Modeling of payments process in the insurance company in view of system dependences

One of the serious problems of the modern insurance market of the Russian Federation is its insufficient theoretical and methodical support. The management efficiency in insurance business depends a lot on the technology of a choice of administrative decisions. The single-channel model of mass service is considered; where the acting flow is a flow of claims on a special kind of insurance, and the process of service is the size of payments for the claims. Two modes of functioning are allocated in the model: with attraction of reserve fund and without it. The parities for probability are received that at the moment of time $t$ volume to payment surpasses $x$. The found parities can be used for the analysis of stability of the insurance company and definition of a maximum level of reserve fund.