On perpetuities with gamma-like tails
2018 ◽
Vol 55
(2)
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pp. 368-389
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Keyword(s):
The One
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Abstract An infinite convergent sum of independent and identically distributed random variables discounted by a multiplicative random walk is called perpetuity, because of a possible actuarial application. We provide three disjoint groups of sufficient conditions which ensure that the right tail of a perpetuity ℙ{X > x} is asymptotic to axce-bx as x → ∞ for some a, b > 0, and c ∈ ℝ. Our results complement those of Denisov and Zwart (2007). As an auxiliary tool we provide criteria for the finiteness of the one-sided exponential moments of perpetuities. We give several examples in which the distributions of perpetuities are explicitly identified.
1964 ◽
Vol 4
(2)
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pp. 223-228
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Keyword(s):
1980 ◽
Vol 30
(1)
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pp. 5-14
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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)
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pp. 153-162
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2014 ◽
Vol 46
(01)
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pp. 256-278
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Keyword(s):
1969 ◽
Vol 10
(3-4)
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pp. 429-441
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