相关论文: On a positivity preserving numerical scheme for ju…

This paper is concerned with the numerical approximation of stochastic ordinary differential equations, which satisfy a global monotonicity condition. This condition includes several equations with super-linearly growing drift and diffusion…

We study the convergence of a drift implicit scheme for one-dimensional SDEs that was considered by Alfonsi for the Cox-Ingersoll-Ross (CIR) process. Under general conditions, we obtain a strong convergence of order 1. In the CIR case,…

For stochastic processes of non-commuting random variables we formulate a Cox-Ingersoll-Ross (CIR) stochastic differential equation in the context of free probability theory which was introduced by Voicelescu. By transforming the classical…

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…

Recently, emerging epidemics like COVID-19 and its variants require predictive mathematical models to implement suitable responses in order to limit their negative and profound impact on society. The SIR (Susceptible-InfectedRemoved) system…

In this paper we propose an explicit and positivity preserving scheme for the mean reverting CEV model which converges in the mean square sense with convergence order $a(a-1/2)$.

In this paper, local linear estimators are adapted for the unknown infinitesimal coefficients associated with continuous-time asset return model with jumps, which can correct the bias automatically due to their simple bias representation.…

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…

We present a positivity-preserving method for multi-resolution simulations of compressible flows involving extreme conditions such as near vacuum and strong discontinuities. The novelty of this work is due to two aspects. First we extend…

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,…

This paper analyzes the problem of starting and stopping a Cox-Ingersoll-Ross (CIR) process with fixed costs. In addition, we also study a related optimal switching problem that involves an infinite sequence of starts and stops. We…

In this paper, we establish the weak convergence rate of density-dependent stochastic differential equations with bounded drift driven by $\alpha$-stable processes with $\alpha\in(1,2)$. The well-posedness of these equations has been…

We consider an economic agent (a household or an insurance company) modelling its surplus process by a deterministic process or by a Brownian motion with drift. The goal is to maximise the expected discounted spendings/dividend payments,…

In this paper, we consider a one-dimensional jump-type Cox-Ingersoll-Ross process driven by a Brownian motion and a subordinator, whose growth rate is an unknown parameter. Considering the process observed continuously or discretely at high…

In this article, we study the asymptotic behaviour of L\'evy processes with no positive jumps conditioned to stay positive. We establish integral tests for the lower envelope at 0 and at $+\infty$ and an analogue of Khintchin's law of the…

To construct positivity-preserving numerical methods, a vast majority of existing works employ transformation techniques such as the Lamperti transformation or logarithmic transformation. However, using these techniques often leads to the…

Stochastic modelling of fatigue (and other material's deterioration), as well as of cumulative damage in risk theory, are often based on compound sums of independent random variables, where the number of addends is represented by an…

In this paper, we are interested in constructing a scheme solving compressible Navier--Stokes equations, with desired properties including high order spatial accuracy, conservation, and positivity-preserving of density and internal energy…

Affine jump-diffusions constitute a large class of continuous-time stochastic models that are particularly popular in finance and economics due to their analytical tractability. Methods for parameter estimation for such processes require…

This paper establishes strong and weak convergence rates for slow-fast systems driven by $\alpha$-stable processes with jump coefficients. Unlike existing studies on multiscale systems driven by additive L\'{e}vy white noise, our model…