18 Premiums in the Individual and Collective Risk Models (p.407)
Jan Iwanik and Joanna Nowicka-Zagrajek
The premium is the price for the good "insurance" sold by an insurance company. The right pricing is vital since too low a price level results in a loss, while with too high prices a company can price itself out of the market. It is the actuary’s task to and methods of premium calculation (also called premium calculation principles), i.e. rules saying what premium should be assigned to a given risk.
We present the most important types of premiums in Section 18.1; for more premium calculation principles, that are not considered here, see Straub (1988) and Young (2004). We focus on the monetary payout made by the insurer in connection with insurable losses and we ignore premium loading for expenses and profit.
The goal of insurance modeling is to develop a probability distribution for the total amount paid in bene.ts. This allows the insurance company to manage its capital account and honor its commitments. Therefore, we describe two standard models: the individual risk model in Section 18.2 and the collective risk model in Section 18.3. In both cases, we determine the expectation and variance of the portfolio, consider the approximation of the distribution of the aggregate claims, and present formulae for the considered premiums. It is worth mentioning here that the collective risk model can also be applied to quantifying regulatory capital for operational risk, for example to model a yearly operational risk variable (Embrechts, Furrer, and Kaufmann, 2003).
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