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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Keyword(s):
Let (Y n , N n ) n≥1 be independent and identically distributed bivariate random variables such that the N n are positive with finite mean ν and the Y n have a common heavy-tailed distribution F. We consider the process (Z n ) n≥1 defined by Z n = Y n - Σ n-1, where It is shown that the probability that the maximum M = max n≥1 Z n exceeds x is approximately as x → ∞, where F' := 1 - F. Then we study the integrated tail of the maximum of a random walk with long-tailed increments and negative drift over the interval [0, σ], defined by some stopping time σ, in the case in which the randomly stopped sum is negative. Finally, an application to risk theory is considered.
Asymptotic Probabilities of an Exceedance Over Renewal Thresholds with an Application to Risk Theory
2005 ◽
Vol 42
(1)
◽
pp. 153-162
◽
2007 ◽
Vol 39
(1)
◽
pp. 221-244
◽
2007 ◽
Vol 39
(01)
◽
pp. 221-244
◽
2009 ◽
Vol 46
(2)
◽
pp. 559-570
◽
2009 ◽
Vol 46
(02)
◽
pp. 559-570
◽
2014 ◽
Vol 51
(01)
◽
pp. 136-151
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Keyword(s):
2007 ◽
Vol 27
(1)
◽
pp. 11-24
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1994 ◽
Vol 31
(04)
◽
pp. 949-957
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Keyword(s):
Keyword(s):
Keyword(s):