Norkin B. V.
On the solution of the basic integral equation of actuarial mathematics by the method of successive approximations
Ukr. Mat. Zh. - 2007. - 59, № 12. - pp. 1689–1698
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.