Abstract
Paul R. Halmos recently hailed the fast Fourier transform as one of the 22 most significant developments in mathematics in the last 75 years. This paper provides an application of this tool to the computation of aggregate loss distributions from arbitrary frequency and severity distributions. All necessary mathematics is developed in the paper, complete algorithms are given, and examples are provided. Sufficient details are given to allow implementation in any computer language, and sample APL computer language routines are given. The final section includes a discussion of excess loss distributions where computation is not limited to the fast Fourier transform based algorithm.
Reinsurance Research - Loss Distributions, Size of
Volume
LXXIX
Page
57-133
Year
1992
Categories
Business Areas
Reinsurance
Aggregate Excess/Stop Loss
Financial and Statistical Methods
Aggregation Methods
Collective Risk Model
Financial and Statistical Methods
Aggregation Methods
Fourier
Financial and Statistical Methods
Loss Distributions
Frequency
Financial and Statistical Methods
Loss Distributions
Severity
Publications
Proceedings of the Casualty Actuarial Society
Prizes
Dorweiler Prize
