Asymptotic distribution theory for mathematical finance
| Project/Area Number |
24684006
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| Research Category |
Grant-in-Aid for Young Scientists (A)
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| Allocation Type | Partial Multi-year Fund |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Osaka University |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥8,840,000 (Direct Cost: ¥6,800,000、Indirect Cost: ¥2,040,000)
Fiscal Year 2015: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2014: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2013: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2012: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
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| Keywords | 数理ファイナンス / インプライド・ボラティリティ / 漸近展開 / 確率解析 / 中心極限定理 / 安定収束 / 取引費用 / 確率制御 / ボラティリティ / デルタヘッジ / 最適ヘッジ戦略 / 同質化 / 国際研究者交流（フランス） / ヘッジ戦略 / 国際研究者交流 / フランス：イギリス / 確率積分 / 強近似 / 離散ヘッジ / 凸リスク測度 / オイラー丸山近似 / 停止時刻 |
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| Outline of Final Research Achievements |
We extend asymptotic distribution theory of stochastic processes to find explicit solutions to problems in mathematical finance. They include optimal hedging problem under transaction costs, for which we constructed explicit hedging strategies minimizing relative asymptotic hedging error or asymptotic error variance. These results can be seen as developments in approximation theory of stochastic integrals. We studied also small-time asymptotics of stochastic processes which are models for financial asset prices. We derived and validated an asymptotic expansion of marginal distribution to show in particular that models with fractional Brownian motion explain the term structure of option price data.
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Report
(6 results)
Research Products
(29 results)
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[Journal Article] The YUIMA Project: A Computational Framework for Simulation and Inference of Stochastic Differential Equations2014
Author(s)
A. Brouste, M. Fukasawa, H. Hino, S. Iacus, K. Kamatani, Y. Koike, H. Masuda, R. Nomura, T. Ogihara, Y. Shimuzu, M. Uchida and N. Yoshida
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Journal Title
Journal of Statistical Software
Volume: 57
Pages: 4-4
Related Report
Peer Reviewed
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