2016 Fiscal Year Final Research Report
A Study of Levy Processes in Finance
| Project/Area Number |
26380402
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Money/ Finance
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| Research Institution | Hosei University |
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Principal Investigator |
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| Research Collaborator |
YOSHIKAWA Daisuke 北海学園大学, 経営学部, 准教授
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Keywords | ファイナンス / 確率解析 / レヴィ過程 / 時間変更レヴィ過程 / デリバティブ / 資産価格 / 最適配当政策 / プライシング・カーネル |
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| Outline of Final Research Achievements |
This study has addressed an application of Levy and time-changed Levy processes to the field of finance and extended classical financial theory based on normal distributions. Levy processes are a class of non-Gaussian stochastic processes for describing jumps in asset price dynamics and dividend streams, and time-changed Levy processes are their generalization with stochastic time change, which can be regarded as a generalization of stochastic volatility. They have been applied to the four problems: path-dependent option pricing, asset pricing in exchange economy, optimal dividend policy for a firm, and reproducing U-shaped pricing kernels. In these problems, analytical representations of derivative prices, asset prices, and decision rules for optimal policy were derived from financial models we proposed. In addition, numerical examples were provided for deeply understanding our mathematical results. As a result, four academic papers were published in international journals.
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| Free Research Field |
ファイナンス
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