论文标题
一般利率模型的分裂方法的收敛
Convergence of a splitting method for a general interest rate model
论文作者
论文摘要
对于广义AIT-Sahalia利率模型，我们证明了一种新型数值方法，即驯服方法的均方体收敛。该方法基于Lamperti变换，分裂和应用驯服数值方法的非线性。分析的主要困难是由模型的非全球lipschitz漂移系数引起的。我们检查了转化后的SDE的溶液的存在，唯一性和矩的界限。然后，我们证明了有界的矩并倒置数值近似的力矩。从某种意义上说，驯服的方法是一种混合方法，即调用一种后退方法以防止解决方案超过零并变得负面。我们成功地恢复了驯服方法的均方一体收敛率。此外，我们证明需要对预防负值进行后退方法的概率可以任意地使其很小。在我们的数值实验中，我们将文献中的其他数值方法比较了实际的参数值。
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 in the sense that a backstop method is invoked to prevent solutions from overshooting zero and becoming negative. We successfully recover the mean-square convergence rate of order one for the tamed-splitting method. In addition we prove that the probability of ever needing the backstop method to prevent a negative value can be made arbitrarily small. In our numerical experiments we compare to other numerical methods in the literature for realistic parameter values.
