Abstract
This chapter discusses some practical considerations in connection with the calculation of stop-loss premiums. A premium calculation principle is a rule that assigns a premium to any risk. In mathematical terms, a risk is a random variable given by its supposedly sufficiently regular distribution. The exponential principle involves the evaluation of the moment generating function of the risk at an argument. The net premium principle and the exponential principle are additive and iterative. Under a mild continuity condition, these two principles can be characterized by certain properties. Also, the exponential principle fits into the framework of the collective theory of risk. The exact calculation of a stop-loss premium is feasible if the claim amount distribution is arithmetic with a sufficiently large span. If F is an arbitrary compound Poisson distribution, the exact calculation of the stop-loss premium can be an extensive procedure and can lead to considerable round-off errors.
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