کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5076616 | 1477216 | 2014 | 10 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Extreme value analysis of the Haezendonck-Goovaerts risk measure with a general Young function
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آمار و احتمال
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
For a risk variable X and a normalized Young function Ï(â
), the Haezendonck-Goovaerts risk measure for X at level qâ(0,1) is defined as Hq[X]=infxâR(x+h), where h solves the equation E[Ï((Xâx)+/h)]=1âq 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.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Insurance: Mathematics and Economics - Volume 59, November 2014, Pages 311-320
Journal: Insurance: Mathematics and Economics - Volume 59, November 2014, Pages 311-320
نویسندگان
Qihe Tang, Fan Yang,