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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

Lundberg approximation for the risk function in an almost homogeneous environment


Authors: M. V. Kartashov and O. M. Stroev
Translated by: Oleg Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 73 (2005).
Journal: Theor. Probability and Math. Statist. 73 (2006), 71-79
MSC (2000): Primary 60J45; Secondary 60A05
Published electronically: January 17, 2007
MathSciNet review: 2213842
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Abstract | References | Similar Articles | Additional Information

Abstract: A generalization of the classical risk process is considered where the premium rate depends on the current reserve of an insurance company. We assume that the corresponding function converges to a limit with the exponential rate and prove that the limit of the exponentially weighted ruin function exists as the initial reserve increases. Two-sided estimates for the limit are found; the estimates show that the limit is positive under certain assumptions on the stability.


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Additional Information

M. V. Kartashov
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kiev 03127, Ukraine
Email: winf@ln.ua

O. M. Stroev
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kiev 03127, Ukraine
Email: kid_kitten@mail.ru

DOI: http://dx.doi.org/10.1090/S0094-9000-07-00682-5
PII: S 0094-9000(07)00682-5
Keywords: Risk function, Lundberg index, Poisson process
Received by editor(s): November 25, 2004
Published electronically: January 17, 2007
Article copyright: © Copyright 2007 American Mathematical Society