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Exact non-ruin probabilities in
arithmetic case
Vasily Chernecky Department of Higher Mathematics,
Odessa State Academy of Refrigeration,
65026 Odessa, Ukraine
Аннотация:
Using the Wiener-Hopf method, for the model with arithmetic distributions of waiting times $T_i$ and claims $Z_i$ in ordinary renewal process,
an exact non-ruin probabilities for an insurance company in terms of
the factorization of the symbol of the discrete Feller-Lundberg equation, are obtained. The delayed stationary process is introduced and
generating function for delay is given. It is proved that the stationary
renewal process in arithmetic case is ordinary if and only if, when
the inter-arrival times have the shifted geometrical distribution. A
formula for exact non-ruin probabilities in delayed stationary process
is obtained. Illustrative examples when the distributions of $T_i$ and
$Z_i$ are shifted geometrical or negative binomial with positive integer
power are considered. In these cases the symbol of the equation is rational functions what allows us to obtain the factorization in explicit
form.
Ключевые слова:
Fundamental equation of the risk theory, ordinary/stationary
renewal process, delayed renewal processes, stationarity, discrete analog of one-sided
Wiener-Hopf integral equation, Riemann boundary-value problem, Wiener-Hopf factorization method.
Образец цитирования:
Vasily Chernecky, “Exact non-ruin probabilities in
arithmetic case”, Theory Stoch. Process., 14(30):3 (2008), 39–52
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/thsp212 https://www.mathnet.ru/rus/thsp/v14/i3/p39
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Страница аннотации: | 59 | PDF полного текста: | 37 | Список литературы: | 14 |
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