标题： 随机微分方程的强泰勒逼近及其在Lévy LIBOR模型中的应用 显示英文标题

标题： Strong Taylor approximation of stochastic differential equations and application to the Lévy LIBOR model

摘要： 本文我们发展了一种方法，用于强逼近由Lévy过程或一般半鞅驱动的随机微分方程（SDE）。 我们的方法的主要组成部分是对SDE的扰动以及由此产生的参数化曲线的泰勒展开。我们将此方法应用于开发LIBOR市场模型的强逼近格式。特别是，我们推导出了比完整SDE模拟更易处理的快速且精确的LIBOR模型衍生品估值算法。 一个关于Lévy LIBOR模型的数值例子说明了我们的方法。 显示英文摘要

摘要： In this article we develop a method for the strong approximation of stochastic differential equations (SDEs) driven by L\'evy processes or general semimartingales. The main ingredients of our method is the perturbation of the SDE and the Taylor expansion of the resulting parameterized curve. We apply this method to develop strong approximation schemes for LIBOR market models. In particular, we derive fast and precise algorithms for the valuation of derivatives in LIBOR models which are more tractable than the simulation of the full SDE. A numerical example for the L\'evy LIBOR model illustrates our method.