Paper: arXiv 2307.11340

Authors: Ludovic Tangpi, Shichun Wang

Abstract

In this paper we further extend the optimal bubble riding model proposed by Tangpi and Wang by allowing for price-dependent entry times. Agents are characterized by their individual entry threshold that represents their belief in the strength of the bubble. Conversely, the growth dynamics of the bubble is fueled by the influx of players. Price-dependent entry naturally leads to a mean field game of controls with common noise and random entry time, for which we provide an existence result. The equilibrium is obtained by first solving discretized versions of the game in the weak formulation and then examining the measurability property in the limit. In this paper, the common noise comes from two sources: the price of the asset which all agents trade, and also the exogenous bubble burst time, which we also discretize and incorporate into the model via progressive enlargement of filtration.

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 presents an advanced theoretical framework using mean field games of controls with common noise, progressive enlargement of filtration, and weak formulations to establish an existence result for optimal bubble riding. However, it is entirely theoretical with negligible empirical backtesting or real-world market data validation.

Research Flowchart

  flowchart TD
    A[Research Goal: Model Optimal Bubble Riding with Price-Dependent Entry] --> B[Model Formulation: MFG of Controls with Common Noise & Random Entry]
    C[Model Inputs: Individual Entry Thresholds & Common Noise Asset Price + Burst Time] --> B
    B --> D[Discretization: Weak Formulation & Progressive Enlargement of Filtration]
    D --> E[Limiting Analysis: Measurability & Convergence Analysis]
    E --> F[Outcome: Existence Result for Mean Field Game Equilibrium]