Proportional convergence and tail-cutting techniques in evaluating aggregate claim distributions

Abstract

Some tail-cutting techniques are developed for an efficient usage of Panjer-type recursions in evaluating aggregate claim distributions for large insurance portfolios. Generally, for a linear recurrence equation, given arbitrary initial values, the computed solutions tend to be proportional to each other. By cutting the left tail of the aggregate claim distribution and using arbitrary initial values, a good approximation of the aggregate claim distribution can be achieved through a simple rescaling. This method can reduce the computing time and avoid underflow/overflow problems.