相关论文: First order strong approximation of Ait-Sahalia-ty…
This article aims to reveal the mean-square convergence rate of the backward Euler method (BEM) for a generalized Ait-Sahaliz interest rate model with Poisson jumps. The main difficulty in the analysis is caused by the non-globally…
This paper focuses on mean-square approximations of a generalized A\"it-Sahalia interest rate model with Poisson jumps. The main challenge in the construction and analysis of time-discrete numerical schemes is caused by a drift that blows…
In this paper, we consider the generalized Ait-Sahaliz interest rate model with Poisson jumps in finance. The analytical properties including the positivity, boundedness and pathwise asymptotic estimations of the solution to the model are…
In this paper, we study analytical properties of the solutions to the generalised delay Ait-Sahalia-type interest rate model with Poisson-driven jump. Since this model does not have explicit solution, we employ several new truncated…
While the original Ait-Sahalia interest rate model has been found considerable use as a model for describing time series evolution of interest rates, it may not possess adequate specifications to explain responses of interest rates to…
We consider a class of general SDEs with a jump integral term driven by a time-inhomogeneous Poisson random measure. We propose a two-parameters Euler-type scheme for this SDE class and prove an optimal rate for the strong convergence with…
An Euler-type framework with equidistant step sizes is proposed for a class of time-changed stochastic differential equations.We establish the strong convergence rate of the standard Euler--Maruyama method under the global Lipschitz…
This paper investigates the strong convergence properties of two Euler-type methods for a class of time-changed stochastic differential equations (TCSDEs) with super-linearly growing drift and diffusion coefficients. Building upon existing…
We develop adaptive time-stepping strategies for It\^o-type stochastic differential equations (SDEs) with jump perturbations. Our approach builds on adaptive strategies for SDEs. Adaptive methods can ensure strong convergence of nonlinear…
We present an adaptive approximation scheme for jump-diffusion SDEs with discontinuous drift and (possibly) degenerate diffusion. This transformation-based doubly-adaptive quasi-Milstein scheme is the first scheme that has strong…
The present work is devoted to strong approximations of a generalized A\"{i}t-Sahalia model arising from mathematical finance. The numerical study of the considered model faces essential difficulties caused by a drift that blows up at the…
The present article aims to design and analyze efficient first-order strong schemes for a generalized A\"{i}t-Sahalia type model arising in mathematical finance and evolving in a positive domain $(0, \infty)$, which possesses a diffusion…
We prove mean-square convergence of a novel numerical method, the tamed-splitting method, for a generalized Ait-Sahalia interest rate model. The method is based on a Lamperti transform, splitting and applying a tamed numerical method for…
We consider the explicit numerical approximations of stochastic differential equations (SDEs) driven by Brownian process and Poisson jump. It is well known that under non-global Lipschitz condition, Euler Explicit method fails to converge…
We study in this article the strong rate of convergence of the Euler-Maruyama scheme and associated with the jump-type equation introduced in Li and Mytnik. We obtain the strong rate of convergence under similar assumptions for strong…
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.…
The paper studies the rate of convergence of the weak Euler approximation for solutions to possibly completely degenerate SDEs driven by Levy processes, with Hoelder-continuous coefficients. It investigates the dependence of the rate on the…
We study the nonparametric estimation of the jump density of a compound Poisson process from the discrete observation of one trajectory over $[0,T]$. We consider the microscopic regime when the sampling rate $\Delta=\Delta_T\rightarrow0$ as…
This work develops Monte Carlo Euler adaptive time stepping methods for the weak approximation problem of jump diffusion driven stochastic differential equations. The main result is the derivation of a new expansion for the omputational…
In this paper, we study a class of super-linear stochastic differential delay equations with Poisson jumps (SDDEwPJs). The convergence and rate of the convergence of the truncated Euler-Maruyama numerical solutions to SDDEwPJs are…