A remark on Wiener process approximation of risk processes

Jan Grandell

ASTIN Bulletin, 1972, vol. 7, issue 1, 100-101

Abstract: In Bohman the following model is considered. Our notation follows Bohman.Let Z1, Z2, … be a sequence of independent random variables with distribution function F and put Put and define X byX = inf{n; Sn > U, Sk ≤ U for k = 1, …, n − 1}.Bohman shows that if U → ∞ in such a way that U/σ → ∞ and then where G(α, x) is the distribution function for the time when a Wiener process X(t) with EX(t) = αt and Var X(t) = t first crosses the level 1.Let N be an integer, which in a certain sense corresponds to “time”, and consider P(X ≤ N). This is thus the probability of ruin before the N:th claim.

Date: 1972
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