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faculty: "FEB" and publication year: "2004"
| Authors | Q. Tang, G.Sh. Tsitsiashvili | | Title | Randomly weighted sums of subexponential random variables with application to ruin theory |
| Journal | Extremes |
| Volume | 6 |
| Year | 2004 |
| Issue | 3 |
| Pages | 171-188 |
| ISSN | 13861999 |
| Faculty | Faculty of Economics and Business |
| Institute/dept. | FEB: Research Institute in Economics and Econometrics Amsterdam (RESAM) |
| Abstract | Let {X k , 1 k n} be n independent and real-valued random variables with common subexponential distribution function, and let {k, 1 k n} be other n random variables independent of {X k , 1 k n} and satisfying a k b for some 0 < a b < for all 1 k n. This paper proves that the asymptotic relations P (max1 m n k=1 m k X k > x) P (sum k=1 n k X k > x) sum k=1 n P ( k X k > x) hold as x . In doing so, no any assumption is made on the dependence structure of the sequence { k , 1 k n}. An application to ruin theory is proposed. |
| Document type | Article |
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