Recursive and moment-based approximation of aggregate loss distribution

Determining the distribution of aggregate loss is an important issue for insurers. Basically, the distribution of aggregate loss can be determined using n-fold convolution of the probability density function of severity distribution. However, problems in computation for this method causes findings of new methods to approximate aggregate loss distribution. One of the methods which is widely used and claimed to give a good approximation is Panjer recursion. Panjer introduced a recursion formula which can be used to compute aggregate loss probabilities. This method requirements are discrete severities distribution and (a, b, 0) class frequency distribution. The Panjer recursion method could not be applied if those two requirements are not met, so a discretization process is needed for continuous severity cases. This paper explored the use of Panjer recursion method for continuous severity cases. The method of rounding is used to discretize the continuous severity random variable with span h. It means that random variables which are the discretized version of severity random variables have probabilities in the span of h (h, h, h, and so on). The result improves when the discretization span is small enough. Beside Panjer recursion method, there is a new method, called moment-based, which can be used to approximate aggregate loss distribution using its moments. This method presents an approximation formula of aggregate loss distribution probability density function, which contain coefficients which can be determined by matching its moments with aggregate loss moments. Both of these methods tend to give relatively similar results when the span used in the recursive method is small enough and moments used in moment-based is adequate. The span of discretization for the recursive method is said to be small enough if no jump is seen in cumulative distribution function of severity random variables. moments used in moment-based is said to be adequate if the result using 1 moments give no significant difference.