Paper: arXiv 2406.02155

Abstract

This paper presents an asset pricing model in an incomplete market involving a large number of heterogeneous agents based on the mean field game theory. In the model, we incorporate habit formation in consumption preferences, which has been widely used to explain various phenomena in financial economics. In order to characterize the market-clearing equilibrium, we derive a quadratic-growth mean field backward stochastic differential equation (BSDE) and study its well-posedness and asymptotic behavior in the large population limit. Additionally, we introduce an exponential quadratic Gaussian reformulation of the asset pricing model, in which the solution is obtained in a semi-analytic form.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper is mathematically dense, involving advanced concepts like mean field games, quadratic-growth BSDEs, and probabilistic reformulations, but it presents a theoretical model without empirical data, backtesting, or implementation details.

Research Flowchart

  flowchart TD
  A["Research Goal: Develop Asset Pricing Model with Habit Formation"] --> B["Model Setup: Incomplete Market & Heterogeneous Agents"]
  B --> C["Methodology: Mean Field Game Theory & BSDE"]
  C --> D["Key Inputs: Population Size N & Habit Formation"]
  D --> E["Computational Process: Quadratic-Growth BSDE & Asymptotic Analysis"]
  E --> F["Reformulation: Exponential Quadratic Gaussian Formulation"]
  F --> G["Outcome: Market-Clearing Equilibrium Solution"]
  G --> H["Result: Semi-Analytic Solution for Asset Prices"]

Cited References (42)

  1. Mean-Field Equilibrium Price Formation With Exponential Utility — → 2304.07108
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  4. A Random-Supply Mean Field Game Price Model (2021) — link
  5. Equilibrium Price Formation with a Major Player and its Mean Field Limit (2021) — link
  6. Strong Convergence to the Mean Field Limit of a Finite Agent Equilibrium (2020) — link
  7. Mean Field Exponential Utility Game: A Probabilistic Approach (2020) — link
  8. A mean‐field game approach to equilibrium pricing in solar renewable energy certificate markets (2020) — link
and 34 more
  1. A Mean Field Game Approach to Equilibrium Pricing with Market Clearing Condition (2020) — link
  2. A mean field game price model with noise (2020) — link
  3. A Mean-Field Game Approach to Price Formation (2020) — link
  4. Probabilistic Theory of Mean Field Games with Applications II: Mean Field Games with Common Noise and Master Equations (2018) — link
  5. Probabilistic Theory of Mean Field Games with Applications I: Mean Field FBSDEs, Control, and Games (2018) — link
  6. Stochastic Differential Equations, Backward SDEs, Partial Differential Equations (2014) — link
  7. Making mean-variance hedging implementable in a partially observable market (2013) — link
  8. Financial Asset Pricing Theory (2013) — link
  9. Forward-Backward Stochastic Differential Equations and Controlled McKean Vlasov Dynamics (2013) — link
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  15. Fundamentals of Stochastic Filtering (2008) — link
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  32. Price formation in financial markets: a game-theoretic perspective
  33. (iv) X 10 is an R -valued, bounded, and F 10 -measurable random variable representing agent-1’s initial stock of habits
  34. Principal agent mean field games in Renewable Energy

1 of 42 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.