Prediction in a mixed Poisson cluster model. Issue 3 (2nd July 2016)

• Record Type: Journal Article
• Authors: Matsui, Muneya; Rolski, Tomasz
• Is Part Of: Stochastic models. Volume 32:Issue 3(2016)
• Page Start: 460
• Page End: 480
• Publication Date: 2016-07-02
• Subjects: Conditional moments -- IBNR losses -- Lévy processes -- mixed non-homogeneous Poisson process -- prediction -- risk reserve; Primary 60K30; 60G55 -- Secondary 90Bxx; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/15326349.2016.1170614
• Languages: English
• ISSNs: 1532-6349

Abstract

ABSTRACT: Motivated by insurance applications, a mixed Poisson cluster model is considered, where the cluster center process is a mixed Poisson process and descendant processes are additive processes. Each point of the center process represents a claim's reported time and descendant processes are interpreted as processes of the corresponding payments or number of payments. In this study, we focus on the process aggregating all separate claim's payment processes. Given the past observations, we study prediction of future increments and their mean-squared errors, also revealing the dependency between future increments from non-reported (IBNR) claims and the past available information. In the existing literature, they are independent since models were considered with a purely Poissonian center process. We derive computationally reasonable expressions for predictors and their variances.