| Project/Area Number |
17K14209
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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 |
Basic analysis
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| Research Institution | Shibaura Institute of Technology |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 確率微分方程式 / 離散・連続時間最大値 / 確率密度関数 / リスク計算 / モンテカルロシミュレーション / グリークス / 確率論 |
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| Outline of Final Research Achievements |
Researches of probability density functions and sensitivities concerning solutions of stochastic differential equations have been done. Regarding the former, the author obtained lower and upper bounds of the density function of discrete time maximum of the solution. The author then proved that the density function of the discrete time maximum converges to that of the continuous time maximum of the solution. Finally, the author proved the positivity of the density function of the continuous time maximum, and a relationship between the density functions of the continuous time maximum and the solution itself.The paper on these results has been accepted for publication in an international journal.
Regarding the latter, the author obtained a formula to compute risks of financial products depending on maxima of the solution of stochastic differential equations with coefficients dependent on the time and space parameter. Some numerical techniques applied to the formula also have been derived.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究では、従来はあまり十分に研究がなされていなかったが、応用上極めて重要である確率微分方程式の解の最大値に関する、理論・応用研究を行った。本研究は複雑な金融商品のリスク管理に応用可能な研究である。2008年に発生したリーマンショックが複雑な金融商品のリスクの未熟な扱いによって引き起こされたことを鑑みると、学術的（かつ客観的）立場から金融実務に繋がる研究を行えたことは、金融システムの安定への寄与という点で意義があると考えている。
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