Impact of the stress factor on the price of widow’s pensions. Proofs
Authors:
V. V. Golomozyĭ, M. V. Kartashov and Yu. M. Kartashov
Translated by:
S. Kvasko
Journal:
Theor. Probability and Math. Statist. 92 (2016), 17-22
MSC (2010):
Primary 60J45; Secondary 60A05, 60K05
DOI:
https://doi.org/10.1090/tpms/979
Published electronically:
August 10, 2016
MathSciNet review:
3553423
Full-text PDF Free Access
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Additional Information
Abstract: This is a continuation of a recent paper by the authors (in Modern Problems in Insurance Mathematics, E. A. A. Series, Springer, New York, 2014, pp. 223–237) containing proofs of the results announced therein. We consider the model of joint life insurance with a stress factor. The proofs use the method of a maximal coupling for time inhomogeneous Markov chains. The stability of expectations of a function of a Markov moment is proved.
References
- Y. Kartashov, V. Golomozyĭ, and N. Kartashov, The impact of stress factors on the price of widow’s pensions, Modern Problems in Insurance Mathematics (D. Silvestrov and A. Martin-Löf, eds.), E. A. A. Series, Springer, 2014, pp. 223–237. MR3330687
- V. V. Golomozyĭ, Stability of time in-homogeneous Markov chains, Visn. Kyiv. Univer. Ser. Phys. Math. 4 (2009), 10–15. (Ukrainian)
- V. V. Golomoziĭ, A subgeometric estimate for the stability of time-homogeneous Markov chains, Teor. Ĭmovīr. Mat. Stat. 81 (2009), 31–45 (Ukrainian, with English, Russian and Ukrainian summaries); English transl., Theory Probab. Math. Statist. 81 (2010), 35–50. MR 2667308, DOI 10.1090/S0094-9000-2010-00808-8
- N. V. Kartashov, Strong stable Markov chains, VSP, Utrecht; TBiMC Scientific Publishers, Kiev, 1996. MR 1451375
- N. V. Kartashov, The ergodicity and stability of quasi-homogeneous Markov semigroups of operators, Teor. Ĭmovir. Mat. Stat. 72 (2005), 54–62; English transl. in Theor. Probability and Math. Statist. 72 (2006), 59–68.
- M. V. Kartashov and V. V. Golomoziĭ, Maximal coupling and stability of discrete Markov chains. I, Teor. Ĭmovīr. Mat. Stat. 86 (2011), 81–91 (Ukrainian, with English, Russian and Ukrainian summaries); English transl., Theory Probab. Math. Statist. 86 (2013), 93–104. MR 2986452, DOI 10.1090/S0094-9000-2013-00891-6
- M. V. Kartashov and V. V. Golomozyĭ, Maximal coupling procedure and stability of discrete Markov chains. II, Theory Probab. Math. Statist. 87 (2013), 65–78. Translation of Teor. Ǐmovīr. Mat. Stat. No. 87 (2012), 58–70. MR 3241447, DOI 10.1090/S0094-9000-2014-00905-9
- Torgny Lindvall, Lectures on the coupling method, Dover Publications, Inc., Mineola, NY, 2002. Corrected reprint of the 1992 original. MR 1924231
- S. P. Meyn and R. L. Tweedie, Markov chains and stochastic stability, Communications and Control Engineering Series, Springer-Verlag London, Ltd., London, 1993. MR 1287609, DOI 10.1007/978-1-4471-3267-7
References
- Y. Kartashov, V. Golomozyĭ, and N. Kartashov, The impact of stress factors on the price of widow’s pensions, Modern Problems in Insurance Mathematics (D. Silvestrov and A. Martin-Löf, eds.), E. A. A. Series, Springer, 2014, pp. 223–237. MR3330687
- V. V. Golomozyĭ, Stability of time in-homogeneous Markov chains, Visn. Kyiv. Univer. Ser. Phys. Math. 4 (2009), 10–15. (Ukrainian)
- V. V. Golomozyĭ, A subgeometrical estimate for stability for time-homogeneous Markov chains, Teor. Ĭmovir. Mat. Stat. 81 (2009), 35–50; English transl. in Theor. Probability and Math. Statist. 81 (2010), 31–46. MR 2667308
- N. V. Kartashov, Strong Stable Markov Chains, VSP/“TViMS”, Utrecht/Kiev, The Netherlands/Ukraine, 1996. MR 1451375
- N. V. Kartashov, The ergodicity and stability of quasi-homogeneous Markov semigroups of operators, Teor. Ĭmovir. Mat. Stat. 72 (2005), 54–62; English transl. in Theor. Probability and Math. Statist. 72 (2006), 59–68.
- N. V. Kartashov and V. V. Golomozyĭ, Maximal coupling procedure and stability of discrete Markov chains. I, Teor. Ĭmovir. Mat. Stat. 86 (2012), 81–92; English transl. in Theor. Probability and Math. Statist. 86 (2013), 93–104. MR 2986452
- N. V. Kartashov and V. V. Golomozyĭ, Maximal coupling procedure and stability of discrete Markov chains. II, Teor. Ĭmovir. Mat. Stat. 87 (2012), 47–59; English transl. in Theor. Probability and Math. Statist. 87 (2013), 65–78. MR 3241447
- T. Lindvall, Lectures on Coupling Method, Dover Publication, 2002. MR 1924231
- S. P. Meyn and R. L. Tweedie, Markov Chains and Stochastic Stability, Springer-Verlag, 1993. MR 1287609
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Additional Information
V. V. Golomozyĭ
Affiliation:
Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Academician Glushkov Avenue, 6, Kyiv 03127, Ukraine
M. V. Kartashov
Affiliation:
Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Academician Glushkov Avenue, 6, Kyiv 03127, Ukraine
Email:
nkartashov@skif.com.ua
Yu. M. Kartashov
Affiliation:
Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Academician Glushkov Avenue, 6, Kyiv 03127, Ukraine
Keywords:
Coupling method,
maximal coupling,
discrete Markov chains,
stability of distributions of Markov chains
Received by editor(s):
December 23, 2014
Published electronically:
August 10, 2016
Article copyright:
© Copyright 2016
American Mathematical Society
