arXiv research

This paper conditions non-linear infinite-dimensional diffusion processes.

The mathematical model of a linear system with the short memory about own stochastic behavior is proposed. It is assumed that the system is under a continual influence of independent stochastic impulses. In a short memory approximation the expression of the stochastic process is found. An application of the model propo…

Universal approximation for stochastic processes using Brownian motion.

Stochastic gradient descent approximates Gaussian process posteriors efficiently.

In this paper we investigate general linear stochastic volatility models with correlated Brownian noises. In such models the asset price satisfies a linear SDE with coefficient of linearity being the volatility process. This class contains among others Black-Scholes model, a log-normal stochastic volatility model and H…

Stochastic gradient descent improves Gaussian process regression.

New numerical method for non-linear asset price model with CEV volatility.

In applications of Gaussian processes where quantification of uncertainty is of primary interest, it is necessary to accurately characterize the posterior distribution over covariance parameters. This paper proposes an adaptation of the Stochastic Gradient Langevin Dynamics algorithm to draw samples from the posterior …

The paper studies stochastic gradient descent with infinite variance gradients.

Broadens Jourdain and Martini's method to non-linear stochastic processes.

New PEMs improve network inference from time-series data.

Graph convolutional networks adapt the architecture of convolutional neural networks to learn rich representations of data supported on arbitrary graphs by replacing the convolution operations of convolutional neural networks with graph-dependent linear operations. However, these graph-dependent linear operations are d…

We introduce the implicit processes (IPs), a stochastic process that places implicitly defined multivariate distributions over any finite collections of random variables. IPs are therefore highly flexible implicit priors over functions, with examples including data simulators, Bayesian neural networks and non-linear tr…

Efficiently simulates the Heston model with large time steps using a novel method.

Modeling price formation with interacting Hawkes processes leading to stochastic volatility with leverage.

Study optimizes trading in multiple assets with cross-effects.

Linear autoregressive models serve as basic representations of discrete time stochastic processes. Different attempts have been made to provide non-linear versions of the basic autoregressive process, including different versions based on kernel methods. Motivated by the powerful framework of Hilbert space embeddings o…

Nonlinear RNNs' memory capacity varies widely, making it impractical.

New SDEs from affine and polynomial perspectives for path-dependent processes.

Improved SGD for robust linear and ReLU regression with adversarial corruptions.

ES reduces high-probability regret in stochastic linear bandits.

State space models (SSMs) provide a flexible framework for modeling complex time series via a latent stochastic process. Inference for nonlinear, non-Gaussian SSMs is often tackled with particle methods that do not scale well to long time series. The challenge is two-fold: not only do computations scale linearly with t…

Paper solves time-inconsistent control problems with BSDEs.

Two-layer networks learn hard GLMs with SGD in high dimensions.

It is well-known from the work of Schönbucher (2005) that the marginal laws of a loss process can be matched by a unit increasing time inhomogeneous Markov process, whose deterministic jump intensity is called local intensity. The Stochastic Local Intensity (SLI) models such as the one proposed by Arnsdorf and Halperin…

Study optimizes investment strategies in markets with contagious price jumps.

Geometry arising from two diffusion operators (smooth semi-elliptic, second order differential operators) on different spaces but intertwined by a smooth map is described. Particular cases arise from Riemannian submersions when the operators are Laplace-Beltrami operators, from equivariant operators on the total space …

In this paper, we study curvature dimension conditions on birth-death processes which correspond to linear graphs, i.e., weighted graphs supported on the infinite line or the half line. We give a combinatorial characterization of Bakry and Émery's $CD(K,n)$ condition for linear graphs and prove the triviality of edge w…

Paper develops methods for solving complex stochastic equations using Malliavin calculus.

Study on martingale property and moment explosions in signature volatility models.

LatentFlow simplifies conditioning of stochastic processes without training.

Paper proves existence and uniqueness of solutions to PIDEs in Bessel spaces for option pricing.

Proposes a new method combining Reservoir Computing and Normalizing Flow for predicting stochastic dynamical systems.

Introduces Neural-Brownian Motion for modeling dynamics under learned uncertainty.

We introduce a nonparametric approach for estimating drift and diffusion functions in systems of stochastic differential equations from observations of the state vector. Gaussian processes are used as flexible models for these functions and estimates are calculated directly from dense data sets using Gaussian process r…

Two new methods solve large-scale stochastic convex problems with linear constraints.

Unified framework for inference in complex nonlinear processes.

Variational inference has experienced a recent surge in popularity owing to stochastic approaches, which have yielded practical tools for a wide range of model classes. A key benefit is that stochastic variational inference obviates the tedious process of deriving analytical expressions for closed-form variable updates…

The paper develops a deep signature approach for option pricing under non-Markovian stochastic volatility models.

This paper studies the question of filtering and maximizing terminal wealth from expected utility in a partially information stochastic volatility models. The special features is that the only information available to the investor is the one generated by the asset prices, and the unobservable processes will be modeled …

Method predicts future rewards from past actions in a linear Gaussian system.

This paper deals with an optimal position management problem for a market maker who has to face uncertain customer order flows in an illiquid market, where the market maker's continuous trading incurs a stochastic linear price impact. Although the execution timing is uncertain, the market maker can also ask its OTC cou…

Paper introduces a new method for Transformers with linear complexity.

Proposes a new method to extend Gaussian processes for non-Gaussian data.

New method solves optimal stopping problems using rough path signatures.

We introduce a Bernstein-type inequality which serves to uniformly control quadratic forms of gaussian variables. The latter can for example be used to derive sharp model selection criteria for linear estimation in linear regression and linear inverse problems via penalization, and we do not exclude that its scope of a…

We introduce a linear space of finitely additive measures to treat the problem of optimal expected utility from consumption under a stochastic clock and an unbounded random endowment process. In this way we establish existence and uniqueness for a large class of utility maximization problems including the classical one…

Neural model accelerates SDDP for stochastic optimization.