2014 Fiscal Year Final Research Report
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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| Keywords | 破産理論 / 確率過程 / 数理統計 |
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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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| Free Research Field |
保険数理
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