Beta transform and discounted aggregate claims under dependency

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.