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Gerber-Shiu 関数の展開公式
https://chuo-u.repo.nii.ac.jp/records/2000129
https://chuo-u.repo.nii.ac.jp/records/20001299cacee5c-34eb-4fcc-9cde-52e3414097ee
名前 / ファイル | ライセンス | アクション |
---|---|---|
1347-9938-42-03.pdf
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Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||||||||||
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公開日 | 2023-09-13 | |||||||||||||
タイトル | ||||||||||||||
言語 | ja | |||||||||||||
タイトル | Gerber-Shiu 関数の展開公式 | |||||||||||||
タイトル | ||||||||||||||
言語 | en | |||||||||||||
タイトル | An Expansion Formula to the Gerber-Shiu Function | |||||||||||||
言語 | ||||||||||||||
言語 | jpn | |||||||||||||
キーワード | ||||||||||||||
言語 | en | |||||||||||||
主題Scheme | Other | |||||||||||||
主題 | the Gerber-Shiu function | |||||||||||||
キーワード | ||||||||||||||
言語 | en | |||||||||||||
主題Scheme | Other | |||||||||||||
主題 | the jump diffusion model | |||||||||||||
キーワード | ||||||||||||||
言語 | en | |||||||||||||
主題Scheme | Other | |||||||||||||
主題 | an expansion formula to the Gerber-Shiu function | |||||||||||||
キーワード | ||||||||||||||
言語 | en | |||||||||||||
主題Scheme | Other | |||||||||||||
主題 | Pollaczek-Khintchine formula | |||||||||||||
資源タイプ | ||||||||||||||
資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||||||||||
資源タイプ | departmental bulletin paper | |||||||||||||
著者 |
西岡,國雄
× 西岡,國雄
× 北村,仁代
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抄録 | ||||||||||||||
内容記述タイプ | Abstract | |||||||||||||
内容記述 | In order to incorporate the effects of operational risks and economic fluctuations, we define the surplus process {R(t)} of an insurance company, by jump diffusion model R(t) = x + t + σB(t) −ΣN(t)k=0Uk, x≥ 0. (See (Ⅰ.6) for more informations). The company goes to ruin at a moment of τ ≡ inf{t >0 : R(t) < 0}. When it occurs, important quantities are the surplus R(τ−) immediately prior to τ, and the deficit |R(τ)|. Therefore, given a suitable penalty function W(z, y)for y, z ≥ 0, the severity of ruin is defined by the Gerber-Shiu function ψ(x) = Ex[e−ατ W( R(τ−), | R(τ) |) ], where α ≥ 0 is a fixed discount rate. One of main topics on the risk theory is to analyze ψ, because ψ can be various quantities related to the risk theory. To this end, we present an expansion formula to ψ under a general claim size distribution and a general W. In the special case of σ = 0, W ≡ 1,and α = 0, our formula becomes to the Pollaczek-Khintchine formula whose usefulness is well known. |
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言語 | en | |||||||||||||
書誌情報 |
ja : 企業研究 号 42, p. 31-50, 発行日 2023-02-28 |
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出版者 | ||||||||||||||
言語 | ja | |||||||||||||
出版者 | 企業研究所 | |||||||||||||
ISSN | ||||||||||||||
収録物識別子タイプ | ISSN | |||||||||||||
収録物識別子 | 1347-9938 | |||||||||||||
権利 | ||||||||||||||
言語 | ja | |||||||||||||
権利情報 | この資料の著作権は、資料の著作者または学校法人中央大学に帰属します。著作権法が定める私的利用・引用を超える使用を希望される場合には、掲載誌発行部局へお問い合わせください。 | |||||||||||||
フォーマット | ||||||||||||||
内容記述タイプ | Other | |||||||||||||
内容記述 | application/pdf | |||||||||||||
著者版フラグ | ||||||||||||||
出版タイプ | VoR | |||||||||||||
出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 |