40  Session 31: Research Frontiers · Course Synthesis

Unit 5 — Split Track (final session before reunification)
Book Chapter 21 (Future Research Directions)
Track 1 source Class 26 (Research Frontiers) + Classes 28-29 (advanced)
Track 2 source Class 26 + Classes 28, 29 (Neural SDE, Network)
Assessment milestone PS4 due (start of class)
ImportantPS4 due today

Submit PS4 (track-specific) at the start of class. Late penalty applies per syllabus.

40.1 Both Tracks: Course Synthesis (Common 30 Minutes)

Tracks meet together for the first 30 minutes for course synthesis, then split for track-specific frontier discussion.

40.1.1 Common Synthesis Slide Briefs

Slide 31.1 — Title

  • Title: “Research Frontiers and Course Synthesis”
  • Subtitle: “Where the framework goes next · What you’ve built”

Slide 31.2 — What You’ve Built (Course Arc)

  • Title: “The 32-session arc, summarized”
  • Visual: Timeline showing all 32 sessions with milestone markers
  • Five units:
    • Unit 1 (Sessions 1–5): Why DCF fails ✓
    • Unit 2 (Sessions 6–10): Measurement + theory ✓
    • Unit 3 (Sessions 11–18): Decision + application ✓
    • Unit 4 (Sessions 19–24): Math intuition bridges ✓
    • Unit 5 (Sessions 25–31): Split track ✓
  • Capstone (Session 32): Project presentations

Slide 31.3 — Key Takeaways for Both Tracks

  • Title: “What every student should walk away with”
  • Conceptual:
    • DCF systematically misvalues private market assets
    • Liquidity is stochastic and collectively determined
    • Jensen bias is real and computable
    • The McKean-Vlasov externality creates ~2.3%/yr welfare loss
  • Practical:
    • GE-LAV provides valuation, exit, portfolio, regulatory tools
    • Asset class differences matter (PE, VC, infrastructure, credit)
    • Cross-asset hedge demand is large in stress
  • Strategic:
    • The valuation hierarchy DCF ⊊ LAV ⊊ GE-LAV is provably strict
    • Adoption will happen gradually
    • Track 1 students will work with this framework; Track 2 students will extend it

Slide 31.4 — The Most Important Numbers

  • Title: “Numbers worth memorizing”
  • OU calibration: \(\kappa = 0.45\)/yr, \(\sigma_L = 0.32\), \(\bar{L} = 1.0\)
  • Jensen bias 5/10/15/20 yr: 0.8%/1.7%/2.5%/3.6% (affine approx) or 2.0%/6.2%/11.6%/15.0% (closed-form)
  • Crisis amplification: 4.31×
  • Welfare gap: ~2.3%/yr
  • Hedge demand at normal: ~8 percentage points

40.2 Track 1: Practitioner Frontiers (45 Additional Minutes)

40.2.1 Track 1 Learning Objectives

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

  1. Identify the most promising practitioner applications of GE-LAV expected over next 5 years.
  2. Discuss the institutional adoption barriers and how they may be overcome.
  3. Recognize the open practitioner questions (regime detection, multi-asset extensions, calibration improvements).

40.2.2 Track 1 Slide Briefs

Slide T1-31.1 — Adoption Trajectory

  • Title: “How GE-LAV will be adopted”
  • Phase 1 (next 1–2 years): Academic adoption and citation
  • Phase 2 (3–5 years): Voluntary adoption by sophisticated LPs (pensions, sovereign wealth funds)
  • Phase 3 (5–10 years): Regulatory inclusion (Solvency II review cycles, IPEV updates)
  • Phase 4 (10+ years): Standard methodology, replacing DCF as default

Slide T1-31.2 — Open Practitioner Questions

  • Title: “What practitioners need next”
  • Real-time regime detection:
    • When has the calibration changed? Is the current \(L_t\) stable or transient?
    • Statistical tools for regime identification needed
  • Multi-asset extensions:
    • GE-LAV calibrated independently per asset class
    • Cross-asset coupling needs more empirical work
  • Synthetic exposures:
    • GP-led continuation funds, NAV loans, structured secondaries
    • GE-LAV applies in principle; need clean implementations

Slide T1-31.3 — Career Implications

  • Title: “Where this knowledge fits in your career”
  • For LP allocators:
    • Defensible methodology for IC decisions
    • Better stress testing
    • Tactical allocation framework
  • For GPs:
    • Better valuation methodology
    • LP relationship management
    • Continuation fund pricing
  • For consultants and advisors:
    • Differentiated analytical capability
    • Regulatory advisory work
  • For regulators:
    • Quantitative basis for stress testing
    • Pigouvian-style policy proposals

40.3 Track 2: Research Frontiers (45 Additional Minutes)

40.3.1 Track 2 Learning Objectives

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

  1. Identify the most promising theoretical extensions of GE-LAV (jumps, multi-asset, neural SDE).
  2. Articulate open research questions in MFG theory applied to private markets.
  3. Recognize the connection between GE-LAV and adjacent research areas (systemic risk, optimal execution, central clearing).

40.3.2 Track 2 Slide Briefs

Slide T2-31.1 — Theoretical Extensions

  • Title: “Where GE-LAV theory is incomplete”
  • Jump-diffusion extension:
    • Compound Poisson jumps in \(L_t\) (Lévy OU)
    • Book Ch. 13 sketches; full theory still developing
  • Multi-asset GE-LAV:
    • Coupled mean-field equilibria across asset classes
    • Open: existence theorem for the multi-asset system
  • Neural SDE calibration:
    • Data-driven parameter estimation using neural networks
    • Class 29 covers; more research needed

Slide T2-31.2 — Open Research Questions

  • Title: “What’s not yet known”
  • Quantitative open questions:
    • Stability boundaries (when does \(\kappa > \gamma\) fail in practice?)
    • Rate of convergence for finite-N MFG
    • Robust calibration under regime uncertainty
  • Methodological open questions:
    • When to use master equation vs. simulations
    • High-dimensional generalizations
  • Empirical open questions:
    • Test the Pigouvian tax welfare gap empirically
    • Cross-validate calibration on subsamples

Slide T2-31.3 — Connections to Adjacent Fields

  • Title: “GE-LAV in the broader research landscape”
  • Systemic risk literature:
    • GE-LAV provides an asset-pricing companion to Acemoglu et al. network models
  • Optimal execution:
    • Similar fixed-point structure (impact depends on flow, flow depends on impact)
    • Adapt MFG techniques across both areas
  • Central clearing literature:
    • GE-LAV-style Pigouvian instruments analog to default fund / margin requirements
  • Climate finance:
    • Long-duration risk pricing; transition risk dynamics

Slide T2-31.4 — Career Implications for Researchers

  • Title: “Where this matters for research careers”
  • PhD students:
    • Thesis topics in MFG, private market valuation, systemic risk
    • Connection to leading research (Carmona, Delarue, Lasry, Lions)
  • Academic finance:
    • Empirical papers on the Jensen bias, welfare gap
    • Theoretical papers on extensions
  • Quant researchers:
    • Implementation of master equation
    • Calibration techniques

40.4 Both Tracks: Pre-Session 32 Preparation

40.4.1 What’s Due Session 32

  • Final paper: 20 pages excluding references and appendices
  • Project presentation: 20 min + 5 min Q&A
  • Submit: Both via course site by start of Session 32

40.4.2 Last-Minute Project Preparation

  • Re-read your draft: Address every peer review comment
  • Sleep before the presentation: Prepared and rested beats stressed and over-prepared
  • Bring backup: Print slides AND have them on a USB; technology fails
  • Time yourself: 20 minutes is fast; rehearse exactly to time

40.4.3 Session 32 Logistics

  • Location: [TBD] — confirm room assignment via course site
  • Order: Random selection on day of session
  • Q&A: 5 minutes — every Q&A is graded
  • After all presentations: Brief course synthesis and farewell

40.4.4 Office Hours

  • This week: Extended office hours available
  • Schedule via course site calendar
  • Limit: 30 minutes per student to allow access for everyone

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