2020 Fiscal Year Final Research Report
A new automatic differentiation and its application to computational finance
Project/Area Number |
19K13736
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Research Category |
Grant-in-Aid for Early-Career Scientists
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Allocation Type | Multi-year Fund |
Review Section |
Basic Section 07060:Money and finance-related
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Research Institution | Hitotsubashi University |
Principal Investigator |
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Project Period (FY) |
2019-04-01 – 2021-03-31
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Keywords | 自動微分法 |
Outline of Final Research Achievements |
We provided a new automatic differentiation scheme for solutions to partial differential equations using a weak approximation approach of stochastic differential equations. Some numerical approximation schemes for related automatic differentiation problems are also obtained. Furthermore, we proposed a deep learning method combined with the automatic differentiation scheme for high-dimensional nonlinear partial differential equations and nonlinear pricing problems in finance.
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Free Research Field |
ファイナンス、数値解析
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Academic Significance and Societal Importance of the Research Achievements |
研究成果の学術的・社会的意義は、不確実性を伴う数理モデルにおける様々なリスク量のパラメータ感応度の高精度近似を可能にした点である。これは数理ファイナンス・金融工学の理論面だけでなく、金融実務のリスクヘッジやリスクマネジメントにおいても重要な意味を持つ。また、本研究課題で得られた成果はファイナンスにとどまらず、自然科学・社会科学の様々な確率モデルへの応用も可能であると考えられる。
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