Computation of Compound Distributions I: Aliasing Errors and Exponential Tilting

Numerical evaluation of compound distributions is one of the central numerical tasks in insurance mathematics. Two widely used techniques are Panjer recursion and transform methods. Many authors have pointed out that aliasing errors imply the need to consider the whole distribution if transform methods are used, a potential drawback especially for heavy- tailed distributions. We investigate the magnitude of aliasing errors and show that this problem can be solved by a suitable change of measure.

KEYWORDS Total claim size distribution, ruin probabilities, random sums, transformation, aliasing, change of measure.