Subexponential Distributions

2014 ◽  
Author(s):  
Claudia Klüppelberg
Keyword(s):  
Subexponential Distributions

scholarly journals Multivariate subexponential distributions

1992 ◽  
Vol 42 (1) ◽  
pp. 49-72 ◽  
Author(s):  
Daren B.H. Cline ◽  
Sidney I. Resnick
Keyword(s):  
Subexponential Distributions

scholarly journals Second order subexponential distributions

1991 ◽  
Vol 51 (1) ◽  
pp. 73-87 ◽  
Author(s):  
J. L. Geluk ◽  
A. G. Pakes
Keyword(s):  
Positive Function ◽  
Second Order ◽  
Subexponential Distributions

AbstractThe class of subexponential distributions S is characterized by F(0) = 0, 1 − F(2)(x) ~ 2(1 − F(x)) as x → ∞. In this paper we consider a subclass of S for which the relation 1 − F(2)(x) − 2(1 − F(x)) + (1 − F(x))2 = o(a(x)) as x → ∞ holds, where α is a positive function satisfying α(X) = 0(1 − F(x)) (x → ∞).

scholarly journals On the Distribution of the Surplus Prior and at Ruin

1999 ◽  
Vol 29 (2) ◽  
pp. 227-244 ◽  
Author(s):  
Hanspeter Schmidli
Keyword(s):  
Asymptotic Behaviour ◽  
Ruin Probability ◽  
Poisson Model ◽  
Subexponential Distributions ◽  
Compound Poisson ◽  
Initial Capital ◽  
Compound Poisson Model ◽  
Explicit Expressions

AbstractConsider a classical compound Poisson model. The safety loading can be positive, negative or zero. Explicit expressions for the distributions of the surplus prior and at ruin are given in terms of the ruin probability. Moreover, the asymptotic behaviour of these distributions as the initial capital tends to infinity are obtained. In particular, for positive safety loading the Cramer case, the case of subexponential distributions and some intermediate cases are discussed.

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