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dynamic risk measure : ウィキペディア英語版
dynamic risk measure
In financial mathematics, a conditional risk measure is a random variable of the financial risk (particularly the downside risk) as if measured at some point in the future. A risk measure can be thought of as a conditional risk measure on the trivial sigma algebra.
A dynamic risk measure is a risk measure that deals with the question of how evaluations of risk at different times are related. It can be interpreted as a sequence of conditional risk measures.
==Conditional risk measure==
A mapping \rho_t: L^\left(\mathcal_T\right) \rightarrow L^_t = L^\left(\mathcal_t\right) is a conditional risk measure if it has the following properties:
; Conditional cash invariance
: \forall m_t \in L^_t: \; \rho_t(X + m_t) = \rho_t(X) - m_t
; Monotonicity
: \mathrm \; X \leq Y \; \mathrm \; \rho_t(X) \geq \rho_t(Y)
; Normalization
: \rho_t(0) = 0
If it is a conditional convex risk measure then it will also have the property:
; Conditional convexity
: \forall \lambda \in L^_t, 0 \leq \lambda \leq 1: \rho_t(\lambda X + (1-\lambda) Y) \leq \lambda \rho_t(X) + (1-\lambda) \rho_t(Y)
A conditional coherent risk measure is a conditional convex risk measure that additionally satisfies:
; Conditional positive homogeneity
: \forall \lambda \in L^_t, \lambda \geq 0: \rho_t(\lambda X) = \lambda \rho_t(X)

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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