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Performance analysis with truncated heavy{tailed distributions

Summary: Performance analysis
with truncated heavy{tailed distributions
Sren Asmussen y Mats Pihlsgard z
November 10, 2004
This paper deals with queues and insurance risk processes where
a generic service time, resp. generic claim, has the form U ^ K for
some r.v. U with distribution B which is heavy{tailed, say Pareto
or Weibull, and a typically large K, say much larger than EU . We
study the compound Poisson ruin probability (u) or, equivalently,
the tail P(W > u) of the M=G=1 steady{state waiting time W . In
the rst part of the paper, we present numerical values of (u) for
di erent values of K by using the classical Siegmund algorithm as well
as a more recent algorithm designed for heavy{tailed claims/service
times, and compare the results to di erent approximations of (u)
in order to gure out the threshold between the light{tailed regime
and the heavy{tailed regime. In the second part, we investigate the
asymptotics as K ! 1 of the asymptotic exponential decay rate
= (K) in a more general truncated Levy process setting, and give
a discussion of some of the implications for the approximations.


Source: Asmussen, Søren - Department of Mathematical Sciences, Aarhus Universitet


Collections: Mathematics