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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 that satisfies properties of monotonicity, sub-additivity, homogeneity, and translational invariance. ==Properties== Consider a random outcome viewed as an element of a linear space of measurable functions, defined on an appropriate probability space. A functional → is said to be coherent risk measure for if it satisfies the following properties: ; Normalized : That is, the risk of holding no assets is zero. ; Monotonicity : That is, if portfolio always has better values than portfolio under almost all scenarios then the risk of should be less than the risk of . E.g. If is an in the money call option (or otherwise) on a stock, and is also an in the money call option with a lower strike price. ; Sub-additivity : Indeed, the risk of two portfolios together cannot get any worse than adding the two risks separately: this is the diversification principle. ; Positive homogeneity : Loosely speaking, if you double your portfolio then you double your risk. ; Translation invariance If is a deterministic portfolio with guaranteed return and then : The portofolio is just adding cash to your portfolio . In particular, if then . 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
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