Abstract
This paper is a natural sequel to part I. The latter paper described an experience rating scheme for fleets of cars based on the stop-loss principle. The stop-loss deductible was chosen to be proportional to the risk volume of the fleet. It was shown that under rather general conditions the pure premium as a function of the risk volume approached a straight line when the risk volume increased to infinity. In the current paper we discuss the behaviour of the variance of the total volume at risk. This will enable the insurer to estimate the asymptotics of a premium calculated according to the variance principle or according to the standard deviation principle. We also formulate our results in a slightly different fashion than used in part I. We assume that the claim number distribution takes a specific form akin to that of a compound Poisson distribution.
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