Convergence of Insurance Payout Stochastic Processes to Generalized Poisson Process

Abstract

We consider stochastic processes describing the size of a company’s insurance payouts in the case of a growing number of clients. Convergence of such processes in Skorokhod space is proved. As a result, a functional limit theorem for risk processes is obtained, which allows us to use well-known formulas for estimating an insurance company’s ruin probability in the considered case.