期刊名称：HIER Discussion Paper Series / Harvard Institute of Economic Research
出版年度：2005
卷号：2005
出版社：Harvard Institute of Economic Research
摘要：We present a unified approach to value at risk analysis under heavy-tailedness
using new majorization theory for linear combinations of thick-tailed random
variables that we develop. Among other results, we show that the stylized fact
that portfolio diversification is always preferable is reversed for extremely
heavy-tailed risks or returns. The stylized facts on diversification are
nevertheless robust to thick-tailedness of risks or returns as long as their
distributions are not extremely long-tailed. We further demonstrate that the
value at risk is a coherent measure of risk if distributions of risks are not
extremely heavy-tailed. However, coherency of the value at risk is always
violated under extreme thick-tailedness. Extensions of the results to the case
of dependence, including convolutions of a-symmetric distributions and models
with common stochs are provided.
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