Approximation of ruin probability and ruin time in discrete Brownian risk models

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Serval ID
serval:BIB_7F9613726984
Type
Article: article from journal or magazin.
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Title
Approximation of ruin probability and ruin time in discrete Brownian risk models
Journal
Scandinavian Actuarial Journal
Author(s)
Jasnovidov Grigori
ISSN
0346-1238
1651-2030
Publication state
In Press
Pages
1-18
Language
english
Abstract
We analyze the classical Brownian risk models discussing the approxima-
tion of ruin probabilities (classical, γ-reflected, Parisian and cumulative
Parisian) for the case that ruin can occur only on specific discrete grids. A
practical and natural grid of points is for instance G(1) = {0,1,2,...}, which
allows us to study the probability of the ruin on the first day, second day,
and so one. For such a discrete setting, there are no explicit formulas for the
ruin probabilities mentioned above. In this contribution we derive accurate
approximations of ruin probabilities for uniform grids by letting the initial
capital to grow to infinity.
Keywords
Brownian motion, γ-reflected risk model, Parisian ruin probability, cumulative Parisian ruin, ruin time approximation
Create date
24/02/2020 15:15
Last modification date
24/03/2020 6:20
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