| 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 |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Tokyo Institute of Technology |
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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)
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| Co-Investigator(Kenkyū-buntansha) |
楠岡 成雄 東京大学, 大学院・数理科学研究科, 教授 (00114463)
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| 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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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥3,630,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥630,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2007: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2006: ¥900,000 (Direct Cost: ¥900,000)
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| Keywords | 確率論 / 数理工学 / アルゴリズム / 数理ファイナンス / デリバティブ / 確率微分方程式 / 確率諭 |
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| 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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