Stochastic successive approximation method for assessing the insolvency risk of an insurance company

Abstract

A stochastic successive approximation method is analyzed with a view to solving risk assessment problems that are reduced to a renewal integral equation and, in particular, to assessing the insolvency risk of an insurance company. Integrals in the equation are evaluated approximately, for example, by the Monte Carlo method. Iterations of the method are proved to converge uniformly with probability one. Theoretical results are illustrated by numeral computations.

Mathematical Model of Banking Operation

“…In [31], the bankruptcy probability in a complex Poisson model was estimated by the Monte Carlo method. The papers [32][33][34] consider a risk process with arrival of claims in an insurance company, described by the general process of restoration and deterministic nonlinear monotonically increasing intensity of arrival of preiums. An algorithm is presented to construct successive approximations for nonruin probability.…”