THE METHOD OF SUCCESSIVE APPROXIMATIONS FOR CALCULATING THE PROBABILITY OF BANKRUPTCY OF A RISK PROCESS IN A MARKOVIAN ENVIRONMENT

摘要

A generalized model of a classical risk process describing the evolution of the capital of an insurance company in a random environment is considered. A system of integral equations for the bankmptcy probability if a function of initial state. The possibility of applying the method of successive approximation to solve the system is analyzed. The method generates approximations that converge from above and below to the solution.