Research for simulation schemes of stochastic differential equations and its application to mathematical finance.
| Project/Area Number |
23730297
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Public finance/Monetary economics
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| Research Institution | Japanese Red Cross College of Nursing (2012)
The University of Tokyo (2011) |
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Principal Investigator |
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| Project Period (FY) |
2011 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 確率数値解析 / 高次弱近似 / 数理ファイナンス / 確率微分方程式 / 楠岡近似 / ファイナンス / デリバティブ価格付け |
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| Research Abstract |
Numerical calculation of stochastic differential equations has been applied in many fields such as mathematical finance. However, there has been a difficulty of speeding up of calculation. The higher-order approximation of SDEs introduced by Kusuoka (Kusuoka approximation) theoretically gives the possibility of improvement of this problem. The research representative and Syoiti Ninomiya successfully constructed an algorithm (NN algorithm) of the Kusuoka approximation (2009).The research representative found that the numbers of conditions for variance-covariance matrix could be drastically reduced and proved the possibility of extension of the integration scheme applied in the NN algorithm as well as showed that the range of application of the Kusuoka approximation can be extended. Also, software library of higher-order approximation including the NN algorithm was constructed and released for its spread.
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Report
(3 results)
Research Products
(7 results)
