%0 Journal Article
%T Asymptotic Analysis for Spectral Risk Measures Parameterized by Confidence Level
%A Takashi Kato
%J Journal of Mathematical Finance
%P 197-226
%@ 2162-2442
%D 2018
%I Scientific Research Publishing
%R 10.4236/jmf.2018.81015
%X We study the asymptotic behavior of the difference as , where is a risk measure equipped with a confidence level parameter , and where X and Y are non-negative random variables whose tail probability functions are regularly varying. The case where is the value-at-risk (VaR) at ¦Á, is treated in [1]. This paper investigates the case where is a spectral risk measure that converges to the worst-case risk measure as . We give the asymptotic behavior of the difference between the marginal risk contribution and the Euler contribution of Y to the portfolio X+Y . Similarly to [1], our results depend primarily on the relative magnitudes of the thicknesses of the tails of X and Y. Especially, we find that is asymptotically equivalent to the expectation (expected loss) of Y if the tail of Y is sufficiently thinner than that of X. Moreover, we obtain the asymptotic relationship as , where is a constant whose value likewise changes according to the relative magnitudes of the thicknesses of the tails of X and Y. We also conducted a numerical experiment, finding that when the tail of X is sufficiently thicker than that of Y, does not increase monotonically with ¦Á and takes a maximum at a confidence level strictly less than 1.
%K Spectral Risk Measures
%K Quantitative Risk Management
%K Asymptotic Analysis
%K Extreme Value Theory
%K Euler Contribution
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=82779