Beta transform and discounted aggregate claims under dependency

Zhehao Zhang*, Shuanming Li

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


This paper starts with the Beta transform and discusses the stochastic ordering properties of this transform under different parameter settings. Later, the distribution of discounted aggregate claims in a compound renewal risk model with dependence between inter-claim times and claim sizes is studied. Recursive formulas for moments and joint moments are expressed in terms of the Beta transform of the inter-claim times and claim severities. Particularly, our moments formula is more explicit and computation-friendly than earlier ones in the references. Lastly, numerical examples are provided to illustrate our results.

Original languageEnglish
Pages (from-to)241-267
Number of pages27
JournalAnnals of Actuarial Science
Issue number2
Publication statusPublished - 1 Sept 2019
Externally publishedYes


  • Beta distributional transform
  • Copula
  • Discounted aggregate claims
  • Renewal risk process
  • Stochastic ordering

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