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.
Researchers study the geometric properties of a specific type of stable processes.
We investigate the class of tempered stable distributions and their associated processes. Our analysis of tempered stable distributions includes limit distributions, parameter estimation and the study of their densities. Regarding tempered stable processes, we deal with density transformations and compute their -var…
Stable processes emerge as limits of deep neural networks with symmetric stable distributions.
We offer new formulas for European option pricing under tempered stable processes.
We develop methods to estimate lag and parameters for multiple stable autoregressive processes.
New financial models use tempered stable subordination for better correlation dynamics.
Characterizes Lévy-driven Ornstein-Uhlenbeck processes linked to tempered stable distributions.
The paper evaluates functions of stable Lévy processes and their extrema efficiently.
Upper bound on withdrawal success for geometric Levy alpha-stable wealth process.
In this paper we consider the problem of finding stable maxima of expensive (to evaluate) functions. We are motivated by the optimisation of physical and industrial processes where, for some input ranges, small and unavoidable variations in inputs lead to unacceptably large variation in outputs. Our approach uses multi…
We consider a stable Cox--Ingersoll--Ross process driven by a standard Wiener process and a spectrally positive strictly stable Lévy process, and we study asymptotic properties of the maximum likelihood estimator (MLE) for its growth rate based on continuous time observations. We distinguish three cases: subcritical, c…
Spaces of polynomials are shown to be Euclidean balls.
Study normal tempered stable processes for energy derivative pricing.
Develops a Monte Carlo algorithm for tempered stable process extrema.
Adaptive importance sampling for estimating point process statistics.
This chapter is an attempt to present a mathematical theory of compound fractional Poisson processes. The chapter begins with the characterization of a well-known Lévy process: The compound Poisson process. The semi-Markov extension of the compound Poisson process naturally leads to the compound fractional Poisson proc…
Motivated by applications to insurance mathematics, we prove some heavy-traffic limit theorems for processes which encompass the fractionally differentiated random walk as well as some FARIMA processes, when the innovations are in the domain of attraction of a nonGaussian stable distribution.
Motivated by applications to insurance mathematics, we prove some heavy-traffic limit theorems for process which encompass the fractionally integrated random walk as well as some FARIMA processes, when the innovations are in the domain of attraction of a nonGaussian stable distribution.
This paper introduces Non-Autonomous Input-Output Stable Network(NAIS-Net), a very deep architecture where each stacked processing block is derived from a time-invariant non-autonomous dynamical system. Non-autonomy is implemented by skip connections from the block input to each of the unrolled processing stages and al…
We investigate exponential stock models driven by tempered stable processes, which constitute a rich family of purely discontinuous Lévy processes. With a view of option pricing, we provide a systematic analysis of the existence of equivalent martingale measures, under which the model remains analytically tractable. Th…
Study prices energy derivatives using specific stochastic processes.
This paper studies large-width asymptotics for ReLU neural networks with α-Stable initializations.
We study the use of "sign -stable random projections" (where ) for building basic data processing tools in the context of large-scale machine learning applications (e.g., classification, regression, clustering, and near-neighbor search). After the processing by sign stable random projections, the inner pr…
New method estimates tempered stable Lévy models with high accuracy.
We investigate the class of -stable Poisson-Kingman random probability measures (RPMs) in the context of Bayesian nonparametric mixture modeling. This is a large class of discrete RPMs which encompasses most of the the popular discrete RPMs used in Bayesian nonparametrics, such as the Dirichlet process, Pitman-Yor p…
This paper removes the finite variance assumption for deep convolutional neural networks.
The paper examines the behavior of Weierstrass measures on stable curves as they approach a nodal stable curve.
In this paper, we will discuss an approximation of the characteristic function of the first passage time for a Levy process using the martingale approach. The characteristic function of the first passage time of the tempered stable process is provided explicitly or by an indirect numerical method. This will be applied …
In this article, we first propose the modified Hannan-Rissanen Method for estimating the parameters of the autoregressive moving average (ARMA) process with symmetric stable noise and symmetric stable generalized autoregressive conditional heteroskedastic (GARCH) noise. Next, we propose the modified empirical character…
Study of deep Stable neural networks with various activation functions.
Model selection on validation data is an essential step in machine learning. While the mixing of data between training and validation is considered taboo, practitioners often violate it to increase performance. Here, we offer a simple, practical method for using the validation set for training, which allows for a conti…
A fast Monte Carlo method for additive processes and option pricing.
New method estimates volatility for processes with jumps of unbounded variation.
Under the Basel II standards, the Operational Risk (OpRisk) advanced measurement approach is not prescriptive regarding the class of statistical model utilised to undertake capital estimation. It has however become well accepted to utlise a Loss Distributional Approach (LDA) paradigm to model the individual OpRisk loss…
Bayesian deep neural networks converge to processes with α-stable marginals under infinite variance weights.
We analyze the Levy processes produced by means of two interconnected classes of non stable, infinitely divisible distribution: the Variance Gamma and the Student laws. While the Variance Gamma family is closed under convolution, the Student one is not: this makes its time evolution more complicated. We prove that -- a…
Any two equivalent discrete curves must have the same invariants at the corresponding points under an affine transformation. In this paper, we construct the moving frame and invariants for the discrete centroaffine curves, which could be used to discriminate the same discrete curves from different graphics, and estimat…
New method improves stability of Gaussian process approximations.
We introduce a simple model for equity index derivatives. The model generalizes well known Lèvy Normal Tempered Stable processes (e.g. NIG and VG) with time dependent parameters. It accurately fits Equity index implied volatility surfaces in the whole time range of quoted instruments, including small time horizon (few …
We provide analytical tools for pricing power options with exotic features (capped or log payoffs, gap options ...) in the framework of exponential Lévy models driven by one-sided stable or tempered stable processes. Pricing formulas take the form of fast converging series of powers of the log-forward moneyness and of …
Stable algebraic filters improve neural network performance.
A new nonparametric approach for system identification has been recently proposed where the impulse response is seen as the realization of a zero--mean Gaussian process whose covariance, the so--called stable spline kernel, guarantees that the impulse response is almost surely stable. Maximum entropy properties of the …
Method predicts LFSM increments from past observations using codifference.
New method stabilizes tensegrity structures suitable for engineering.
Stable neural flows ensure robustness and efficiency in deep learning.
New model captures time-varying volatility with stochastic exponential tails.
Research on long-range memory in financial and social systems using various models.
The challenge to fruitfully merge state-of-the-art techniques from mathematical finance and numerical analysis has inspired researchers to develop fast deterministic option pricing methods. As a result, highly efficient algorithms to compute option prices in Lévy models by solving partial integro differential equations…