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This article provides a self-contained overview of the theory of rational asset price bubbles. We cover topics from basic definitions, properties, and classical results to frontier research, with an emphasis on bubbles attached to real…

General Economics · Economics 2024-02-05 Tomohiro Hirano , Alexis Akira Toda

In the Cont-Bouchaud model [cond-mat/9712318] of stock markets, percolation clusters act as buying or selling investors and their statistics controls that of the price variations. Rather than fixing the concentration controlling each…

Statistical Mechanics · Physics 2009-10-31 Dietrich Stauffer , D. Sornette

We develop a uniform test for detecting and dating explosive behavior of a strictly stationary GARCH$(r,s)$ (generalized autoregressive conditional heteroskedasticity) process. Namely, we test the null hypothesis of a globally stable GARCH…

Econometrics · Economics 2018-12-11 Stefan Richter , Weining Wang , Wei Biao Wu

We consider the problem of governing systemic risk in a banking system model. The banking system model consists in an initial value problem for a system of stochastic differential equations whose dependent variables are the log-monetary…

Risk Management · Quantitative Finance 2018-12-19 Lorella Fatone , Francesca Mariani

We propose a formulation to construct new classes of financial price processes based on the insight that the key variable driving prices $P$ is the earning-over-price ratio $\gamma \simeq 1/P$, which we refer to as the earning yield and is…

Mathematical Finance · Quantitative Finance 2023-06-21 Li Lin , Didier Sornette

In retrospect, the experimental findings on competitive market behavior called for a revival of the old, classical, view of competition as a collective higgling and bargaining process (as opposed to price-taking behaviors) founded on…

General Finance · Quantitative Finance 2023-07-04 Sabiou Inoua , Vernon Smith

We study a generic model for self-referential behaviour in financial markets, where agents attempt to use some (possibly fictitious) causal correlations between a certain quantitative information and the price itself. This correlation is…

Condensed Matter · Physics 2007-05-23 Matthieu Wyart , Jean-Philippe Bouchaud

We present a exactly soluble model for financial time series that mimics the long range volatility correlations known to be present in financial data. Although our model is `monofractal' by construction, it shows apparent multiscaling as a…

Condensed Matter · Physics 2015-06-25 Jean-Philippe Bouchaud , Marc Potters , Martin Meyer

We develop and justify methodology to consistently test for long-horizon return predictability based on realized variance. To accomplish this, we propose a parametric transaction-level model for the continuous-time log price process based…

Econometrics · Economics 2022-02-03 Meng-Chen Hsieh , Clifford Hurvich , Philippe Soulier

The principal aim of this work is the evidence on empirical way that catastrophic bifurcation breakdowns or transitions, proceeded by flickering phenomenon, are present on notoriously significant and unpredictable financial markets.…

Statistical Finance · Quantitative Finance 2014-02-18 M. Kozłowska , T. Gubiec , T. R. Werner , M. Denys , A. Sienkiewicz , R. Kutner , Z. Struzik

Bubbles in the interstellar medium are produced by astrophysical sources, which continuously or explosively deposit large amount of energy into the ambient medium. These expanding bubbles can drive shocks in front of them, which dynamics is…

High Energy Astrophysical Phenomena · Physics 2015-06-12 M. V. Medvedev , A. Loeb

Catastrophic failures have momentous impact in many scientific and technological fields but remain challenging to understand and predict. One key difficulty lies in the burstiness of rupture phenomena, which typically involve a series of…

Geophysics · Physics 2024-09-19 Qinghua Lei , Didier Sornette

This paper presents a method for forecasting limit order book durations using a self-exciting flexible residual point process. High-frequency events in modern exchanges exhibit heavy-tailed interarrival times, posing a significant challenge…

Statistical Finance · Quantitative Finance 2026-04-02 Kyungsub Lee

We amend and extend the Chiarella model of financial markets to deal with arbitrary long-term value drifts in a consistent way. This allows us to improve upon existing calibration schemes, opening the possibility of calibrating individual…

Trading and Market Microstructure · Quantitative Finance 2026-02-11 Jutta G. Kurth , Adam A. Majewski , Jean-Philippe Bouchaud

A central problem of Quantitative Finance is that of formulating a probabilistic model of the time evolution of asset prices allowing reliable predictions on their future volatility. As in several natural phenomena, the predictions of such…

Statistical Finance · Quantitative Finance 2012-09-25 Fulvio Baldovin , Dario Bovina , Francesco Camana , Attilio L. Stella

We document a well-developed log-periodic power-law antibubble in China's stock market, which started in August 2001. We argue that the current stock market antibubble is sustained by a contemporary active unsustainable real-estate bubble…

Statistical Mechanics · Physics 2008-12-02 W. -X. Zhou , D. Sornette

The onset of turbulence in pipe flow has been a fundamental challenge in physics, applied mathematics, and engineering for over 140 years. To date, the precursor of this laminar-turbulent transition is recognized as transient turbulent…

Fluid Dynamics · Physics 2025-06-10 Jiashun Guan , Jianjun Tao

A rational bubble is a situation in which the asset price exceeds its fundamental value defined by the present discounted value of dividends in a rational equilibrium model. We discuss the recent development of the theory of rational…

Theoretical Economics · Economics 2025-09-03 Tomohiro Hirano , Alexis Akira Toda

Many active funds hold concentrated portfolios. Flow-driven trading in these securities causes price pressure, which pushes up the funds' existing positions resulting in realized returns. We decompose fund returns into a price pressure…

General Finance · Quantitative Finance 2024-05-22 Philippe van der Beck , Jean-Philippe Bouchaud , Dario Villamaina

We propose a clustered local projection (clustered LP) method to estimate impulse response functions in a class of time-varying models where parameter variation is linked to a low-dimensional matrix of observables. We show that the…

Econometrics · Economics 2026-05-04 Ana Maria Herrera , Elena Pesavento , Alessia Scudiero
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