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We study fractional stochastic volatility models in which the volatility process is a positive continuous function $\sigma$ of a continuous Gaussian process $\widehat{B}$. Forde and Zhang established a large deviation principle for the…

Mathematical Finance · Quantitative Finance 2018-08-06 Archil Gulisashvili

This work is devoted to studying asymptotic behaviors for Volterra type McKean-Vlasov stochastic differential equations with small noise. By applying the weak convergence approach, we establish the large and moderate deviation principles.…

Probability · Mathematics 2024-10-11 Shanqi Liu , Yaozhong Hu , Hongjun Gao

We prove a moderate deviation principle for the continuous time interpolation of discrete time recursive stochastic processes. The methods of proof are somewhat different from the corresponding large deviation result, and in particular the…

Probability · Mathematics 2014-01-24 Paul Dupuis , Dane Johnson

In this paper, we prove the large deviation principle (LDP) for stochastic differential equations driven by stochastic integrals in one dimension. The result can be proved with a minimal use of rough path theory, and this implies the LDP…

Probability · Mathematics 2025-01-03 Ryoji Takano

In this paper, our work is devoted to studying Volterra type McKean-Vlasov stochastic differential equations with singular kernels. Firstly, the well-posedness of Volterra type McKean-Vlasov stochastic differential equations are…

Probability · Mathematics 2023-11-14 Shanqi Liu , Hongjun Gao

The goal of this paper is to study the Moderate Deviation Principle (MDP) for a system of stochastic reaction-diffusion equations with a time-scale separation in slow and fast components and small noise in the slow component. Based on weak…

Probability · Mathematics 2022-02-03 Ioannis Gasteratos , Michael Salins , Konstantinos Spiliopoulos

In this paper, we are concerned with stochastic Volterra equations with singular kernels and H\"older continuous coefficients. We first establish the well-posedness of these equations by utilising the Yamada-Watanabe approach. Then, we aim…

Probability · Mathematics 2024-07-03 Huijie Qiao , Jiang-Lun Wu

We demonstrate the large deviation property for the mild solutions of stochastic evolution equations with monotone nonlinearity and multiplica- tive noise. This is achieved using the recently developed weak convergence method, in studying…

Probability · Mathematics 2010-03-17 Hassan Dadashi-Arani , Bijan Z. Zangeneh

We study small-time central limit theorems for stochastic Volterra integral equations with H\"older continuous coefficients and general locally square integrable Volterra kernels. We prove the convergence of the finite-dimensional…

Probability · Mathematics 2026-02-27 Martin Friesen , Stefan Gerhold , Kristof Wiedermann

Pathwise uniqueness is established for a class of one-dimensional stochastic Volterra equations driven by Brownian motion with singular kernels and H\"older continuous diffusion coefficients. Consequently, the existence of unique strong…

Probability · Mathematics 2025-03-03 David J. Prömel , David Scheffels

Motivated by empirical evidence for rough volatility models, this paper investigates continuous-time mean-variance (MV) portfolio selection under the Volterra Heston model. Due to the non-Markovian and non-semimartingale nature of the…

Portfolio Management · Quantitative Finance 2020-01-30 Bingyan Han , Hoi Ying Wong

In this paper, we are interested in comparing solutions to stochastic Volterra equations for the convex order on the space of continuous $\R^d$-valued paths and for the monotonic convex order when $d=1$. Even if in general these solutions…

Probability · Mathematics 2022-11-21 Benjamin Jourdain , Gilles Pagès

A moderate deviations principle for the law of a stochastic Burgers equation is proved via the weak convergence approach. In addition, some useful estimates toward a central limit theorem are established.

Probability · Mathematics 2020-01-17 Rachid Belfadli , Lahcen Boulanba , Mohamed Mellouk

We offer a simple method Monte Carlo for computation of Volterra's and spherical type multiple integrals with weak (integrable) singularities. An elimination of infinity of variance is achieved by incorporating singularities in the density,…

Numerical Analysis · Mathematics 2014-05-27 E. Ostrovsky , L. Sirota

Using the weak convergence approach, we prove the large deviation principle (LDP) for solutions to quasilinear stochastic evolution equations with small Gaussian noise in the critical variational setting, a recently developed general…

Probability · Mathematics 2026-02-23 Esmée Theewis , Mark Veraar

This papers deals with a construction and convergence analysis of a finite difference scheme for solving time-fractional porous medium equation. The governing equation exhibits both nonlocal and nonlinear behaviour making the numerical…

Numerical Analysis · Mathematics 2019-04-05 Łukasz Płociniczak

Our study aims to specify the asymptotic error distribution in the discretization of a stochastic Volterra equation with a fractional kernel. It is well-known that for a standard stochastic differential equation, the discretization error,…

Numerical Analysis · Mathematics 2021-12-17 Masaaki Fukasawa , Takuto Ugai

This paper presents the error analysis of numerical methods on graded meshes for stochastic Volterra equations with weakly singular kernels. We first prove a novel regularity estimate for the exact solution via analyzing the associated…

Numerical Analysis · Mathematics 2023-09-01 Xinjie Dai , Jialin Hong , Derui Sheng

We consider stochastic volatility dynamics driven by a general H\"older continuous Volterra-type noise and with unbounded drift. For these so-called SVV-models, we consider the explicit computation of quadratic hedging strategies. While the…

Mathematical Finance · Quantitative Finance 2024-07-16 Giulia Di Nunno , Anton Yurchenko-Tytarenko

We study discrete-time simulation schemes for stochastic Volterra equations, namely the Euler and Milstein schemes, and the corresponding Multi-Level Monte-Carlo method. By using and adapting some results from Zhang [22], together with the…

Numerical Analysis · Mathematics 2022-03-08 Alexandre Richard , Xiaolu Tan , Fan Yang