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Risk contagion under regular variation and asymptotic tail independence. (arXiv:1603.09406v2 [math.ST] UPDATED)
来源于:arXiv
Risk contagion concerns any entity dealing with large scale risks. Suppose
(X,Y) denotes a risk vector pertaining to two components in some system. A
relevant measurement of risk contagion would be to quantify the amount of
influence of high values of Y on X. This can be measured in a variety of ways.
In this paper, we study two such measures: the quantity E[max(X-t,0)|Y > t]
called Marginal Mean Excess (MME) as well as the related quantity E[X|Y > t]
called Marginal Expected Shortfall (MES). Both quantities are indicators of
risk contagion and useful in various applications ranging from finance,
insurance and systemic risk to environmental and climate risk. We work under
the assumptions of multivariate regular variation, hidden regular variation and
asymptotic tail independence for the risk vector (X,Y). Many broad and useful
model classes satisfy these assumptions. We present several examples and derive
the asymptotic behavior of both MME and MES as the threshold t tends to
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