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Theory of Probability and Mathematical Statistics

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On the ruin probability of an insurance company dealing in a $ BS$-market


Authors: A. V. Baev and B. V. Bondarev
Translated by: V. V. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 74 (2006).
Journal: Theor. Probability and Math. Statist. 74 (2007), 11-23
MSC (2000): Primary 60E15, 60H05, 60H30; Secondary 62P05
DOI: https://doi.org/10.1090/S0094-9000-07-00693-X
Published electronically: June 25, 2007
MathSciNet review: 2336774
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Abstract | References | Similar Articles | Additional Information

Abstract: We study a mathematical model of an insurance company that shares its capital by investing it in both stocks and bonds. The basic tool to describe the evolution of the stock price is the Ornstein-Uhlenbeck process. We construct an estimate for the ruin probability of an insurance company as a function of the initial capital. The distribution of the capital between stocks and bonds is found for which this estimate is minimal.


References [Enhancements On Off] (What's this?)

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Additional Information

A. V. Baev
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty for Mathematics, Donetsk State University, Universitets’ka Street 24, 83055 Donetsk, Ukraine
Email: tv@matfak.dongu.donetsk.ua

B. V. Bondarev
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty for Mathematics, Donetsk State University, Universitets’ka Street 24, 83055 Donetsk, Ukraine
Email: bvbondarev@cable.netlux.org

DOI: https://doi.org/10.1090/S0094-9000-07-00693-X
Keywords: Poisson measure, stochastic integral, investor's portfolio, ruin probability
Received by editor(s): January 11, 2005
Published electronically: June 25, 2007
Article copyright: © Copyright 2007 American Mathematical Society