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Lundberg approximation for the risk function in an almost homogeneous environment
Author(s):
M.
V.
Kartashov;
O.
M.
Stroev
Translated by:
Oleg Klesov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 73
(2005).
Journal:
Theor. Probability and Math. Statist.
No. 73
(2006),
71-79.
MSC (2000):
Primary 60J45;
Secondary 60A05
Posted:
January 17, 2007
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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.
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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:
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):
25/NOV/2004
Posted:
January 17, 2007
Copyright of article:
Copyright
2007,
American Mathematical Society
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