Paper: arXiv 2311.15793

Authors: Francesca Biagini, Andrea Mazzon, Thilo Meyer-Brandis, Katharina Oberpriller

Abstract

This is a supplement to the paper “Liquidity based modeling of asset price bubbles via random matching”. The supplement is organized as follows. First, we prove Theorem 3.13 in [1] which provides the existence of the dynamical system D introduced in Definition 3.6 in [1]. Second, we show some properties of D which are summarized in Theorem 3.14 in [1]. In the following, we only state the basic setting and refer to [1] for definitions.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 1.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: This supplementary paper is purely theoretical, providing rigorous mathematical proofs for dynamic systems and asset price bubble modeling established in the main paper. While it features high mathematical complexity, it completely lacks empirical validation or backtesting.

Research Flowchart

  flowchart TD
    A[Research Goal: Validate Dynamical System D for Asset Price Bubbles] --> B[Inputs: Basic Settings & Definitions from Primary Paper]
    B --> C[Methodology: Random Matching & Liquidity-Based Modeling]
    C --> D[Mathematical Proof: Existence of Dynamical System D]
    C --> E[Property Analysis: Structural Behaviors of System D]
    D --> F[Outcome: Proof of Theorem 3.13]
    E --> G[Outcome: Proof of Theorem 3.14 Properties]

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