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Theory of Probability and Mathematical Statistics

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Some inequalities for the risk function in the time and space nonhomogeneous Cramér-Lundberg risk model


Authors: M. V. Kartashov and V. V. Golomozyĭ
Translated by: N. N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 98 (2018).
Journal: Theor. Probability and Math. Statist. 98 (2019), 243-254
MSC (2010): Primary 91B30; Secondary 60J25
DOI: https://doi.org/10.1090/tpms/1074
Published electronically: August 19, 2019
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider a generalized Cramér-Lundberg risk model with a time nonhomogeneous Poisson process of insurance claims where the intensity of premiums depends on the current insurance capital. Some explicit bounds are found for the exponential normalized uniform distance between

(a)
the risk function in a time nonhomogeneous model and that in a time homogeneous but space nonhomogeneous model,
(b)
the risk functions in a time homogeneous model or in a space nonhomogeneous model and that in a time and space homogeneous model.
It is assumed that the intensity of premiums approaches a constant as the current insurance capital increases.

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Additional Information

M. V. Kartashov
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, Kyiv Taras Shevchenko National University, Volodymyrs’ka Street, 64/13, Kyiv 01601, Ukraine
Email: nkartashov@skif.com.ua

V. V. Golomozyĭ
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, Kyiv Taras Shevchenko National University, Volodymyrs’ka Street, 64/13, Kyiv 01601, Ukraine
Email: vitaliy.golomoziy@gmail.com

DOI: https://doi.org/10.1090/tpms/1074
Keywords: Time and space nonhomogeneous Markov processes, ruin probability, Cram\'er--Lundberg risk model
Received by editor(s): November 2, 2017
Published electronically: August 19, 2019
Additional Notes: M. V. Kartashov passed away on January 1, 2018. See the tribute to him by the Theory of Probability and Mathematical Statistics Editorial Board in this issue
Article copyright: © Copyright 2019 American Mathematical Society