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
MathSciNet review:
3824690
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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.
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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
