| Project/Area Number |
16K00036
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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 |
Mathematical informatics
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| Research Institution | Keio University |
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Principal Investigator |
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| Project Period (FY) |
2016-10-21 – 2022-03-31
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| Project Status |
Completed (Fiscal Year 2021)
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| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2020: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2019: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 保険数理 / Levy過程 / 最適配当境界 / リサンプリング / M推定量 / 破産理論 / 経験過程 / 危険理論 / Wiener-Poisson過程 / V統計量 / U統計量 / Hawkes過程 / INAR過程 / 複合ポアソン過程 / 統計的推定 / 統計数学 / 配当戦略 |
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| Outline of Final Research Achievements |
In this study, we established a statistical inference theory for optimal dividend barrier in the field of ruin theory, a branch of actuarial science.
The insurer's surplus is modeled in terms of three factors: initial capital, premium income, and claim payments, and is represented classically by the Cramer-Lundberg model and in recent years by the Levy insurance model.
The optimal dividend barrier is a threshold on this surplus, defined as the threshold that minimizes a certain loss function. In this study, we propose a statistical method for estimating the optimal dividend barrier, and we derive the consistency and asymptotic normality of the estimator in the case of the Levy insurance model, and confirm the usefulness of the proposed method through simulations.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究では、最適配当境界を統計的に推定するために、観測されたパスの増分をリサンプリングした疑似的なサンプルパスを複数生成し、それを使って損失関数の推定量を構成し、それを最小化した閾値を最適配当境界の推定量と定義する。この推定量はそれぞれのパスをランダム要素を見たときのM推定量の1つと定義することができ、興味のあるパラメータがサンプルパスの影響を受けるような場合の問題に一般化できる。本研究の結果は一般のM推定量の枠組みに拡張できることから、保険数理の分野のみならず多くの分野への活用が期待できる。
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