A new weak approximation scheme of diffusion and its application to Finance

一种新的扩散弱近似方案及其在金融中的应用

• 批准号: 15540110
• 负责人: NINOMIYA Syoiti
• 金额: $ 1.92万
• 依托单位: Tokyo Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540110/
• 关键词: Stochastic Differential Equation; Numerical Method; Simulation; quasi-Monte Carlo; 確立微分方程式; 微分方程式の数値解法; 数理ファイナンス; ファイナンス; Runge-Kutta法; 高速化; 金融派生商品; 拡散過程; 確率微分方程式の数値解法

The object of this project is to establish the Kusuoka approximation. Kusuoka approximation is a new scheme that approximate E[f(X(T)] where X(t) denotes a diffusion process and f a function with some regularity. This problem is called weak approximation. By using the Kusuoka approximation, it is expected that we can reduce the number of the dimension of the domain of integration which arises in the last step of the approximation. This integral dimension is a very critical factor if we use quasi-Monte Carlo techniques. In this project, we have achieved the following successes :1. The discovery of a versatile algorithm that enables us to apply the Kusuoka approximation easily to any diffusion processes described by SDEs.2. The algorithm above also is compatible with quasi-Monte Carlo method.3. We have applied the algorithm to financial derivative pricing problem and showed that our new algorithm makes at least 800 times faster calculation than existing methods.

这个项目的目的是建立Kusuoka近似。Kusuoka近似是一种近似E[f(X(T)]的新格式，其中X(T)表示扩散过程，f表示具有一定规律性的函数。这个问题叫做弱近似。通过使用Kusuoka近似，我们期望可以减少在近似的最后一步产生的积分域的维数。如果我们使用拟蒙特卡罗技术，这个积分维数是一个非常关键的因素。在这个项目中，我们取得了以下成功：1。发现了一种通用算法，使我们能够轻松地将Kusuoka近似应用于sdes描述的任何扩散过程。该算法还与拟蒙特卡罗方法兼容。将该算法应用于金融衍生品定价问题，结果表明，新算法的计算速度比现有方法至少快800倍。

项目成果

A partial Sompling method Applied to the Kusuoka approximation

应用于Kusuoka近似的部分Sompling方法

• 发表时间: 2003
• 期刊: Monte Carlo methods and Applications 9
• 作者: Shigeo Kusuoka;Syoiti Ninomiya;二宮祥一
• 通讯作者: 二宮祥一

A new simulation method of diffusion processes applied to Finance

应用于金融的扩散过程新模拟方法

• 发表时间: 2004
• 期刊: Proceedings of the Ritsumeikan International Symposium (Ed.by Akahori,Ogawa,Watanabe)
• 作者: 楠岡成雄;二宮祥一
• 通讯作者: 二宮祥一

A partical sampling method applied to the Kusuoka approximation

应用于Kusuoka近似的粒子采样方法

• 发表时间: 2003
• 期刊: Monte Carlo Methods and Applications Vol.9
• 作者: Shigeo Kusuoka;Syoiti Ninomiya;二宮祥一;Syoiti Ninomiya
• 通讯作者: Syoiti Ninomiya

T.Fujita, Sh.Ito, S.Ninomiya: "Generalized ramder Corput sequence and its application to Numerical Integration"Monte Carlo Method and its application. (to appear). (2002)

T.Fujita、Sh.Ito、S.Ninomiya：“广义 ramder Corput 序列及其在数值积分中的应用”蒙特卡罗方法及其应用。

Syoiti Ninomiya: "A new simulation scheme : Application of the Kusuoka Approximation to Finance problems"Mathematics and Computers in Simulation. (to appear).

Syoiti Ninomiya：“一种新的模拟方案：Kusuoka 近似在金融问题中的应用”模拟中的数学和计算机。