Premium control in an insurance system, an approach using linear control theory

The problem of finding good premium control methods in an insurance business is considered. A mathematical model of the cash flows and the reserves is discussed, and a linear control law with feed back for the premium is proposed. The behaviour of the system is analysed using the methods of control theory. It is shown that stability is maintained only if the feed back is not too strong and that undesirable oscillations can easily be produced caused by delays in the system. The problem of determining the control so that a desired solidity is obtained is considered, and it is shown how a quantitative measure of the necessary solidity can naturally be introduced.