Characterizes critical points in convex double and triple bubbles.
problem Critical points of double and triple bubbles in convex shapes.
method Characterization through stationary varifolds in Rn and R3. result Characterization of critical points in convex shapes.
Survey on soap bubble partitions and their stability.
problem Characterizing and stabilizing soap bubble partitions.
method Survey and analysis of recent research.
result Recent advancements in multi-bubble isoperimetric minimizers and stability.
Bubbles are essential in certain economic models with high growth and low interest rates.
problem Asset price bubbles exceeding fundamental values.
method Developed the Bubble Necessity Theorem in economic models with specific growth and interest rate conditions.
result Bubbles are inevitable in certain economic scenarios with high growth and low interest rates.
Study Yang-Mills connections on four-manifolds, derive obstructions to bubbling.
problem Bubbling configurations in Yang-Mills fields on four-manifolds.
method Derived Pohozaev type compatibility between weak limit connection and bubbles, involving Weyl tensor.
result Obstructions to certain bubbling configurations on CP2.
Rational bubbles form in nonstationary models of real assets.
problem Understanding the emergence of rational bubbles in real assets.
method Developed economic models showing bubbles inevitably emerge in nonstationary systems.
result Bubbles in real assets are inevitable and can be analyzed using mathematical theorems.
Existence of double bubbles with high constant mean curvatures in Riemannian manifolds.
problem Existence of double bubbles with high constant mean curvatures in Riemannian manifolds.
method Perturbations of geodesic standard double bubbles centered at critical points of the ambient scalar curvature and aligned along eigen-vectors of the ambient Ricci tensor, with general multiplicity results via Lusternik-Schnirelman theory.
result Existence of double bubbles with high constant mean curvatures in Riemannian manifolds.
Defines speculative bubbles in discrete-time models based on discounted stock price losing mass.
problem Characterizing speculative bubbles in discrete-time models.
method Introduces a new definition based on discounted stock price behavior and provides probabilistic characterizations.
result Speculative bubbles in discrete time are linked to solutions of a linear Volterra integral equation.
Degenerate solutions found in 2D H-system bubbles with higher degrees.
problem Existence of degenerate solutions in H-system bubbles with degree ≥ 3.
method Algebraic characterization of degenerate bubbles.
result Degenerate solutions can exist for H-system bubbles with degree ≥ 3.
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…
Continuous time analysis of bubble formation in harmonic maps.
problem Understanding bubble formation in harmonic map heat flow.
method Continuous time approach to analyze bubbling sequences.
result Solutions approach multi-bubble configurations in continuous time.
Trading bubbles form when traders adapt to price mismatches.
problem Self-sustained price bubbles driven by adaptive trading behavior.
method Multi-agent model illustrating price bubble formation and statistical properties.
result Price bubbles can be driven by adaptive investment strategies.
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…
Solves the quintuple bubble problem on spheres and Euclidean spaces.
problem Minimizing total perimeter of multiple bubbles enclosing fixed volumes.
method Developed spectral theory of Jacobi operator and new bubble deformation method.
result Confirmed quintuple bubble conjecture on spheres and Euclidean spaces.
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.
problem Determining if AI investments are a bubble or a sustainable technology.
method Hybrid review and diagnostic framework combining asset pricing foundations and modern econometric methods.
result AI investments show both genuine fundamentals and bubble-like fragilities.
Study on metric bubbles in complex dimensions 1 and 2.
problem Understanding degenerations of Kähler-Einstein metrics.
method Investigation of metric bubble trees for non-collapsing cases.
result Description of a conjectural higher-dimensional picture.
Modeling stochastic arbitrage bubbles in Black-Scholes framework.
problem Analyzing arbitrage bubbles in financial markets.
method Developed a generalized Black-Scholes equation with stochastic arbitrage bubbles.
result The Black-Scholes model is a low-energy limit of a stochastic model.
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.
problem Tackles bubble prediction of NFTs.
method Applied logarithmic periodic power law (LPPL) model to NFT price data.
result NFTs, Decentraland, and ArtBlocks are in bubbles, while Ethereum Name Service is in a negative bubble.
Study asset price bubbles in markets with short sales prohibitions and model uncertainty.
problem Investigating asset price bubbles in markets with short sales prohibitions and model uncertainty.
method Introducing a novel definition of the fundamental price and analyzing the types and characterization of bubbles using a new fundamental theorem of asset pricing and superhedging duality.
result Two distinct types of bubbles arise depending on the maturity structure of the asset, and conditions for their existence are provided.
Study reveals investor behavior in NFT bubbles.
problem Understanding retail investor behavior in asset bubbles.
method Systematic study of NFTs using public blockchain data.
result Sophisticated investors outperform others in NFT bubbles.
Study of immersions with Willmore energy leading to spherical and catenoid bubbles.
problem Classifying immersions with specific energy properties.
method Analyzing sequences of weak immersions with diverging conformal classes, applying Möbius transformations, and strong Wloc2,2-limits. result Obtaining spherical and catenoid bubbles as limits of immersions.
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…
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.
problem Understanding causal bubbling in spacetimes.
method Example of a globally hyperbolic spacetime with a continuous metric, splitting orthogonally into timelike and spacelike parts.
result The synthetic timelike curvature-dimension (TCD) condition does not prevent causal bubbling.
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…
The classic double bubble theorem says that the least-perimeter way to enclose and separate two prescribed volumes in RN is the standard double bubble. We seek the optimal double bubble in RN 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 …
Study describes limits of non-collapsing K3 surfaces using algebraic data.
problem Understanding limits of non-collapsing polarized K3 surfaces.
method Explicit description via period mapping and algebro-geometric data.
result Bubbling limits depend solely on algebro-geometric data.
We introduce the concept of "negative bubbles" as the mirror image of standard financial bubbles, in which positive feedback mechanisms may lead to transient accelerating price falls. To model these negative bubbles, we adapt the Johansen-Ledoit-Sornette (JLS) model of rational expectation bubbles with a hazard rate de…
Study predicts market bubbles using machine learning and financial news sentiment.
problem Predicting market bubbles in the S&P 500 index.
method Three-step approach combining financial news sentiment and macroeconomic indicators.
result Proposed three-step ensemble approach significantly improves bubble prediction accuracy.
Study on asset price dynamics in OLG economies with and without a bubbly asset.
problem Analyzing asset price dynamics and optimality in OLG economies with an asset that yields dividends.
method Deriving conditions for three scenarios of equilibrium existence, providing a complete characterization of the equilibrium set, and investigating the relationship between asset price behaviors and optimality.
result A bubbly equilibrium exists if and only if the interest rate is lower than the population growth rate and the sum of per capita dividends is finite.
There is a growing concern in recent years over the potential formation of bubbles in the Chinese real estate market. This paper aims to conduct a series of bubble diagnostic analysis over nine representative Chinese cities from two aspects. First, we investigate whether the prices had been significantly deviating from…
Study bubbling Kahler metrics using algebraic geometry.
problem Analyzing the degeneration of Kahler metrics with Euclidean volume growth.
method Algebraic construction of birational modifications to simplify degenerations, comparing with analytic constructions.
result Provide a framework to compare algebraic and analytic approaches to bubbling phenomena.
Recent academic work has developed a method to determine, in real time, if a given stock is exhibiting a price bubble. Currently there is speculation in the financial press concerning the existence of a price bubble in the aftermath of the recent IPO of LinkedIn. We analyze stock price tick data from the short lifetime…
Degenerations of rank-two bundles on threefolds lead to isolated point singularities, with rigidity and bubbling properties.
problem Degenerations of rank-two vector bundles on complex threefolds to a rank-two torsion-free sheaf with an isolated point singularity.
method Proving a rigidity identity and using it to obtain smoothability obstructions and construct local smoothings.
result Smoothability obstructions and local smoothings are obtained, with a rigidity identity linking algebraic bubbling multiplicity and Ext-length.
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 …
Modeling financial bubbles and crashes with a cubic momentum function.
problem Capturing the micro-level dynamics of investor behavior and panic selling.
method Introducing a cubic function of market momentum to model trend-following and sudden crashes.
result The model successfully replicates complex, nonlinear bubble dynamics.
Wave maps can have multiple bubbling solutions at blow-up points.
problem Non-uniqueness of bubbling solutions in wave maps.
method Example construction of multiple bubbling solutions.
result First known example of non-uniqueness of bubbling for dispersive equations.
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…
Following our previous investigation of the USA Standard and Poor index anti-bubble that started in August 2000, we analyze thirty eight world stock market indices and identify 21 anti-bubble. An ``anti-bubble'' is defined as a self-fulfilling decreasing price created by positive price-to-price feedbacks feeding overal…
Classifies low energy maps from curved surfaces into spheres.
problem Classifying maps from surfaces of constant curvature into spheres.
method Analyzes maps with low energy and degree ±1, focusing on bubble configurations.
result Maps are quantitively close to a bubble configuration with specific radii.
A new model detects financial bubbles with high accuracy.
problem Quantifying and detecting financial bubbles.
method Hyped Log-Periodic Power Law Model (HLPPL) with sentiment scores and hype index.
result Achieved an average annualized return of 34.13% during backtesting.
Investigates price dynamics of two assets with and without bubbles, deriving conditions for equilibrium prices.
problem Understanding price dynamics and bubbles in multi-asset markets.
method Derives sufficient and necessary conditions for average equilibrium price dynamics in a two-asset model.
result Assets with positive average dividends display hump-shaped bubbles, while those with constant fundamental values show misvaluation effects.
Study on optimal bubble riding with price-dependent entry times in a mean field game model.
problem Optimal bubble riding with price-dependent entry times.
method Mean field game of controls with common noise and random entry time, existence result obtained through discretization and limit analysis.
result Existence of equilibrium in the mean field game model.
The paper examines Indian market bubbles using financial ratios.
problem Detecting bubbles in emerging markets like India is challenging.
method Utilizes financial ratios and the Philips et al 2015 right-tailed unit test.
result Identifies various bubble episodes in the Indian market.