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.
Optimal learning for parametric prophet inequalities with exponential-type distributions
In this paper we describe a procedure to simplify any given triangulation of the 3-sphere using Pachner moves. We obtain an explicit exponential-type bound on the number of Pachner moves needed for this process. This leads to a new recognition algorithm for the 3-sphere.
The paper tackles sampling from Gibbs measures with constrained support, providing a sampling guarantee.
We prove a Paley-Wiener Theorem for a class of symmetric spaces of the compact type, in which all root multiplicities are even. This theorem characterizes functions of small support in terms of holomorphic extendability and exponential type of their (discrete) Fourier transforms. We also provide three independent new p…
A self-organized model with social percolation process is proposed to describe the propagations of information for different trading ways across a social system and the automatic formation of various groups within market traders. Based on the market structure of this model, some stylized observations of real market can…
Based on the minute-by-minute data of the Hang Seng Index in Hong Kong and the analysis of probability distribution and autocorrelations, we find that the index fluctuations for the first few minutes of daily opening show behaviors very different from those of the other times. In particular, the properties of tail dist…
Exponential Lasso improves Lasso's robustness to outliers and heavy-tailed noise.
We prove existence, uniqueness, and regularity of viscosity solutions to the stationary and evolution obstacle problems defined by a class of nonlocal operators that are not stable-like and may have supercritical drift. We give sufficient conditions on the coefficients of the operator to obtain Hölder and Lipschitz con…
In this paper we develop a symbolic technique to obtain asymptotic expressions for ruin probabilities and discounted penalty functions in renewal insurance risk models when the premium income depends on the present surplus of the insurance portfolio. The analysis is based on boundary problems for linear ordinary differ…
We consider a log-Riemann surface with a finite number of ramification points and finitely generated fundamental group. The log-Riemann surface is equipped with a local holomorphic difffeomorphism $π: \mathcal{S} \to \C$. We prove that is biholomorphic to a compact Riemann surface with finit…
New approach to concentration inequalities for unbounded state space dynamical systems.
Bounds on chemical reaction network relaxation rates using convex analysis.
Study on Kyle-Back model with risk aversion and non-Gaussian beliefs.
The distribution of recurrence times or return intervals between extreme events is important to characterize and understand the behavior of physical systems and phenomena in many disciplines. It is well known that many physical processes in nature and society display long range correlations. Hence, in the last few year…
Optimal insurance and investment strategy under exponential preferences in a correlated market model.
Form a pure mathematical point of view, common functional forms representing different physical phenomena can be defined. For example, rates of chemical reactions, diffusion and heat transfer are all governed by exponential-type expressions. If machine learning is used for physical problems, inferred from domain knowle…
Study infinite-dimensional Toda manifold at irregular singularity, revealing non-uniqueness of formal solutions.
Given two networks with the same training loss on a dataset, when would they have drastically different test losses and errors? Better understanding of this question of generalization may improve practical applications of deep networks. In this paper we show that with cross-entropy loss it is surprisingly simple to ind…
A main puzzle of deep neural networks (DNNs) revolves around the apparent absence of "overfitting", defined in this paper as follows: the expected error does not get worse when increasing the number of neurons or of iterations of gradient descent. This is surprising because of the large capacity demonstrated by DNNs to…
Study on stock price formation on trees with multi-population and non-rational agents.
Study on hedging and valuation of basis risk in incomplete markets with partial information.
The key to generalization is controlling the complexity of the network. However, there is no obvious control of complexity -- such as an explicit regularization term -- in the training of deep networks for classification. We will show that a classical form of norm control -- but kind of hidden -- is present in deep net…
Volterra signature provides a clear, interpretable feature for history-dependent systems.
We analyze the income distribution of employees for 9 consecutive years (2001-2009) using a complete social security database for an economically important district of Romania. The database contains detailed information on more than half million taxpayers, including their monthly salaries from all employers where they …
While deep learning is successful in a number of applications, it is not yet well understood theoretically. A satisfactory theoretical characterization of deep learning however, is beginning to emerge. It covers the following questions: 1) representation power of deep networks 2) optimization of the empirical risk 3) g…
Develops a lifting theory for exponential maps in semi-Riemannian geometry.
Study proves existence, uniqueness, and positivity of solutions to a complex volatility model.
Study of geodesics on SL(n) with Hilbert-Schmidt metric, revealing complex dynamics in higher dimensions.
Concentration inequalities form an essential toolkit in the study of high dimensional (HD) statistical methods. Most of the relevant statistics literature in this regard is based on sub-Gaussian or sub-exponential tail assumptions. In this paper, we first bring together various probabilistic inequalities for sums of in…