 (Multi-Asset, adapted for VC) + new
Track 2 source Classes 8 (McKean-Vlasov) + 15 (MFG Fixed Point)

35.1 Track 1: VC + Secondaries Valuation Lab

35.1.1 Track 1 Learning Objectives

By the end of this session, Track 1 students will be able to:

  1. Apply GE-LAV to a venture capital fund position (different cash flow profile from buyout).
  2. Adjust the calibration for asset classes with thinner secondary market data.
  3. Value a specific VC secondary opportunity using GE-LAV.
  4. Distinguish LP-led from GP-led secondary structures and apply GE-LAV to each.
  5. Communicate findings to a hypothetical VC GP and IC.

35.1.2 Track 1 Pre-Class Assignment

  • Read: VC secondary case (distributed); skim recent Lazard or Evercore VC secondary report
  • Try: Platform exercise on a sample VC position

35.1.3 Track 1 In-Class Outline (75 minutes)

Time Segment Format
0:00–0:10 VC vs. buyout: cash flow profile differences Lecture
0:10–0:25 Calibrating GE-LAV for VC (parameter adjustments) Lecture + worked example
0:25–0:50 Lab: value a real VC secondary opportunity Group work
0:50–1:05 LP-led vs. GP-led secondaries Lecture + discussion
1:05–1:15 Group recommendations + synthesis Presentations

35.2 Track 2: McKean-Vlasov Mean-Field Game Proofs

35.2.1 Track 2 Learning Objectives

By the end of this session, Track 2 students will be able to:

  1. State and prove the propagation of chaos for the GE-LAV mean-field system (Theorem 13.4).
  2. Derive the Schauder fixed-point existence argument for MFG equilibrium (Theorem 13.2).
  3. State and verify the stability condition \(\kappa > \gamma\) for uniqueness (Theorem 13.3).
  4. Implement an MFG fixed-point iteration numerically.
  5. Discuss the limits of the framework: when stability fails, what happens.

35.2.2 Track 2 Pre-Class Assignment

  • Read: Book Chapter 13 in full, including all proofs
  • Pre-read: Carmona & Delarue, Probabilistic Theory of Mean-Field Games, Chapter 1 — at least sections 1.1–1.3

35.2.3 Track 2 In-Class Outline (75 minutes)

Time Segment Format
0:00–0:10 Setup: the GE-LAV McKean-Vlasov SDE Lecture
0:10–0:30 Propagation of chaos: statement + proof sketch Lecture
0:30–0:50 Schauder fixed-point: existence of MFG equilibrium Lecture
0:50–1:05 Stability condition and uniqueness Lecture
1:05–1:15 Numerical MFG iteration Code walkthrough

35.2.4 Track 2 Discussion Questions

  1. The propagation of chaos rate is \(1/\sqrt{N}\). At \(N = 10,000\), error is ~1%. But private markets have concentration (a few mega-LPs hold most of the AUM). Does that violate the i.i.d. assumption? How would you account for concentration?
  2. The stability condition \(\kappa > \gamma\) is satisfied empirically. But in a hypothetical “panic” scenario, could the system enter an unstable regime? What would the off-equilibrium dynamics look like?
  3. The MFG framework assumes Markov dynamics. Real markets have memory (regret, anchoring). How would non-Markov extensions change the proofs?

35.3 Both Tracks: Cross-Audit

Students in either track may audit the other track’s session via recording. Track 1 students benefit from hearing the MFG existence proof (it explains why GE-LAV works); Track 2 students benefit from the applied VC case (it grounds the math).

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