Extreme value analysis of the Haezendonck-Goovaerts risk measure with a general Young function

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<title>Extreme value analysis of the Haezendonck-Goovaerts risk measure with a general Young function</title>
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<namePart>Tang, Qihe</namePart>
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<abstract displayLabel="Summary">For a risk variable X and a normalized Young function f(·), the HaezendonckGoovaerts risk measure for X at level q?(0,1) is defined as Hq[X]=infx?R(x+h), where h solves the equation View the MathML source if Pr(X>x)>0 or is 0 otherwise. In a recent work, we implemented an asymptotic analysis for Hq[X] with a power Young function for the Fréchet, Weibull and Gumbel cases separately. A key point of the implementation was that h can be explicitly solved for fixed x and q, which gave rise to the possibility to express Hq[X] in terms of x and q. For a general Young function, however, this does not work anymore and the problem becomes a lot harder. In the present paper, we extend the asymptotic analysis for Hq[X] to the case with a general Young function and we establish a unified approach for the three extreme value cases. In doing so, we overcome several technical difficulties mainly due to the intricate relationship between the working variables x, h and q.</abstract>
<note type="statement of responsibility">Qihe Tang, Fan Yang</note>
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<title>Insurance : mathematics and economics</title>
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<publisher>Oxford : Elsevier, 1990-</publisher>
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<identifier type="issn">0167-6687</identifier>
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<text>03/11/2014 Volumen 59 Número 1 - noviembre 2014 </text>
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