2005 Fiscal Year Final Research Report Summary
A new weak approximation scheme of diffusion and its application to Finance
| Project/Area Number |
15540110
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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, Graduate School of Innovation Management, Professor, 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) |
KUSUOKA Shigeo Univ.of Tokyo, Graduate School of Mathematical Science, Professor, 大学院・数理科学研究科, 教授 (00114463)
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| Project Period (FY) |
2003 – 2005
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| Keywords | Stochastic Differential Equation / Numerical Method / Simulation / quasi-Monte Carlo |
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| Research Abstract |
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.
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