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3 - Aggregate-loss models

from Part I - Loss models

Published online by Cambridge University Press:  05 June 2012

Yiu-Kuen Tse
Affiliation:
Singapore Management University
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Summary

Having discussed models for claim frequency and claim severity separately, we now turn our attention to modeling the aggregate loss of a block of insurance policies. Much of the time we shall use the terms aggregate loss and aggregate claim interchangeably, although we recognize the difference between them as discussed in the last chapter. There are two major approaches in modeling aggregate loss: the individual risk model and the collective risk model. We shall begin with the individual risk model, in which we assume there are n independent loss prospects in the block. As a policy may or may not have a loss, the distribution of the loss variable in this model is of the mixed type. It consists of a probability mass at point zero and a continuous component of positive losses. Generally, exact distribution of the aggregate loss can only be obtained through the convolution method. The De Pril recursion, however, is a powerful technique to compute the exact distribution recursively when the block of policies follow a certain set-up.

On the other hand, the collective risk model treats the aggregate loss as having a compound distribution, with the primary distribution being the claim frequency and the secondary distribution being the claim severity. The Panjer recursion can be used to compute the distribution of the aggregate loss if the claim-frequency distribution belongs to the (a, b, 0) class and the claimseverity distribution is discretized or approximated by a discrete distribution.

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Nonlife Actuarial Models
Theory, Methods and Evaluation
, pp. 86 - 112
Publisher: Cambridge University Press
Print publication year: 2009

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  • Aggregate-loss models
  • Yiu-Kuen Tse, Singapore Management University
  • Book: Nonlife Actuarial Models
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511812156.006
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  • Aggregate-loss models
  • Yiu-Kuen Tse, Singapore Management University
  • Book: Nonlife Actuarial Models
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511812156.006
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Aggregate-loss models
  • Yiu-Kuen Tse, Singapore Management University
  • Book: Nonlife Actuarial Models
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511812156.006
Available formats
×