2018 Fiscal Year Final Research Report
Numerical analysis for SDE and non-colliding stochastic processes
| Project/Area Number |
17H06833
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Basic analysis
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| Research Institution | Osaka University |
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Principal Investigator |
Taguchi Dai 大阪大学, 基礎工学研究科, 助教 (70804657)
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| Research Collaborator |
Li Libo
Ngo Hoang-Long
Naganuma Nobuaki
Tanaka Akihiro
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| Project Period (FY) |
2017-08-25 – 2019-03-31
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| Keywords | 確率微分方程式 / CIR過程 / Levy過程 / Euler-Maruyama近似 |
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| Outline of Final Research Achievements |
Recently, CIR processes (Cox-Ingersoll-Ross processes) and CEV processes (constant elasticity of variance processes) are widely used in mathematical finance, and are extended in various directions, such as extending to the Jump type by using the Levy processes. These stochastic processes have some boundary conditions, such as not taking negative values or not staying at the boundary. The research achievements of this study are to introduce a discrete approximation scheme with the same boundary conditions as these stochastic processes, and provide their rate of convergence.
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| Free Research Field |
確率数値解析
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| Academic Significance and Societal Importance of the Research Achievements |
確率微分方程式に対する離散近似はEuler-Maruyama近似が広く用いられるが、対応する確率微分方程式と同様の境界条件を満たすとは限らない。本研究で得られた成果では、対応する確率微分方程式と同様の境界条件を持つ離散近似を構成することができ、近年広く研究されている境界付き確率過程に対する数値解析が可能となる。また、確率微分方程式は楕円型偏微分方程式と深い関係が知られているため、確率論を用いた数値解析（モンテカルロ法）を適用することができる。
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