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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 Coherent risk measure ： ウィキペディア英語版 Coherent risk measure In the fields of Actuarial Science and financial economics there are a number of ways that risk can be defined; to clarify the concept theoreticians have described a number of properties that a risk measure might or might not have. A coherent risk measure is a function $\backslash varrho$ that satisfies properties of monotonicity, sub-additivity, homogeneity, and translational invariance. ==Properties== Consider a random outcome $X$ viewed as an element of a linear space $\backslash mathcal$ of measurable functions, defined on an appropriate probability space. A functional $\backslash varrho\; :\; \backslash mathcal$ → $\backslash R\; \backslash cup\; \backslash$ is said to be coherent risk measure for $\backslash mathcal$ if it satisfies the following properties: ; Normalized : $\backslash varrho(0)\; =\; 0$ That is, the risk of holding no assets is zero. ; Monotonicity : $\backslash mathrm\backslash ;\; Z\_1,Z\_2\; \backslash in\; \backslash mathcal\; \backslash ;\backslash mathrm\backslash ;\; Z\_1\; \backslash leq\; Z\_2\; \backslash ;\; \backslash mathrm\; ,\backslash ;\; \backslash mathrm\; \backslash ;\; \backslash varrho(Z\_1)\; \backslash geq\; \backslash varrho(Z\_2)$ That is, if portfolio $Z\_2$ always has better values than portfolio $Z\_1$ under almost all scenarios then the risk of $Z\_2$ should be less than the risk of $Z\_1$. E.g. If $Z\_1$ is an in the money call option (or otherwise) on a stock, and $Z\_2$ is also an in the money call option with a lower strike price. ; Sub-additivity : $\backslash mathrm\backslash ;\; Z\_1,Z\_2\; \backslash in\; \backslash mathcal\; ,\backslash ;\; \backslash mathrm\backslash ;\; \backslash varrho(Z\_1\; +\; Z\_2)\; \backslash leq\; \backslash varrho(Z\_1)\; +\; \backslash varrho(Z\_2)$ Indeed, the risk of two portfolios together cannot get any worse than adding the two risks separately: this is the diversification principle. ; Positive homogeneity : $\backslash mathrm\backslash ;\; \backslash alpha\; \backslash ge\; 0\; \backslash ;\; \backslash mathrm\; \backslash ;\; Z\; \backslash in\; \backslash mathcal\; ,\backslash ;\; \backslash mathrm\; \backslash ;\; \backslash varrho(\backslash alpha\; Z)\; =\; \backslash alpha\; \backslash varrho(Z)$ Loosely speaking, if you double your portfolio then you double your risk. ; Translation invariance If $A$ is a deterministic portfolio with guaranteed return $a$ and $Z\; \backslash in\; \backslash mathcal$ then : $\backslash varrho(Z\; +\; A)\; =\; \backslash varrho(Z)\; -\; a$ The portofolio $A$ is just adding cash $a$ to your portfolio $Z$. In particular, if $a=\backslash varrho(Z)$ then $\backslash varrho(Z+A)=0$. 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「Coherent 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.