Beta transform and discounted aggregate claims under dependency

Zhehao Zhang and Shuanming Li

Annals of Actuarial Science, 2019, vol. 13, issue 2, 241-267

Abstract: 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.

Date: 2019
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