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Teoriya Veroyatnostei i ee Primeneniya, 2002, Volume 47, Issue 3, Pages 549–553
DOI: https://doi.org/10.4213/tvp3693 (Mi tvp3693) 		 
This article is cited in 65 scientific papers (total in 65 papers)

Short Communications

The Cramer–Lundberg model with stochastic premium process

A. V. Boikov

Steklov Mathematical Institute, Russian Academy of Sciences
Full-text PDF (495 kB) Citations (65)
DOI: https://doi.org/10.4213/tvp3693
Abstract: In this paper the problem of ruin is considered for an insurance company. The premium process is a linear function of time in the classic Cramer–Lundberg model. The premium process is stochastic and it is also independent of a risk process. The nonruin probability is chosen as a measure of the payment ability. Integral equations and exponential bounds are obtained similarly with the classic Cramer–Lundberg model. That model with a discounting factor was also investigated in [L. S. Jilina, Prikladna Statistika, Aktuarna ta Finansova Matematika, 1 (2000), pp. 67–78 (in Russian)].
Keywords: Cramer–Lundberg model, martingale, stochastic premiums, integral equation, exponential bounds, adjustment coefficient.
Received: 25.06.2002
English version:
Theory of Probability and its Applications, 2003, Volume 47, Issue 3, Pages 489–493
DOI: https://doi.org/10.1137/S0040585X9797987
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. V. Boikov, “The Cramer–Lundberg model with stochastic premium process”, Teor. Veroyatnost. i Primenen., 47:3 (2002), 549–553; Theory Probab. Appl., 47:3 (2003), 489–493
Citation in format AMSBIB
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\paper The Cramer--Lundberg model with stochastic premium process
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\pages 549--553
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\transl
\jour Theory Probab. Appl.
\yr 2003
\vol 47
\issue 3
\pages 489--493
\crossref{https://doi.org/10.1137/S0040585X9797987}
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  • https://doi.org/10.4213/tvp3693
  • https://www.mathnet.ru/eng/tvp/v47/i3/p549
    • This publication is cited in the following 65 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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