Stochastic Analysis and Statistical Inference for Insurance Ruin Risks
| Project/Area Number |
24740061
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Waseda University (2014)
Osaka University (2012-2013) |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 破産理論 / 確率過程 / 数理統計 / 保険数理 / 漸近理論 / レヴィ型リスクモデル / 破産関連リスク量 / 再生方程式 / 国際情報交換(アメリカ，カナダ，中国) |
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| Outline of Final Research Achievements |
As a generalization of the classical insurance ruin theory, we investigated a generalized Gerber-Shiu analysis under Levy insurance risk models. Main results are an extension of the ruin-related risk (Gerber-Shiu function) to a integral type functional of the insurance surplus, the derivation of its renewal type equation, and a representation theorem by a scale function for a spectrally negative Levy process. Moreover, we studied an inflation risk model written by a stochastic differential equation, and gave a bound of ruin probability and an optimal strategy of a reinsurance. In statistical analysis, we gave an approximation by the Edgeworth type expansion of ruin probability, inference for the Gerber-Shiu function from a discrete samples, and investigated the statistical error with the rate of convergence. We also show by simulations that these methodologies numerically work well.
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Report
(4 results)
Research Products
(26 results)
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[Journal Article] The YUIMA Project: A Computational Framework for Simulation and Inference of Stochastic Differential Equations2014
Author(s)
Alexandre Brouste, Masaaki Fukasawa, Hideitsu Hino, Stefano Iacus, Kengo Kamatani, Yuta Koike, Hiroki Masuda, Ryosuke Nomura, Teppei Ogihara, Yasutaka Shimuzu, Masayuki Uchida, Nakahiro Yoshida
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Journal Title
Journal of Statistical Software
Volume: 57
Pages: 1-51
Related Report
Peer Reviewed / Open Access
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