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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク distortion risk measure ： ウィキペディア英語版 distortion risk measure In financial mathematics, a distortion risk measure is a type of risk measure which is related to the cumulative distribution function of the return of a financial portfolio. == Mathematical definition == The function $\backslash rho\_g:\; L^p\; \backslash to\; \backslash mathbb$ associated with the distortion function $g:\; ()\; \backslash to\; ()$ is a ''distortion risk measure'' if for any random variable of gains $X\; \backslash in\; L^p$ (where $L^p$ is the Lp space) then : $\backslash rho\_g(X)\; =\; -\backslash int\_0^1\; F\_^(p)\; d\backslash tilde(p)\; =\; \backslash int\_^0\; \backslash tilde(F\_(x))dx\; -\; \backslash int\_0^\; g(1\; -\; F\_(x))\; dx$ where $F\_$ is the cumulative distribution function for $-X$ and $\backslash tilde$ is the dual distortion function $\backslash tilde(u)\; =\; 1\; -\; g(1-u)$.〔 If $X\; \backslash leq\; 0$ almost surely then $\backslash rho\_g$ is given by the Choquet integral, i.e. $\backslash rho\_g(X)\; =\; -\backslash int\_0^\; g(1\; -\; F\_(x))\; dx.$ Equivalently, $\backslash rho\_g(X)\; =\; \backslash mathbb^$ is the probability measure generated by $g$, i.e. for any $A\; \backslash in\; \backslash mathcal$ the sigma-algebra then $\backslash mathbb(A)\; =\; g(\backslash mathbb(A))$. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「distortion risk measure」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.