Paper: arXiv 2410.01352

Abstract

This paper studies an asset pricing model in a partially observable market with a large number of heterogeneous agents using the mean field game theory. In this model, we assume that investors can only observe stock prices and must infer the risk premium from these observations when determining trading strategies. We characterize the equilibrium risk premium in such a market through a solution to the mean field backward stochastic differential equation (BSDE). Specifically, the solution to the mean field BSDE can be expressed semi-analytically by employing an exponential quadratic Gaussian framework. We then construct the risk premium process, which cannot be observed directly by investors, endogenously using the Kalman-Bucy filtering theory. In addition, we include a simple numerical simulation to visualize the dynamics of our market model.

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 dense with advanced mathematics, including mean field backward stochastic differential equations (BSDEs), Kalman-Bucy filtering, and exponential quadratic Gaussian (EQG) frameworks, which demand a high level of mathematical sophistication. However, it lacks empirical rigor as it contains only a simple numerical simulation for visualization, with no backtesting, real market data, or performance metrics.

Research Flowchart

  flowchart TD
  Start["Research Goal: Model asset pricing in a partially observable market with many agents"] --> Methodology["Methodology: Mean Field Game Theory"]
  
  Methodology --> Inputs["Inputs: Stock prices & volatility"]
  
  Inputs --> Process1["Process 1: Kalman-Bucy Filtering"]
  Process1 --> Process2["Process 2: Mean Field BSDE Solution<br/>via Exponential Quadratic Gaussian"]
  
  Process2 --> Outputs["Computational Outcome<br/>Endogenous Risk Premium Process"]
  
  Outputs --> Findings["Key Findings: Semi-analytical equilibrium<br/>Risk premium inferred from prices<br/>Numerical simulation visualization"]