Representation theorem for AVaR under a submodular capacity
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摘要: 从分位数函数的角度出发, 首先定义了金融头寸在容度空间下的\,VaR\,和\,AVaR. 然后综合运用\,Choquet\,积分的性质以及概率测度空间下\,AVaR\,的结果, 建立了基于二次交替容度的\,AVaR\,的表示定理. 进一步得到了基于二次交替容度的\,AVaR\,为一致性风 险度量, 推广了经典的结果.Abstract: From the viewpoints of quantile functions, we gave the definition of AVaR of financial positions under a capacity. Then, using the classical results of AVaR under the probability measure, we established the representation theorem for AVaR under the submodular capacity. As a byproduct of this representation theorem, we proved that AVaR under a submodular capacity is a coherent risk measure, which generalized the classical results.
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Key words:
- AVaR /
- quantile function /
- representation theorem /
- submodular capacity
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