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Abstract:
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A number of approximations to the distribution of random sum have been discussed in the literature. This topic is of high interest, especially in the field of actuarial science. For example, actuaries are interested in modelling total amount paid in all claims occurring in a fixed time period on a group of insurance policies. For most combinations of claim counts and claim size distributions, the exact distribution of aggregate claims is not available analytically. In this situation, one is bound to use suitable approximation methods. For judging the goodness of the approximations in this context, the relative errors may be considered. In this paper, we have considered several distributions for the random sum, and made numerical comparisons with the exact results in terms of relative errors. The exact results are obtained through simulations.
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