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.
The study examines how market trade randomness influences price and return volatility.
Price and return predictions are limited by economic complexity, not just volatility.
We observe that the iterated tangent group of a Lie group may be realized as a double cross product of the 2nd order tangent group, with the Lie algebra of the base Lie group. Based on this observation, we derive the 2nd order Euler-Lagrange equations on the 2nd order tangent group from the 1st order Euler-Lagrange equ…
Second-order economic theory considers new variables to improve price volatility predictions.
This paper is devoted to study the Lie algebra of linear symmetries of a homogenous 2nd order ODE, by the method of Kushner, Lychagin and Robstov.
The artificial neural network is a popular framework in machine learning. To empower individual neurons, we recently suggested that the current type of neurons could be upgraded to 2nd order counterparts, in which the linear operation between inputs to a neuron and the associated weights is replaced with a nonlinear qu…
In 1896 Tresse gave a complete description of relative differential invariants for the pseudogroup action of point transformations on the 2nd order ODEs. The purpose of this paper is to review, in light of modern geometric approach to PDEs, this classification and also discuss the role of absolute invariants and the eq…
We show that for two dimensional manifolds M with negative Euler characteristic there exists subsets of the space of smooth Riemannian metrics which are invariant and either parabolic or backwards-parabolic for the 2nd order RG flow. We also show that solutions exists globally on these sets. Finally, we establish the e…
The hybrid Monte Carlo algorithm (HMCA) is applied for Bayesian parameter estimation of the realized stochastic volatility (RSV) model. Using the 2nd order minimum norm integrator (2MNI) for the molecular dynamics (MD) simulation in the HMCA, we find that the 2MNI is more efficient than the conventional leapfrog integr…
Paper analyzes coexisting hidden and self-excited attractors in an economic system.
New stable HOIF estimators for statistical functionals.
Natural gradient descent is an optimization method traditionally motivated from the perspective of information geometry, and works well for many applications as an alternative to stochastic gradient descent. In this paper we critically analyze this method and its properties, and show how it can be viewed as a type of 2…
Current economic theories miss most of economic dynamics.
We solve the metrisability problem for the six Painlevé equations, and more generally for all 2nd order ODEs with Painlevé property, and determine for which of these equations their integral curves are geodesics of a (pseudo) Riemannian metric on a surface.
Econophysics is a new research field, which makes an attempt to bring economics in the fold of natural sciences or specifically attempts for a "physics of economics". The term Econophysics was formally born in Kolkata in 1995. The entry on Econophysics in The New Palgrave Dictionary of Economics, 2nd Ed., Vol 2, Macmil…
These are lecture notes of the Summer school on the geometry of differential equations held in Nordfjordeid, Norway in 1996. They cover geometric structures related to scalar second order ODEs, the construction of the associated Cartan connection, techniques for computing invariants of differential equations starting f…
Modeling business cycles via collective risk fluctuations in economic agents' risk space.
Productions functions map the inputs of a firm or a productive system onto its outputs. This article expounds generalizations of the production function that include state variables, organizational structures and increasing returns to scale. These extensions are needed in order to explain the regularities of the empiri…
Examines financial risks' impact on EU-15 economic growth.
The equivalence problem for second order ODEs given modulo point transformations is solved in full analogy with the equivalence problem of nondegenerate 3-dimensional CR structures. This approach enables an analog of the Feffereman metrics to be defined. The conformal class of these (split signature) metrics is well de…
I consider the geometry of the general class of scalar 2nd-order differential equations with parabolic symbol, including non-linear and non-evolutionary parabolic equations. After defining the appropriate -structure to model parabolic equations, I apply Cartan techniques to determine local geometric invariants (quan…
We provide five examples of conformal geometries which are naturally associated with ordinary differential equations (ODEs). The first example describes a one-to-one correspondence between the Wuenschmann class of 3rd order ODEs considered modulo contact transformations of variables and (local) 3-dimensional conformal …
We prove new results on existence of solutions for the prescribed gaussian curvature problem on the euclidean sphere S^2. Those results are achieved by relating this problem with the holomorphic triples theory on Riemann surfaces. We think this approach might be applied to study some other semi-linear elliptic equation…
The n-dimensional Lorentzian manifolds with vanishing second covariant derivative of the Riemann tensor (2-symmetric spacetimes) are characterized and classified. The main result is that either they are locally symmetric or they have a covariantly constant null vector field, in this case defining a subfamily of Brinkma…
Paper formulates governing equations for membrane O surfaces.
The paper proposes a new model for predicting and analyzing economic variables.
We formulate thermodynamics of economic systems in terms of an arbitrary probability distribution for a conserved economic quantity. As in statistical physics, thermodynamic macroeconomic variables emerge as the mean value of microeconomic variables and their determination is reduced to the computation of the partition…
Simplified proof for Frank and Lieb's inequality on Heisenberg group.
Study uses remotely sensed data to infer economic outcomes in experiments and quasi-experiments.
We introduce and compare new variability measures based on risk quantiles.
Economics does not need a scientific revolution. Economics needs accurate measurements according to high standards of natural sciences and meticulous work on revealing empirical relationships between measured variables.
In this paper, we consider nonlinear PDEs in a port-Hamiltonian setting based on an underlying jet-bundle structure. We restrict ourselves to systems with 1-dimensional spatial domain and 2nd-order Hamiltonian including certain dissipation models that can be incorporated in the port- Hamiltonian framework by means of a…
This paper provides an attempt to formalize Hayek's notion of spontaneous order within the framework of the Arrow-Debreu economy. Our study shows that if a competitive economy is enough fair and free, then a spontaneous economic order shall emerge in long-run competitive equilibria so that social members together occup…
In this paper we consider the cohomology of a closed arithmetic hyperbolic 3-manifold with coefficients in the local system defined by the even symmetric powers of the standard representation of SL(2,C). The cohomology is defined over the integers and is a finite abelian group. We show that the order of the 2nd cohomol…
Bayesian MS-VAR process improves option pricing models.
New measures and tests for high-order interactions in complex data.
Bayesian MS-VAR model for pricing equity-linked life insurance products.
The macroeconomic climate influences operations with regard to, e.g., raw material prices, financing, supply chain utilization and demand quotas. In order to adapt to the economic environment, decision-makers across the public and private sectors require accurate forecasts of the economic outlook. Existing predictive f…
Machine learning models predict US economic recessions using Treasury term spreads.
Paper introduces a new method for calibrating ESGs to both historical and forward-looking data.
Paper proposes a new MAR model for global economic forecasting.
We describe a simple, low-level approach for embedding probabilistic programming in a deep learning ecosystem. In particular, we distill probabilistic programming down to a single abstraction---the random variable. Our lightweight implementation in TensorFlow enables numerous applications: a model-parallel variational …
Long-range correlation in financial time series reflects the complex dynamics of the stock markets driven by algorithms and human decisions. Our analysis exploits ultra-high frequency order book data from NASDAQ Nordic over a period of three years to numerically estimate the power-law scaling exponents using detrended …
This paper compares analytical and numerical solutions of the Black-Scholes model.
The paper uses deep neural networks to estimate economic models without separability restrictions.
We develop a statistical mechanical approach based on the replica method to study the design space of deep and wide neural networks constrained to meet a large number of training data. Specifically, we analyze the configuration space of the synaptic weights and neurons in the hidden layers in a simple feed-forward perc…
Contrary to conventional economic growth theory, which reduces a country's output to one aggregate variable (GDP), product diversity is central to economic development, as recent 'economic complexity' research suggests. A country's product diversity reflects its diversity of knowhow or 'capabilities'. Researchers propo…
For each simple Lie algebra (excluding, for trivial reasons, type ) we find the lowest possible degree of an invariant second-order PDE over the adjoint variety in , a homogeneous contact manifold. Here a PDE has degree if is a polynomi…