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"]