arXiv research

Characterizes critical points in convex double and triple bubbles.

Survey on soap bubble partitions and their stability.

An elementary proof found for the double bubble problem in a specific norm.

Continuous time analysis of bubble formation in harmonic maps.

The generalized soap bubble problem seeks the least perimeter way to enclose and separate n given volumes in R^m. We study the possible configurations for perimeter minimizing bubble complexes enclosing more than two regions. We prove that perimeter minimizing planar bubble complexes with equal pressure regions and wit…

Solves the quintuple bubble problem on spheres and Euclidean spaces.

Hexagonal norm double bubble problem solved with minimal configurations.

We propose two rational expectation models of transient financial bubbles with heterogeneous arbitrageurs and positive feedbacks leading to self-reinforcing transient stochastic faster-than-exponential price dynamics. As a result of the nonlinear feedbacks, the termination of a bubble is found to be characterized by a …

Episodes of market crashes have fascinated economists for centuries. Although many academics, practitioners and policy makers have studied questions related to collapsing asset price bubbles, there is little consensus yet about their causes and effects. This review and essay evaluates some of the hypotheses offered to …

The bubble is a controversial and important issue. Many methods which based on the rational expectation have been proposed to detect the bubble. However, for some developing countries, epically China, the asset markets are so young that for many companies, there are no dividends and fundamental value, making it difficu…

A new model detects financial bubbles with high accuracy.

Identifying unambiguously the presence of a bubble in an asset price remains an unsolved problem in standard econometric and financial economic approaches. A large part of the problem is that the fundamental value of an asset is, in general, not directly observable and it is poorly constrained to calculate. Further, it…

The paper models cryptocurrency market bubbles using agent-based models.

The paper proves rigidity results for Serrin-type problems in manifolds.

Bubbles are essential in certain economic models with high growth and low interest rates.

We address the double bubble problem for the anisotropic Grushin perimeter $P_α$, $α\geq 0$, and the Lebesgue measure in $\mathbb R^2$, in the case of two equal volumes. We assume that the contact interface between the bubbles lays on either the vertical or the horizontal axis. Since no regularity theory is available i…

Inspired by the question of identifying the start time $τ$ of financial bubbles, we address the calibration of time series in which the inception of the latest regime of interest is unknown. By taking into account the tendency of a given model to overfit data, we introduce the Lagrange regularisation of the normalised …

Study Yang-Mills connections on four-manifolds, derive obstructions to bubbling.

Rational bubbles form in nonstationary models of real assets.

Existence of double bubbles with high constant mean curvatures in Riemannian manifolds.

It is shown that $m$ disjoint sets with fixed Gaussian volumes that partition $\mathbb{R}^{n}$ with minimum Gaussian surface area must be $(m-1)$-dimensional. This follows from a second variation argument using infinitesimal translations. The special case $m=3$ proves the Double Bubble problem for the Gaussian measure,…

Defines speculative bubbles in discrete-time models based on discounted stock price losing mass.

Degenerate solutions found in 2D H-system bubbles with higher degrees.

New cylindrical solutions found for Grushin-type problem.

There are two major streams of literature on the modeling of financial bubbles: the strict local martingale framework and the Johansen-Ledoit-Sornette (JLS) financial bubble model. Based on a class of models that embeds the JLS model and can exhibit strict local martingale behavior, we clarify the connection between th…

This is the third installment of the Financial Bubble Experiment. Here we provide the digital fingerprint of an electronic document in which we identify 27 bubbles in 27 different global assets; for 25 of these assets, we present windows of dates of the most likely ending time of each bubble. We will provide that docum…

On 2 November 2009, the Financial Bubble Experiment was launched within the Financial Crisis Observatory (FCO) at ETH Zurich (\url{http://www.er.ethz.ch/fco/}). In that initial report, we diagnosed and announced three bubbles on three different assets. In this latest release of 23 December 2009 in this ongoing experime…

Trading bubbles form when traders adapt to price mismatches.

This is the second installment of the Financial Bubble Experiment. Here we provide the digital fingerprint of an electronic document in which we identify 7 bubbles in 7 different global assets; for 4 of these assets, we present windows of dates of the most likely ending time of each bubble. We will provide that documen…

Using a recently introduced rational expectation model of bubbles, based on the interplay between stochasticity and positive feedbacks of prices on returns and volatility, we develop a new methodology to test how this model classifies 9 time series that have been previously considered as bubbles ending in crashes. The …

Paper evaluates whether AI is a bubble or a productivity revolution.

Study index bounds for harmonic maps sequences with bubbles.

Study on metric bubbles in complex dimensions 1 and 2.

Modeling stochastic arbitrage bubbles in Black-Scholes framework.

We present an advance bubble detection methodology based on the Log Periodic Power Law Singularity (LPPLS) confidence indicator for the early causal identification of positive and negative bubbles in the Chinese stock market using the daily data on the Shanghai Shenzhen CSI 300 stock market index from January 2002 thro…

Study predicts NFT bubbles using LPPL model.

Study asset price bubbles in markets with short sales prohibitions and model uncertainty.

Study p-Laplacian equation on Riemannian manifolds with positive Ricci curvature.

Study reveals investor behavior in NFT bubbles.

Study of immersions with Willmore energy leading to spherical and catenoid bubbles.

By combining (i) the economic theory of rational expectation bubbles, (ii) behavioral finance on imitation and herding of investors and traders and (iii) the mathematical and statistical physics of bifurcations and phase transitions, the log-periodic power law (LPPL) model has been developed as a flexible tool to detec…

Example of spacetime with causal bubbling, splitting into timelike and spacelike parts.

In the past decade, Bitcoin as an emerging asset class has gained widespread public attention because of their extraordinary returns in phases of extreme price growth and their unpredictable massive crashes. We apply the log-periodic power law singularity (LPPLS) confidence indicator as a diagnostic tool for identifyin…

A general theory of innovation and progress in human society is outlined, based on the combat between two opposite forces (conservatism/inertia and speculative herding "bubble" behavior). We contend that human affairs are characterized by ubiquitous ``bubbles'', which involve huge risks which would not otherwise be tak…

The Johansen-Ledoit-Sornette (JLS) model of rational expectation bubbles with finite-time singular crash hazard rates has been developed to describe the dynamics of financial bubbles and crashes. It has been applied successfully to a large variety of financial bubbles in many different markets. Having been developed fo…

The classic double bubble theorem says that the least-perimeter way to enclose and separate two prescribed volumes in $\mathbb{R}^N$ is the standard double bubble. We seek the optimal double bubble in $\mathbb{R}^N$ with density, which we assume to be strictly log-convex. For $N=1$ we show that the solution is sometime…

We explore geometric aspects of bubble convergence for harmonic maps. More precisely, we show that the formation of bubbles is characterised by the local excess of curvature on the target manifold. We give a universal estimate for curvature concentration masses at each bubble point and show that there is no curvature l…

We introduce a mathematical criterion defining the bubbles or the crashes in financial market price fluctuations by considering exponential fitting of the given data. By applying this criterion we can automatically extract the periods in which bubbles and crashes are identified. From stock market data of so-called the …