Activity of social insurance foundation at relay-hysteresis control of the capital

A mathematical model is proposed for social insurance foundation at relay-hysteresis control of capital of such a foundation. The case is considered when payments for insured accidents form a Poisson flow of events and are uniformly distributed independent random variables with exponential distribution function. The stationary capital distribution density is determined in the frameworks of the assumptions. The procedure is proposed for determination of the control parameters providing for the prescribed probability characteristics of operation of the foundation.