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.
HF-opt uses Hamiltonian dynamics to optimize functions, achieving accelerated rates with randomized integration time.
Simplified uHMC with time integration improves accuracy and efficiency.
RHMC accelerates sampling from log-concave distributions.
Paper solves a complex portfolio selection problem with time-inconsistent preferences.
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.
Study optimal hedging for claims with random weights in discrete time.
The usual development of the continuous-time random walk (CTRW) proceeds by assuming that the present is one of the jumping times. Under this restrictive assumption integral equations for the propagator and mean escape times have been derived. We generalize these results to the case when the present is an arbitrary tim…
The paper analyzes the randomized midpoint method for Langevin diffusions, revealing biases and asymptotic properties.
Improved efficiency in HMC samplers reduces dissipative behavior.
New method samples from time-integrated stochastic bridges using neural networks.
We review statistical properties of models generated by the application of a (positive and negative order) fractional derivative operator to a standard random walk and show that the resulting stochastic walks display slowly-decaying autocorrelation functions. The relation between these correlated walks and the well-kno…
We find a simple expression for the probability density of in terms of its distribution function and the distribution function for the time integral of . The relation is obtained with a change of measure argument where expectations over events determined by the time integral…
The paper defines and analyzes set-valued stochastic integrals for Lévy processes.
New method uses graphene transistors for efficient non-uniform random number generation.
By appealing to renewal theory we determine the equations that the mean exit time of a continuous-time random walk with drift satisfies both when the present coincides with a jump instant or when it does not. Particular attention is paid to the corrections ensuing from the non-Markovian nature of the process. We show t…
Study on neural networks with non-normal interactions reveals unique spectral properties.
The continuous-time random walk (CTRW) is a pure-jump stochastic process with several applications in physics, but also in insurance, finance and economics. A definition is given for a class of stochastic integrals driven by a CTRW, that includes the Ito and Stratonovich cases. An uncoupled CTRW with zero-mean jumps is…
Global approximation for piecewise linear paths via signatures.
HMC improves Gaussian sampling efficiency with long, random steps.
We introduce a method for non-uniform random number generation based on sampling a physical process in a controlled environment. We demonstrate one proof-of-concept implementation of the method that reduces the error of Monte Carlo integration of a univariate Gaussian by 1068 times while doubling the speed of the Monte…
Analyzes the generalization and training errors of the random feature model over time.
In this paper, we consider the nonparametric least square regression in a Reproducing Kernel Hilbert Space (RKHS). We propose a new randomized algorithm that has optimal generalization error bounds with respect to the square loss, closing a long-standing gap between upper and lower bounds. Moreover, we show that our al…
Formula for integrating random variables on hyperbolic surfaces.
Develops path integral for spiked tensor model dynamics.
As integrated circuits have become progressively more complex, constrained random stimulus has become ubiquitous as a means of stimulating a designs functionality and ensuring it fully meets expectations. In theory, random stimulus allows all possible combinations to be exercised given enough time, but in practice with…
In this paper we propose a new model for volatility fluctuations in financial time series. This model relies on a non-stationary gaussian process that exhibits aging behavior. It turns out that its properties, over any finite time interval, are very close to continuous cascade models. These latter models are indeed wel…
Study on risk measures using distorted Choquet integrals with random distortions.
We study an optimal multiple stopping problem for call-type payoff driven by a spectrally negative Levy process. The stopping times are separated by constant refraction times, and the discount rate can be positive or negative. The computation involves a distribution of the Levy process at a constant horizon and hence t…
New sampling method for Heston model reduces complexity.
In the setting proposed by Hughston & Rafailidis (2005) we consider general interest rate models in the case of a Brownian market information filtration . Let be a square-integrable -measurable random variable, and assume the non-degeneracy condition that for all $t<\in…
By the classical Martingale Representation Theorem, replication of random vectors can be achieved via stochastic integrals or solutions of stochastic differential equations. We introduce a new approach to replication of random vectors via adapted differentiable processes generated by a controlled ordinary differential …
Overview of high-dimensional dynamical systems and their applications to machine learning.
RandNet-Parareal uses neural networks to speed up time-parallel PDE solving.
Enhances uncertainty modeling in random PDEs using PINNs and generative models.
A new method for estimating large-scale linear models with improved precision.
Computation of moments of transformed random variables is a problem appearing in many engineering applications. The current methods for moment transformation are mostly based on the classical quadrature rules which cannot account for the approximation errors. Our aim is to design a method for moment transformation for …
The weights of a neural network are typically initialized at random, and one can think of the functions produced by such a network as having been generated by a prior over some function space. Studying random networks, then, is useful for a Bayesian understanding of the network evolution in early stages of training. In…
This paper presents a numerical model to solve the problem of cash accumulation strategies for products with an unknown future price, like assets. Stock prices are modeled by a discretized Wiener Process, and by the means of ordinary integrals this Wiener Process will be exactly matched at a preset terminal time. Three…
We provide an integral representation for the (implied) copulas of dependent random variables in terms of their moment generating functions. The proof uses ideas from Fourier methods for option pricing. This representation can be used for a large class of models from mathematical finance, including Lévy and affine proc…
Innovative extensions to option pricing models using asymmetric Brownian motion and random walk approaches.
Protein function prediction is the important problem in modern biology. In this paper, the un-normalized, symmetric normalized, and random walk graph Laplacian based semi-supervised learning methods will be applied to the integrated network combined from multiple networks to predict the functions of all yeast proteins …
The random subspace method, known as the pillar of random forests, is good at making precise and robust predictions. However, there is not a straightforward way yet to combine it with deep learning. In this paper, we therefore propose Neural Random Subspace (NRS), a novel deep learning based random subspace method. In …
In a series of recent papers Barndorff-Nielsen and Shephard introduce an attractive class of continuous time stochastic volatility models for financial assets where the volatility processes are functions of positive Ornstein-Uhlenbeck(OU) processes. This models are known to be substantially more flexible than Gaussian …
Establishes a link between risk measures and uniform integrability in finance.
We present a probabilistic framework for nonlinearities, based on doubly truncated Gaussian distributions. By setting the truncation points appropriately, we are able to generate various types of nonlinearities within a unified framework, including sigmoid, tanh and ReLU, the most commonly used nonlinearities in neural…
We propose a methodology for computing single and multi-asset European option prices, and more generally expectations of scalar functions of (multivariate) random variables. This new approach combines the ability of Monte Carlo simulation to handle high-dimensional problems with the efficiency of function approximation…
Towards a future where machine learning systems will integrate into every aspect of people's lives, researching methods to interpret such systems is necessary, instead of focusing exclusively on enhancing their performance. Enriching the trust between these systems and people will accelerate this integration process. M…
New method uses Coulomb gases for Monte Carlo integration with reduced errors.