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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 Spectral risk measure ： ウィキペディア英語版 Spectral risk measure A Spectral risk measure is a risk measure given as a weighted average of outcomes where bad outcomes are, typically, included with larger weights. A spectral risk measure is a function of portfolio returns and outputs the amount of the numeraire (typically a currency) to be kept in reserve. A spectral risk measure is always a coherent risk measure, but the converse does not always hold. An advantage of spectral measures is the way in which they can be related to risk aversion, and particularly to a utility function, through the weights given to the possible portfolio returns. == Definition == Consider a portfolio $X$ Then a spectral risk measure $M\_:\; \backslash mathcal\; \backslash to\; \backslash mathbb$ where $\backslash phi$ is non-negative, non-increasing, right-continuous, integrable function defined on $()$ such that $\backslash int\_0^1\; \backslash phi(p)dp\; =\; 1$ is defined by :$M\_(X)\; =\; -\backslash int\_0^1\; \backslash phi(p)\; F\_X^(p)\; dp$ where $F\_X$ is the cumulative distribution function for ''X''.〔 If there are $S$ equiprobable outcomes with the corresponding payoffs given by the order statistics $X\_,\; ...\; X\_$. Let $\backslash phi\backslash in\backslash mathbb^S$. The measure $M\_:\backslash mathbb^S\backslash rightarrow\; \backslash mathbb$ defined by $M\_(X)=-\backslash delta\backslash sum\_^S\backslash phi\_sX\_$ is a spectral measure of risk if $\backslash phi\backslash in\backslash mathbb^S$ satisfies the conditions # Nonnegativity: $\backslash phi\_s\backslash geq0$ for all $s=1,\; \backslash dots,\; S$, # Normalization: $\backslash sum\_^S\backslash phi\_s=1$, # Monotonicity : $\backslash phi\_s$ is non-increasing, that is $\backslash phi\_\backslash geq\backslash phi\_$ if and $,\; \backslash in\backslash$. 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「Spectral 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.