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On the solution of the basic integral equation of actuarial mathematics by the method of successive approximations

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Abstract

We study the basic integral equation of actuarial mathematics for the probability of (non)ruin of an insurance company regarded as a function of the initial capital. We establish necessary and sufficient conditions for the existence of a solution of this equation, general sufficient conditions for its existence and uniqueness, and conditions for the uniform convergence of the method of successive approximations for finding the solution.

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References

  1. R. E. Beard, T. Pentikäinen, and E. Pesonen, Risk Theory. The Stochastic Basis of Insurance, Chapman and Hall, New York (1984).

    MATH  Google Scholar 

  2. B. V. Norkin, “Method of successive approximations for the solution of integral equations in the theory of risk processes,” Kibern. Sist. Anal., No. 4, 10–18 (2004).

  3. B. V. Norkin, “On the determination of the ruin probability of a non-Poisson risk process by the method of successive approximations,” Probl. Upravl. Inform., No. 2, 133–144 (2005).

  4. M. M. Leonenko, Yu. S. Mishura, Ya. M. Parkhomenko, and M. I. Yadrenko, Theoretical-Probability and Statistical Methods in Econometrics and Financial Mathematics [in Ukrainian], Informtekhnika, Kyiv (1995).

    Google Scholar 

  5. S. Asmussen, Ruin Probabilities, World Scientific, Singapore (2000).

    Google Scholar 

  6. A. V. Boikov, “Cramér-Lundberg model with stochastic premiums,” Teor. Ver. Primen., 47, Issue 3, 549–553 (2002).

    MathSciNet  Google Scholar 

  7. L. S. Zhilina, “Estimation of the ruin probability of an insurance company for a certain insurance model,” Prikl. Statist., Aktuar. Finans. Mat. (Donetsk), No. 1, 67–78 (2000).

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Authors and Affiliations

  1. Institute of Cybernetics, Ukrainian National Academy of Sciences, Kiev, Ukraine

    B. V. Norkin

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  1. B. V. Norkin
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 12, pp. 1689–1698, December, 2007.

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Norkin, B.V. On the solution of the basic integral equation of actuarial mathematics by the method of successive approximations. Ukr Math J 59, 1902–1913 (2007). https://doi.org/10.1007/s11253-008-0033-8

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  • DOI: https://doi.org/10.1007/s11253-008-0033-8

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