On perpetuities with light tails
2018 ◽
Vol 50
(4)
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pp. 1119-1154
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Keyword(s):
Abstract In this paper we consider the asymptotics of logarithmic tails of a perpetuity R=D∑j=1∞Qj∏k=1j-1Mk, where (Mn,Qn)n=1∞ are independent and identically distributed copies of (M,Q), for the case when ℙ(M∈[0,1))=1 and Q has all exponential moments. If M and Q are independent, under regular variation assumptions, we find the precise asymptotics of -logℙ(R>x) as x→∞. Moreover, we deal with the case of dependent M and Q, and give asymptotic bounds for -logℙ(R>x). It turns out that the dependence structure between M and Q has a significant impact on the asymptotic rate of logarithmic tails of R. Such a phenomenon is not observed in the case of heavy-tailed perpetuities.
Keyword(s):
Keyword(s):
2009 ◽
Vol 41
(01)
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pp. 13-37
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Asymptotic Probabilities of an Exceedance Over Renewal Thresholds with an Application to Risk Theory
2005 ◽
Vol 42
(01)
◽
pp. 153-162
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2004 ◽
Vol 41
(A)
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pp. 191-212
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2002 ◽
Vol 71
(85)
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pp. 55-62
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