英文标题：
《Splitting and Matrix Exponential approach for jump-diffusion models with
Inverse Normal Gaussian, Hyperbolic and Meixner jumps》
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作者：
Andrey Itkin
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最新提交年份：
2014
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英文摘要：
This paper is a further extension of the method proposed in Itkin, 2014 as applied to another set of jump-diffusion models: Inverse Normal Gaussian, Hyperbolic and Meixner. To solve the corresponding PIDEs we accomplish few steps. First, a second-order operator splitting on financial processes (diffusion and jumps) is applied to these PIDEs. To solve the diffusion equation, we use standard finite-difference methods. For the jump part, we transform the jump integral into a pseudo-differential operator and construct its second order approximation on a grid which supersets the grid that we used for the diffusion part. The proposed schemes are unconditionally stable in time and preserve positivity of the solution which is computed either via a matrix exponential, or via P\'ade approximation of the matrix exponent. Various numerical experiments are provided to justify these results.
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中文摘要：
本文是Itkin，2014提出的方法的进一步扩展，并应用于另一组跳跃扩散模型：逆正态高斯、双曲和Meixner。要解决相应的PIDE，我们只需完成几个步骤。首先，对这些PIDE应用金融过程（扩散和跳跃）的二阶算子分裂。为了求解扩散方程，我们使用标准的有限差分方法。对于跳跃部分，我们将跳跃积分转化为一个伪微分算子，并在一个网格上构造它的二阶近似，该网格超越了我们用于扩散部分的网格。所提出的格式在时间上是无条件稳定的，并保持通过矩阵指数或通过矩阵指数的P’ade近似计算的解的正性。通过各种数值实验验证了这些结果。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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