Paper: arXiv 2603.07213

Authors: Matheus R. Grasselli, Adrien Nguyen-Huu

Abstract

We develop a stochastic macro-financial model in continuous time by integrating two specifications of the Keen economic framework with a financial market driven by a jump-diffusion process. The economic block of the model combines monetary debt-deflation mechanisms with Ponzi-type financial destabilization and is influenced by the financial market through a stochastic interest rate that depends on asset price returns. The financial market block of the model consists of an asset with jump–diffusion price process with endogenous, state-dependent jump intensities driven by speculative credit flows. The model formalizes a feedback loop linking credit expansion, crash risk, perceived return dynamics, and bank lending spreads. Under suitable parameter restrictions, we establish global existence and non-explosion of the coupled system. Numerical experiments illustrate how variations in credit sensitivity and jump parameters generate regimes ranging from stable growth to recurrent boom–bust cycles. The framework provides a tractable setting for analyzing endogenous financial fragility within a mathematically well-posed macro–financial system.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous continuous-time mathematical framework integrating Keen’s stock-flow consistent macroeconomic model with jump-diffusion asset pricing processes. While it establishes analytical properties such as non-explosion and provides scenario-based numerical simulations, it lacks empirical validation against real-world data and market backtesting.

Research Flowchart

  flowchart TD
    A[Research Goal: Model endogenous financial fragility <br>and stock bubbles in a macro-financial system] --> B[Integrated Methodology: Combine Keen SFC framework <br>with Jump-Diffusion asset pricing]
    B --> C[Inputs & Drivers: Speculative credit flows, <br>monetary debt-deflation, and state-dependent jump intensities]
    C --> D[Computational Analysis: Analytical proof of global existence <br>& numerical simulation of feedback loops]
    D --> E[Key Outcome 1: Established mathematical well-posedness <br>and non-explosion of coupled system]
    D --> F[Key Outcome 2: Identified regimes ranging from stable <br>growth to recurrent boom-bust cycles]

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