| The Basic Model |
| Written by theoretic |
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In 1903 the Swedish actuary Filip Lundberg [55] laid the foundations of modern risk theory. Risk theory is a synonym for non-life insurance mathematics, which deals with the modeling of claims that arrive in an insurance business and which gives advice on how much premium has to be charged in order to avoid bankruptcy (ruin) of the insurance company. One of Lundberg’s main contributions is the introduction of a simple model which is capable of describing the basic dynamics of a homogeneous insurance portfolio. By this we mean a portfolio of contracts or policies for similar risks such as car insurance for a particular kind of car, insurance against theft in households or insurance against water damage of one-family homes. There are three assumptions in the model: • Claims happen at the times Т$ satisfying 0 < T\ < T2 < . We call them claim arrivals or claim times or claim arrival times or, simply, arrivals. • The ith claim arriving at time Ti causes the claim size or claim severity Xi. The sequence (Xi) constitutes an iid sequence of non-negative random variables. • The claim size process (Xi) and the claim arrival process (Т$) are mutually independent. |