Lundberg approximation for the risk function in an almost homogeneous environment
Authors:
M. V. Kartashov and O. M. Stroev
Translated by:
Oleg Klesov
Journal:
Theor. Probability and Math. Statist. 73 (2006), 71-79
MSC (2000):
Primary 60J45; Secondary 60A05
DOI:
https://doi.org/10.1090/S0094-9000-07-00682-5
Published electronically:
January 17, 2007
MathSciNet review:
2213842
Full-text PDF Free Access
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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.
References
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References
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- D. C. M. Dickson, The probability of ultimate ruin with a variable premium rate, Scand. Actuar. J. 1991, 75–86.
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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
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
