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Necessary and sufficient conditions of existence and uniqueness of solutions to integral equations of actuarial mathematics

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Abstract

Necessary and sufficient conditions of existence and uniqueness of solutions of integral equations are established for ruin probability as a function of the initial capital of an insurance company. Several sufficient conditions and correctness conditions of the problem of finding ruin probability are also established. A general method of successive approximations for solution of this problem is substantiated.

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References

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Authors and Affiliations

  1. Institute of Program Systems of NANU, Kiev, Ukraine

    B. V. Norkin

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  1. B. V. Norkin
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Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 157–164, September–October 2006.

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Norkin, B.V. Necessary and sufficient conditions of existence and uniqueness of solutions to integral equations of actuarial mathematics. Cybern Syst Anal 42, 743–749 (2006). https://doi.org/10.1007/s10559-006-0113-4

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  • DOI: https://doi.org/10.1007/s10559-006-0113-4

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