Aggregate loss distributions have been a vital area in actuarial work majorly in rate making and reserving. This paper determines how the use of mixture distributions improves estimation of aggregate loss probabilities and consequently increases the accuracy of projecting future reserves. In an attempt to explain the importance of these mixtures in estimation of aggregate loss distributions, we have discretized the claim severity probabilities and applied Discrete Fourier Transform and Panjer recursive model in the estimation of aggregate loss probabilities. This research determines that negative binomial distribution provides better fit for Kenyan data as claim frequency distribution and Generalized Pareto distribution for claim severity provided the best fit. We also found Discrete Fourier Transform as the best model in the estimation of aggregate probabilities for claims data of Kenya insurance sector.

aggregate loss distribution, Panjer recursive model, discrete Fourier transform, discretization, method of rounding.

Received: February 13, 2021; Revised: March 7, 2021; Accepted: March 16, 2021; Published: June 21, 2021

How to cite this article: Cynthia Mwende, Joseph Ottieno and Patrick Weke, Aggregate loss distribution for modeling reserves in insurance and banking sectors in Kenya, Far East Journal of Theoretical Statistics 62(1) (2021), 17-34. DOI: 10.17654/TS062010017

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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