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**publisher and metadata sources**).Abstract The present paper investigates, for the general Andersen model, the asymptotic behaviour of the probability of ruin function when the initial risk reserve tends to infinity. Whereas the… Continue Reading

For a random walk governed by a general distribution function F on (-[infinity], +[infinity]), we establish the exponential and subexponential asymptotic behaviour of the corresponding right… Continue Reading

SummaryLet ℒ denote the class of subexponential distribution functions. For F infinitely divisible on [0, ∞) with Lévy measure v, the following assertions are proved to be… Continue Reading

Let T. = n-' 1=1 CnX,, be a linear combination of order statistics and put Tn* = (T. E (T, ))/ VVar(Tn ). Sufficient conditions on the cn and on the moments of the underlying distribution are… Continue Reading

Abstract We consider the probability of ruin in the extended risk model of Gerber (1970) and Dufresne and Gerber (1991). Their asymptotic estimate is complemented by considering also cases where the… Continue Reading

Abstract In this note we show how the general theory for linear combinations of U -statistics with varying kernel can be applied to discuss estimators for the infinite horizon time probability of… Continue Reading

SummaryLetUn be aU-statistic with kernelh such thatE h (X1,X2)=Ω and VarE [h (X1,X2)|X1]>0.It is shown that the condition
$$E|h (X_1 , X_2 ) - \vartheta |^p \leqslant K^p p^{\gamma p} $$
(whereK and… Continue Reading

Let Gn(x) be the distribution function of the maximum of the successive partial sums of independent and identically distributed random variables and G(x) its limiting distribution function. Under… Continue Reading