2009 Fiscal Year Final Research Report
Construction of new algorithms for numerical weak approximation of Diffusion Processes by Kusuoka scheme and their applications to Finance problems
Project/Area Number |
18540113
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Single-year Grants |
Section | 一般 |
Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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Research Institution | Tokyo Institute of Technology |
Principal Investigator |
NINOMIYA Syoiti Tokyo Institute of Technology, 大学院・イノベーションマネジメント研究科, 教授 (70313377)
|
Co-Investigator(Renkei-kenkyūsha) |
KUSUOKA Shigeo 東京大学, 大学院・数理科学研究科, 教授 (00114463)
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Project Period (FY) |
2006 – 2009
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Keywords | 確率論 / 数理工学 / アルゴリズム |
Research Abstract |
(1) We have succeeded in finding and constructing new higher-order numerical approximation algorithms for diffusion processes. The algorithms are based on the theory of Kusuoka approximation. They enjoy both the numerical robustness and the universality, that is, we can apply them for almost all diffusions. (2) We applied the algorithms to some finance problems and achieved remarkable improvements in : (a) very fast calculation (at least 100 times faster than the state of the art methods) (b) robust discretization (c) universality. (3) We have developed the computer program of the algorithms.
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Research Products
(9 results)