Renewal sums under mixtures of exponentials

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4 Citations (Scopus)


We start with applying two methods to derive formulas of a mixture of exponential process, i.e., a renewal process whose inter-arrival time follows a mixture of exponentials. Further, stochastic order properties are discussed when comparing this process to a Poisson process with the same expectation of inter-arrival times. Based on these properties, formulas and ordering properties are given for the non-discounted compound process as well as the discounted one. Explicit formulas for the density functions are also provided for both cases. Under the discounted compound case, several new results are derived for heavy-tailed distributions. Finally, the Laguerre series approximation is proposed and tested for various common actuarial indices, e.g., VaR, CTE and stop-loss premium.

Original languageEnglish
Pages (from-to)281-301
Number of pages21
JournalApplied Mathematics and Computation
Publication statusPublished - 15 Nov 2018
Externally publishedYes


  • Discounted aggregate claims
  • Laguerre series approximation
  • Mittag-Leffler functions and distributions
  • Mixture of exponentials
  • Stochastic orders


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