A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Proves convergence of mean curvature flow on cylinders with unique continuation.
Investors in stock market are usually greedy during bull markets and scared during bear markets. The greed or fear spreads across investors quickly. This is known as the herding effect, and often leads to a fast movement of stock prices. During such market regimes, stock prices change at a super-exponential rate and ar…
We construct 2-dimensional CAT(-1) groups which contain free subgroups with arbitrary iterated exponential distortion, and with distortion higher than any iterated exponential.
We produce examples of groups of type F_3 with 2-dimensional Dehn functions of the form exp^n(x) (a tower of exponentials of height n), where n is any natural number.
We show that the number of isometry classes of cusped hyperbolic -manifolds that bound geometrically grows at least super-exponentially with their volume, both in the arithmetic and non-arithmetic settings.
New flag-no-square 4-manifolds discovered with unique triangulations.
We prove a new lower bound for the dilatation of an arbitrary pseudo-Anosov map on a surface of genus g with n punctures. Our bound improves the former super-exponential dependence on the genus by a polynomial dependence.
We introduce a model of super-exponential financial bubbles with two assets (risky and risk-free), in which rational investors and noise traders co-exist. Rational investors form expectations on the return and risk of a risky asset and maximize their constant relative risk aversion expected utility with respect to thei…
We analyze a controlled price formation experiment in the laboratory that shows evidence for bubbles. We calibrate two models that demonstrate with high statistical significance that these laboratory bubbles have a tendency to grow faster than exponential due to positive feedback. We show that the positive feedback ope…
The purpose of the present paper is to prove existence of super-exponentially many compact orientable hyperbolic arithmetic -manifolds that are geometric boundaries of compact orientable hyperbolic -manifolds, for any , thereby establishing that these classes of manifolds have the same growth rate w…
Optimal experiments tighten causal effect bounds efficiently.
Let (X,g) be a metrically complete, simply connected Riemannian manifold with bounded geometry and pinched negative curvature, i.e. there are constants a>b>0 such that -a^2<K<-b^2 for all sectional curvatures K. Here bounded geometry is used in the sense that all covariant derivatives of the Riemannian curvature tensor…
We showed how to use trained neural networks to perform Bayesian reasoning in order to solve tasks outside their initial scope. Deep generative models provide prior knowledge, and classification/regression networks impose constraints. The tasks at hand were formulated as Bayesian inference problems, which we approximat…
In the present paper, we show that many combinatorial and topological objects, such as maps, hypermaps, three-dimensional pavings, constellations and branched coverings of the two--sphere admit any given finite automorphism group. This enhances the already known results by Frucht, Cori -- Machì, Širáň -- Škoviera, and …
This paper addresses the general problem of modelling and learning rank data with ties. We propose a probabilistic generative model, that models the process as permutations over partitions. This results in super-exponential combinatorial state space with unknown numbers of partitions and unknown ordering among them. We…
TDA detects financial bubbles through early warning signals.
New method uses hyperbolic space for faster phylogenetic tree inference.
Using a family of modified Weibull distributions, encompassing both sub-exponentials and super-exponentials, to parameterize the marginal distributions of asset returns and their multivariate generalizations with Gaussian copulas, we offer exact formulas for the tails of the distribution of returns of a port…
Keeping a basic tenet of economic theory, rational expectations, we model the nonlinear positive feedback between agents in the stock market as an interplay between nonlinearity and multiplicative noise. The derived hyperbolic stochastic finite-time singularity formula transforms a Gaussian white noise into a rich time…
Graphs indistinguishable by GNNs are fully characterized.
The ability to compose learned skills to solve new tasks is an important property of lifelong-learning agents. In this work, we formalise the logical composition of tasks as a Boolean algebra. This allows us to formulate new tasks in terms of the negation, disjunction and conjunction of a set of base tasks. We then sho…
We applied the Johansen-Ledoit-Sornette (JLS) model to detect possible bubbles and crashes related to the Brexit/Bremain referendum scheduled for 23rd June 2016. Our implementation includes an enhanced model calibration using Genetic Algorithms. We selected a few historical financial series sensitive to the Brexit/Brem…
New method finds large counterexamples by selectively exploring triangulations.
It is important to have fast and effective methods for simplifying 3-manifold triangulations without losing any topological information. In theory this is difficult: we might need to make a triangulation super-exponentially more complex before we can make it smaller than its original size. Here we present experimental …
We construct infinite families of closed hyperbolic surfaces that are local maxima for the systole function on their respective moduli spaces. The systole takes values along a linearly divergent sequence at these local maxima. The only surface corresponding to is the Bolza surface i…
As data sets grow in size, the ability of learning methods to find structure in them is increasingly hampered by the time needed to search the large spaces of possibilities and generate a score for each that takes all of the observed data into account. For instance, Bayesian networks, the model chosen in this paper, ha…
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 …
We develop a strong diagnostic for bubbles and crashes in bitcoin, by analyzing the coincidence (and its absence) of fundamental and technical indicators. Using a generalized Metcalfe's law based on network properties, a fundamental value is quantified and shown to be heavily exceeded, on at least four occasions, by bu…
In the aftermath of the burst of the ``new economy'' bubble in 2000, the Federal Reserve aggressively reduced short-term rates yields in less than two years from 6.5% to 1.25% in an attempt to coax forth a stronger recovery of the US economy. But, there is growing apprehension that this is creating a new bubble in real…
The study quantifies distances between certain hyperbolic surfaces and bounds their number.
It is important to have effective methods for simplifying 3-manifold triangulations without losing any topological information. In theory this is difficult: we might need to make a triangulation super-exponentially more complex before we can make it smaller than its original size. Here we present experimental work that…
For spherically symmetric distributions, efficient quantisation can be achieved with moderate sample sizes.
Develops kernels for matchings, overcoming computational challenges.
Continuous-time Bayesian Networks (CTBNs) represent a compact yet powerful framework for understanding multivariate time-series data. Given complete data, parameters and structure can be estimated efficiently in closed-form. However, if data is incomplete, the latent states of the CTBN have to be estimated by laborious…
New method recovers transportable DAG structures from different datasets.
Let G be an arithmetic Kleinian group, and let O be the associated hyperbolic 3-orbifold or 3-manifold. In this paper, we prove that, in many cases, G is large, which means that some finite index subgroup admits a surjective homomorphism onto a non-abelian free group. This has many consequences, including that O has in…
Using a family of modified Weibull distributions, encompassing both sub-exponentials and super-exponentials, to parameterize the marginal distributions of asset returns and their natural multivariate generalizations, we give exact formulas for the tails and for the moments and cumulants of the distribution of returns o…
The cryptocurrency market surpassed the barrier of \$100 billion market capitalization in June 2017, after months of steady growth. Despite its increasing relevance in the financial world, however, a comprehensive analysis of the whole system is still lacking, as most studies have focused exclusively on the behaviour o…
Hierarchical clustering is a fundamental task often used to discover meaningful structures in data, such as phylogenetic trees, taxonomies of concepts, subtypes of cancer, and cascades of particle decays in particle physics. Typically approximate algorithms are used for inference due to the combinatorial number of poss…
We analyze the properties of arguably the simplest bilinear stochastic multiplicative process, proposed as a model of financial returns and of other complex systems combining both nonlinearity and multiplicative noise. By construction, it has no linear predictability (zero two-point correlation) but a certain nonlinear…
We present a novel analysis extending the recent work of Mizuno et al. [2002] on the hyperinflations of Germany (1920/1/1-1923/11/1), Hungary (1945/4/30-1946/7/15), Brazil (1969-1994), Israel (1969-1985), Nicaragua (1969-1991), Peru (1969-1990) and Bolivia (1969-1985). On the basis of a generalization of Cagan's model …
Hybrid approach combines transformer and Bayesian filtering for robust multiple particle tracking.
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 …
VISTA learns causal structures by integrating local subgraphs, improving accuracy and efficiency.
A method to uniformly sample graph-encoded surfaces of fixed size.
New financial price model using earning yield derived from CIR process.
Study cohomology of surfaces with punctures and boundaries, proving bounds on rational cohomology.
Our analysis of financial data, in terms of super-exponential growth, suggests that the seed of the 2002/03 crisis of the Dutch supermarket giant AHOLD was planted in 1996. It became quite visible in 1999 when the post-bubble destabilization regime was well-developed and acted as the precursor of an inevitable collapse…