arXiv research

The paper models financial asset prices with jumps and evaluates European option prices using numerical methods.

Study simulates Heston-type local stochastic volatility model using particle method.

This work proves a strong convergence result for a geometric EM scheme on Riemannian manifolds.

Motivated by weak convergence results in the paper of Takahashi and Yoshida (2005), we show strong convergence for an accelerated Euler-Maruyama scheme applied to perturbed stochastic differential equations. The Milstein scheme with the same acceleration is also discussed as an extended result. The theoretical results …

Paper studies particle method for LSV model calibration, proving convergence and error bounds.

In the present paper, we introduce a numerical scheme for the price of a barrier option when the price of the underlying follows a diffusion process. The numerical scheme is based on an extension of a static hedging formula of barrier options. For getting the static hedging formula, the underlying process needs to have…

We consider a class of stochastic path-dependent volatility models where the stochastic volatility, whose square follows the Cox-Ingersoll-Ross model, is multiplied by a (leverage) function of the spot price, its running maximum, and time. We propose a Monte Carlo simulation scheme which combines a log-Euler scheme for…

New schemes improve error estimates for sampling from non-log-concave distributions.

Paper develops Euler scheme for fractional delay diff. eqs with additive noise.

The paper presents two schemes for sampling matrices from specific distributions on a manifold.

Enhances learning of structured distributions using nonlinear denoising score matching.

Asymptotic error distribution for approximation of a stochastic integral with respect to continuous semimartingale by Riemann sum with general stochastic partition is studied. Effective discretization schemes of which asymptotic conditional mean-squared error attains a lower bound are constructed. Two applications are …

We consider the approximation of stochastic differential equations (SDEs) with non-Lipschitz drift or diffusion coefficients. We present a modified explicit Euler-Maruyama discretisation scheme that allows us to prove strong convergence, with a rate. Under some regularity and integrability conditions, we obtain the opt…

We propose a novel time discretization for the log-normal SABR model and derive its asymptotic properties.

Proposes a new model to handle negative interest rates using CIR framework.

We consider a discrete-time approximation of paths of an Ornstein--Uhlenbeck process as a mean for estimation of a price of European call option in the model of financial market with stochastic volatility. The Euler--Maruyama approximation scheme is implemented. We determine the estimates for the option price for prede…

We analyze exponential integrability properties of the Cox-Ingersoll-Ross (CIR) process and its Euler discretizations with various types of truncation and reflection at 0. These properties play a key role in establishing the finiteness of moments and the strong convergence of numerical approximations for a class of sto…

We consider the stochastic volatility model $dS_t = σ_t S_t dW_t,dσ_t = ωσ_t dZ_t$, with $(W_t,Z_t)$ uncorrelated standard Brownian motions. This is a special case of the Hull-White and the $β=1$ (log-normal) SABR model, which are widely used in financial practice. We study the properties of this model, discretized in …

New methods solve complex financial equations.

A new algorithm solves high-dimensional nonlinear BSDEs efficiently.

Deep density methods improve filtering in high-dimensional systems.

ISALT uses inference to simulate SDEs with large time-steps, improving efficiency.

We develop and study stability properties of a hybrid approximation of functionals of the Bates jump model with stochastic interest rate that uses a tree method in the direction of the volatility and the interest rate and a finite-difference approach in order to handle the underlying asset price process. We also propos…

Develops a new option pricing model under G-expectation framework.

A new subdivision scheme for Heisenberg group values with central smoothness loss.

Sampling with Markov chain Monte Carlo methods often amounts to discretizing some continuous-time dynamics with numerical integration. In this paper, we establish the convergence rate of sampling algorithms obtained by discretizing smooth Itô diffusions exhibiting fast Wasserstein-$2$ contraction, based on local deviat…

Study proves convergence of interest rate model approximations.

New integration method improves BSDE-based PDE solvers.

ML-EM method speeds up diffusion model sampling.

New findings show score matching's accuracy doesn't ensure numerical stability in diffusion sampling.

Simplified analysis of diffusion models using discrete random variables.

Study applies financial models to predict COVID-19 pandemic.

Paper analyzes Langevin dynamics for multimodal Gaussian mixtures, controlling errors across dimensions.

We analyze the problem of the analytical characterization of the probability distribution of financial returns in the exponential Ornstein-Uhlenbeck model with stochastic volatility. In this model the prices are driven by a Geometric Brownian motion, whose diffusion coefficient is expressed through an exponential funct…

Distributed-OMP recovers sparse vectors with low communication costs.

New risk bound for drift estimator in stochastic models.

Study on statistical estimation over Gaussian MAC, comparing analog and digital schemes.

Paper develops a new method for optimal stopping in American options.

The CEV model is given by the stochastic differential equation $X_t=X_0+\int_0^tμX_sds+\int_0^tσ(X^+_s)^pdW_s$, $\frac{1}{2}\le p<1$. It features a non-Lipschitz diffusion coefficient and gets absorbed at zero with a positive probability. We show the weak convergence of Euler-Maruyama approximations $X_t^n$ to the proc…

Formula for sections on complex manifolds with non-isolated components.

Novel framework synthesizes stochastic trajectories with anticipated structural breaks.

New framework learns physics from output measurements only.

Improved MLMC method for robust and efficient probability and density estimation.

A new method uses Schrödinger bridges for deep conditional generative learning.

The analysis of manifold-valued data requires efficient tools from Riemannian geometry to cope with the computational complexity at stake. This complexity arises from the always-increasing dimension of the data, and the absence of closed-form expressions to basic operations such as the Riemannian logarithm. In this pap…

We develop a general theory of log spaces, in which one can make sense of the basic notions of logarithmic geometry, in the sense of Fontaine-Illusie-Kato. Many of our general constructions with log spaces are new, even in the algebraic setting. In the differentiable setting, our theory yields a framework for treating …

We study the problem of adaptive control of a high dimensional linear quadratic (LQ) system. Previous work established the asymptotic convergence to an optimal controller for various adaptive control schemes. More recently, for the average cost LQ problem, a regret bound of ${O}(\sqrt{T})$ was shown, apart form logarit…

Efficiently calibrates epidemiological models using Bayesian optimization.