Ukrainian Mathematical Journal

, Volume 59, Issue 4, pp 500–512 | Cite as

Evaluation of the probability of bankruptcy for a model of insurance company

  • B. V. Bondarev
  • T. V. Zhmykhova


We study the problem of evaluation of the probability of ruin of an insurance company for infinitely many steps in the case where the company can invest its capital to bank deposits at any time. As a distribution of the amounts of claims to the insurance company, we use the gamma-distribution with the parameters n and α.


Financial Market Functional Differential Equation Bank Account Unique Solvability Insurance Payment 
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    A. V. Mel’nikov, S. N. Volkov, and M. L. Nechaev, Mathematics of Financial Obligations [in Russian], GU VShÉ, Moscow (2001).Google Scholar
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    J. E. Fjelstad, “On certain linear functional differential equations with constant coefficients,” Arch. Math. Naturvid., 50, 1–64 (1949).MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • B. V. Bondarev
    • 1
  • T. V. Zhmykhova
    • 1
  1. 1.Donetsk National UniversityDonetsk

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