A linear control system model for risk reserves

A discrete time, linear, stochastic control system is constructed to model the risk reserves for an insurance company. The model has the autoregressive form. A control is used to regulate the risk reserve. The sequence of controls is determined by two approximations, the normal power approximation of order two and a log normal approximation. These approximations use the first three moments which incorporate the skewness of the distributions that is important for these problems. An example of automobile insurance is considered to compare the two approximations for the stationary control law. It is shown that the two approximations are given stationary controls that closely agree.