A remark on Wiener process approximation of risk processes
- 1 December 1972
- journal article
- research article
- Published by Cambridge University Press (CUP) in ASTIN Bulletin
- Vol. 7 (1) , 100-101
- https://doi.org/10.1017/s0515036100005742
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.Keywords
This publication has 1 reference indexed in Scilit:
- Risk theory and Wiener processesASTIN Bulletin, 1972