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Maxentropic approach to decompound aggregate risk losses

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  • Gomes-Gonçalves, Erika
  • Gzyl, Henryk
  • Mayoral, Silvia

Abstract

A risk manager may be faced with the following problem: she/he has obtained loss data collected during a year, but the data only contains the total number of events and the total loss for that year. She/he suspects that there are different sources of risk, each occurring with a different frequency, and wants to identify the frequency with which each type of event occurs and if possible, the individual losses at each risk event.

Suggested Citation

  • Gomes-Gonçalves, Erika & Gzyl, Henryk & Mayoral, Silvia, 2015. "Maxentropic approach to decompound aggregate risk losses," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 326-336.
    • Handle: RePEc:eee:insuma:v:64:y:2015:i:c:p:326-336
    DOI: 10.1016/j.insmatheco.2015.07.003
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    References listed on IDEAS

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    1. Gomes-Gonçalves, Erika & Gzyl, Henryk & Mayoral, Silvia, 2015. "Two maxentropic approaches to determine the probability density of compound risk losses," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 42-53.
    2. Boris Buchmann & Rudolf Grübel, 2004. "Decompounding poisson random sums: Recursively truncated estimates in the discrete case," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(4), pages 743-756, December.
    3. Pena D. & Prieto F.J., 2001. "Cluster Identification Using Projections," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1433-1445, December.
    4. Venkatram Ramaswamy & Wayne S. Desarbo & David J. Reibstein & William T. Robinson, 1993. "An Empirical Pooling Approach for Estimating Marketing Mix Elasticities with PIMS Data," Marketing Science, INFORMS, vol. 12(1), pages 103-124.
    5. Hamparsum Bozdogan, 1987. "Model selection and Akaike's Information Criterion (AIC): The general theory and its analytical extensions," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 345-370, September.
    6. Martin Bøgsted & Susan Pitts, 2010. "Decompounding random sums: a nonparametric approach," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(5), pages 855-872, October.
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    1. Gomes-Gonçalves, Erika & Gzyl, Henryk & Mayoral, Silvia, 2016. "Loss data analysis: Analysis of the sample dependence in density reconstruction by maxentropic methods," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 145-153.

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