On the solution of the basic integral equation of actuarial mathematics by the method of successive approximations - Norkin, B. V. (Ukrains’kyi Matematychnyi Zhurnal, 2007)
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.