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.
Greedy selection works well in a toy model of independent increments.
Study compares ZBDT model to BDT for financial derivatives valuation.
Non-symmetric rectangular correlation matrices occur in many problems in economics. We test the method of extracting statistically meaningful correlations between input and output variables of large dimensionality and build a toy model for artificially included correlations in large random time series.The results are t…
Three physics-constrained regression exercises for image velocimetry and turbulence modeling.
Modified BDT model includes zero rate jumps for crisis risk.
MDP Playground tests RL agents across various dimensions for better understanding and debugging.
Toy model study shows resampling/reweighting can improve feature learning in imbalanced classification.
A toy model shows how locality can emerge in the universe's Hamiltonian and initial state.
Study explains Graph Convolutional Networks decisions.
We study the relation between the trading behavior of agents and volatility in toy markets of adaptive inductively rational agents. We show that excess volatility, in such simplified markets, arises as a consequence of {\em i)} the neglect of market impact implicit in price taking behavior and of {\em ii)} excessive re…
This is an extended write-up of a talk given in April, 1993 in honor of Raoul Bott's 70th birthday. We first illustrate how some traditional topological and geometric invariants obey ``gluing laws'' inspired by those in classical and quantum field theory. Here we discuss characteristic numbers, particularly the Euler n…
We consider the class of short rate interest rate models for which the short rate is proportional to the exponential of a Gaussian Markov process x(t) in the terminal measure r(t) = a(t) exp(x(t)). These models include the Black, Derman, Toy and Black, Karasinski models in the terminal measure. We show that such intere…
This study examines socio-economic inequality and proposes an international institution to address it.
Analyzed Guyon's volatility model for existence and uniqueness.
We describe some of the algebra underlying the decomposition of planar grid diagrams. This provides a useful toy model for an extension of Heegaard Floer homology to 3-manifolds with parametrized boundary. This paper is meant to serve as a gentle introduction to the subject, and does not itself have immediate topologic…
Random matrix theory predicts neural representations generalize well.
Gradient descent in Gaussian random fields helps understand high-dimensional optimization problems.
We construct an elementary, combinatorial kind of topological quantum field theory, based on curves, surfaces, and orientations. The construction derives from contact invariants in sutured Floer homology and is essentially an elaboration of a TQFT defined by Honda--Kazez--Matic. This topological field theory stores inf…
Study evaluates unsupervised disentanglement methods on a toy dataset.
New insights into how depth and width affect in-context learning in deep models.
SLT explains neural network success by closing theory-practice gap.
Analyze message passing algorithms using free probability theory.
Cryptocurrencies evolve through survival of the fittest, modeled with evolutionary finance.
Proposes a new technique for VAEs using manifold-valued variables.
APD method decomposes neural network parameters into simple, faithful components.
A theory of feature geometry using spectral analysis of weight matrices.
We propose and discuss some toy models of stock markets using the same operatorial approach adopted in quantum mechanics. Our models are suggested by the discrete nature of the number of shares and of the cash which are exchanged in a real market, and by the existence of conserved quantities, like the total number of s…
EGFs use ergodicity to simplify generative flows for easier training and imitation learning.
We introduce stochastic variational inference for Gaussian process models. This enables the application of Gaussian process (GP) models to data sets containing millions of data points. We show how GPs can be vari- ationally decomposed to depend on a set of globally relevant inducing variables which factorize the model …
We use standard perturbation techniques originally formulated in quantum (statistical) mechanics in the analysis of a toy model of a stock market which is given in terms of bosonic operators. In particular we discuss the probability of transition from a given value of the {\em portfolio} of a certain trader to a differ…
J.H.C. Whitehead defined a map from the homotopy of the special orthogonal group to the stable homotopy of spheres. Within a toy model we show how the known computation for kernel leads to nonlinear -models with spherical source (space) and spherical target which admit false vacua…
A new density model using Fourier basis achieves better approximations and compression.
Study analyzes bond traders' views on equity market dynamics.
In this paper we continue our systematic analysis of the operatorial approach previously proposed in an economical context and we discuss a {\em mixed} toy model of a simplified stock market, i.e. a model in which the price of the shares is given as an input. We deduce the time evolution of the portfolio of the various…
We consider the region of closed timelike curves (CTC's) in three-dimensional flat Lorentz spacetimes. The interest in this global geometrical feature goes beyond the purely mathematical. Such spacetimes may be considered lower-dimensional toy models of sourceless Einstein gravity or cosmology. In particular, our inter…
We introduce a toy probabilistic model to analyze job-matching processes in recent Japanese labor markets for university graduates by means of statistical physics. We show that the aggregation probability of each company is rewritten by means of non-linear map under several conditions. Mathematical treatment of the map…
Applying standard Markov chain Monte Carlo (MCMC) algorithms to large data sets is computationally infeasible. The recently proposed stochastic gradient Langevin dynamics (SGLD) method circumvents this problem in three ways: it generates proposed moves using only a subset of the data, it skips the Metropolis-Hastings a…
Systemic risk in banking systems remains a crucial issue that it has not been completely understood. In our toy model, banks are exposed to two sources of risks, namely, market risk from their investments in assets external to the banking system and credit risk from their lending in the interbank market. By and large, …
Method solves Gaussian graphical models on ladder graphs efficiently.
Study shows instability of naked singularities in perfect fluid models.
A clustering algorithm based on the Hausdorff distance is introduced and compared to the single and complete linkage. The three clustering procedures are applied to a toy example and to the time series of financial data. The dendrograms are scrutinized and their features confronted. The Hausdorff linkage relies of firm…
An agent-based computational economical toy model for the emergence of money from the initial barter trading, inspired by Menger's postulate that money can spontaneously emerge in a commodity exchange economy, is extensively studied. The model considered, while manageable, is significantly complex, however. It is alrea…
An interesting toy model has recently been proposed on Schumpeterian economic dynamics by Thurner {\it et al.} following the idea of economist Joseph Schumpeter. Punctuated equilibrium dynamics is shown to emerge from this model and some detail analyses of the time series indicate SOC kind of behaviours. The focus in t…
Three problems in Hermitian geometry for canonical metrics.
To meet the Basel II regulatory requirements for the Advanced Measurement Approaches in operational risk, the bank's internal model should make use of the internal data, relevant external data, scenario analysis and factors reflecting the business environment and internal control systems. One of the unresolved challeng…
Study shows cliff-learning in transfer learning from foundation models.
New PAC bound for meta-learning improves generalization guarantees.
Tree regularization improves deep model interpretability without sacrificing accuracy.