A note on the recursive joint moments of discounted compound dependent renewal sums

Article type: Research Article

Authors: Adékambi, Franck^a; | Essiomle, Kokou^b

Affiliations: [a] School of Economics, University of Johannesburg, Johannesburg, South Africa E-mail: fadekambi@uj.ac.za | [b] School of Economics, University of Johannesburg, Johannesburg, South Africa E-mail: 201900490@student.uj.ac.za

Correspondence: [*] Corresponding author: Franck Adékambi. E-mail: fadekambi@uj.ac.za

Abstract: In this paper, we present recursive joint moments and a linear predictor of aggregate discounted claims under dependency for an ordinary or delayed renewal claims number process. In addition, we present recursive formulas for the joint moments in the trend renewal process. We compare the predictive value of our linear predictor with the simulated value of exponential and Erlang (2,2) claims inter-occurrence times with constant interest rate.

Keywords: Discounted aggregate claims, dependency, linear predictor, joint moments, renewal process, trend renewal process, higher joint moments, interest rate

DOI: 10.3233/RDA-231522

Journal: Risk and Decision Analysis, vol. 9, no. 2-4, pp. 57-71, 2023