Exact non-ruin probabilities in arithmetic case
Using the Wiener-Hopf method, for the model with arithmetic distributions of waiting times Ti and claims Zi 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 de...
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| Datum: | 2008 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2008
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/4567 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Exact non-ruin probabilities in arithmetic case / V. Chernecky // Theory of Stochastic Processes. — 2008. — Т. 14 (30), № 3-4. — С. 39-52. — Бібліогр.: 6 назв.— англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862732442335444992 |
|---|---|
| author | Chernecky, V. |
| author_facet | Chernecky, V. |
| citation_txt | Exact non-ruin probabilities in arithmetic case / V. Chernecky // Theory of Stochastic Processes. — 2008. — Т. 14 (30), № 3-4. — С. 39-52. — Бібліогр.: 6 назв.— англ. |
| collection | DSpace DC |
| description | Using the Wiener-Hopf method, for the model with arithmetic distributions of waiting times Ti and claims Zi 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 Ti and Zi 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.
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| first_indexed | 2025-12-07T19:31:39Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-4567 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0321-3900 |
| language | English |
| last_indexed | 2025-12-07T19:31:39Z |
| publishDate | 2008 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Chernecky, V. 2009-12-07T15:33:34Z 2009-12-07T15:33:34Z 2008 Exact non-ruin probabilities in arithmetic case / V. Chernecky // Theory of Stochastic Processes. — 2008. — Т. 14 (30), № 3-4. — С. 39-52. — Бібліогр.: 6 назв.— англ. 0321-3900 https://nasplib.isofts.kiev.ua/handle/123456789/4567 Using the Wiener-Hopf method, for the model with arithmetic distributions of waiting times Ti and claims Zi 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 Ti and Zi 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. en Інститут математики НАН України Exact non-ruin probabilities in arithmetic case Article published earlier |
| spellingShingle | Exact non-ruin probabilities in arithmetic case Chernecky, V. |
| title | Exact non-ruin probabilities in arithmetic case |
| title_full | Exact non-ruin probabilities in arithmetic case |
| title_fullStr | Exact non-ruin probabilities in arithmetic case |
| title_full_unstemmed | Exact non-ruin probabilities in arithmetic case |
| title_short | Exact non-ruin probabilities in arithmetic case |
| title_sort | exact non-ruin probabilities in arithmetic case |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/4567 |
| work_keys_str_mv | AT cherneckyv exactnonruinprobabilitiesinarithmeticcase |