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A remark on Wiener process approximation of risk processes

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  • Grandell, Jan

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.

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  • Grandell, Jan, 1972. "A remark on Wiener process approximation of risk processes," ASTIN Bulletin, Cambridge University Press, vol. 7(1), pages 100-101, December.
    • Handle: RePEc:cup:astinb:v:7:y:1972:i:01:p:100-101_00
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    Cited by:

    1. Krzysztof Burnecki & Marek A. Teuerle & Aleksandra Wilkowska, 2022. "Diffusion Approximations of the Ruin Probability for the Insurer–Reinsurer Model Driven by a Renewal Process," Risks, MDPI, vol. 10(6), pages 1-16, June.

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