Project/Area Number |
24740061
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Research Category |
Grant-in-Aid for Young Scientists (B)
|
Allocation Type | Multi-year Fund |
Research Field |
General mathematics (including Probability theory/Statistical mathematics)
|
Research Institution | Waseda University (2014) Osaka University (2012-2013) |
Principal Investigator |
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Project Period (FY) |
2012-04-01 – 2015-03-31
|
Project Status |
Completed (Fiscal Year 2014)
|
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)
|
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) |
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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