Reformulation of Some Problems in the Theory of Risk

In classical actuarial theory we are concerned exclusively with expected values. The net premium of an insurance contract is by definition equal to the expected value of the claim payments which will be made under the contract. Similarly the technical reserves of an insurance company are defined as the expected value of the payments to be made under all contracts in the company's portfolio. If the insurance contracts are of long duration, interest is usually taken into account by discounting the value of all payments to some particular point of time. In the following we shall ignore interest, since it is fairly clear that this element can be brought into all formulae without any serious difficulty.