On the backward Euler method for a generalized Ait-Sahalia-type rate model with Poisson jumps

带 Poisson 跳的 Ait-Sahalia 型利率模型的一阶强逼近

First order strong approximation of Ait-Sahalia-type interest rate model with Poisson jumps

针对带 Poisson 跳且系数非全局 Lipschitz 的 Ait-Sahalia 型利率模型，提出保持正值域的 TJABEM，并证明其在 $L^p$ 准则下一阶强收敛。

带Poisson跳的Aït-Sahalia型模型的显式修正Euler逼近

Explicit modified Euler approximations of the Aït-Sahalia type model with Poisson jumps

本文针对带Poisson跳且漂移在原点爆发的广义Aït-Sahalia利率模型，通过引入隐式项与修正函数提出一种显式修正Euler格式，证明其无条件保正且均方收敛阶为1/2，并通过数值实验验证理论。

广义 Ait-Sahalia 模型的无条件保正显式 Euler 型格式

Unconditionally positivity-preserving explicit Euler-type schemes for a generalized Ait-Sahalia model

针对广义 Aït-Sahalia 模型在原点发散的漂移项及保正性难题，提出一种无条件保正的显式 Euler 型格式，在非临界与一般临界情形下均实现 0.5 阶均方收敛率，为 MLMC 模拟提供理论依据。

具有泊松跳跃的广义Ait-Sahalia型利率模型及数值近似的收敛性

Generalized Ait-Sahalia-type interest rate model with Poisson jumps and convergence of the numerical approximation

本文研究了具有泊松跳跃的广义Ait-Sahalia型利率模型的分析性质，并证明了欧拉-马尔可夫（EM）数值解在概率意义下收敛于真实解，同时应用EM解计算金融量。

Ait-Sahalia 型模型的无条件保正逼近：显式 Milstein 型格式

Unconditionally positivity-preserving approximations of the Ait-Sahalia type model: Explicit Milstein-type schemes

针对金融领域广义Aït-Sahalia型模型数值离散难的问题，结合隐式项与校正映射构建显式无条件保正Milstein型格式，证明其一阶均方收敛性，可支撑多层蒙特卡洛方法的最优复杂度，且经数值实验验证。

Convergence of a splitting method for a general interest rate model

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 the nonlinearity. The main difficulty in the analysis is caused by the non-globally Lipschitz drift coefficients of the model. We examine the existence, uniqueness of the solution and boundedness of moments for the transformed SDE.We then prove bounded moments and inverses moments for the numerical approximation. The tamed-splitting method is a hybrid method i…