Risk process with stochastic premiums
The Cramer-Lundberg model with stochastic premiums which is natural generalization of classical dynamic risk model is considered. Using martingale technique the Lundberg inequality for ruin probability is proved and characteristic equations for Lundberg coefficients are presented for certain classes...
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| Datum: | 2008 |
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| Hauptverfasser: | , |
| 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/123456789/4576 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Risk process with stochastic premiums / N. Zinchenko, A. Andrusiv // Theory of Stochastic Processes. — 2008. — Т. 14 (30), № 3-4. — С. 189-208. — Бібліогр.: 36 назв.— англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862625356759957504 |
|---|---|
| author | Zinchenko, N. Andrusiv, A. |
| author_facet | Zinchenko, N. Andrusiv, A. |
| citation_txt | Risk process with stochastic premiums / N. Zinchenko, A. Andrusiv // Theory of Stochastic Processes. — 2008. — Т. 14 (30), № 3-4. — С. 189-208. — Бібліогр.: 36 назв.— англ. |
| collection | DSpace DC |
| description | The Cramer-Lundberg model with stochastic premiums which is natural generalization of classical dynamic risk model is considered. Using martingale technique the Lundberg inequality for ruin probability is proved and characteristic equations for Lundberg coefficients are presented for certain classes of stochastic premiums and claims. The simple diffusion and de Vylder approximations for the ruin probability are introduced and investigated similarly to classical Cramer-Lundberg set-up. The weak and strong invariance principles for risk processes with stochastic premiums are discussed. Certain variants of the strong invariance principle for risk process are proved under various assumptions on claim size distributions. Obtained results are used for investigation the rate of growth of the risk process and its increments. Various modifications of the LIL and Erdos-Renyi-type SSLN are proved both for the cases of small and large claims.
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| first_indexed | 2025-12-07T13:34:45Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-4576 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0321-3900 |
| language | English |
| last_indexed | 2025-12-07T13:34:45Z |
| publishDate | 2008 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Zinchenko, N. Andrusiv, A. 2009-12-07T15:40:47Z 2009-12-07T15:40:47Z 2008 Risk process with stochastic premiums / N. Zinchenko, A. Andrusiv // Theory of Stochastic Processes. — 2008. — Т. 14 (30), № 3-4. — С. 189-208. — Бібліогр.: 36 назв.— англ. 0321-3900 https://nasplib.isofts.kiev.ua/handle/123456789/4576 The Cramer-Lundberg model with stochastic premiums which is natural generalization of classical dynamic risk model is considered. Using martingale technique the Lundberg inequality for ruin probability is proved and characteristic equations for Lundberg coefficients are presented for certain classes of stochastic premiums and claims. The simple diffusion and de Vylder approximations for the ruin probability are introduced and investigated similarly to classical Cramer-Lundberg set-up. The weak and strong invariance principles for risk processes with stochastic premiums are discussed. Certain variants of the strong invariance principle for risk process are proved under various assumptions on claim size distributions. Obtained results are used for investigation the rate of growth of the risk process and its increments. Various modifications of the LIL and Erdos-Renyi-type SSLN are proved both for the cases of small and large claims. en Інститут математики НАН України Risk process with stochastic premiums Article published earlier |
| spellingShingle | Risk process with stochastic premiums Zinchenko, N. Andrusiv, A. |
| title | Risk process with stochastic premiums |
| title_full | Risk process with stochastic premiums |
| title_fullStr | Risk process with stochastic premiums |
| title_full_unstemmed | Risk process with stochastic premiums |
| title_short | Risk process with stochastic premiums |
| title_sort | risk process with stochastic premiums |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/4576 |
| work_keys_str_mv | AT zinchenkon riskprocesswithstochasticpremiums AT andrusiva riskprocesswithstochasticpremiums |