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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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