Prediction in a non-homogeneous Poisson cluster model

TL;DR

This paper introduces a non-homogeneous Poisson cluster model tailored for insurance claims prediction, accommodating seasonal and non-stationary patterns, and provides methods for estimating future claims and their errors.

Contribution

It extends existing Poisson cluster models to handle non-homogeneous data, enabling more accurate predictions in insurance applications with seasonal or evolving claim patterns.

Findings

Model effectively captures seasonality in claims data

Provides formulas for expected future claims and mean squared errors

Numerical examples demonstrate improved prediction accuracy

Abstract

A non-homogeneous Poisson cluster model is studied, motivated by insurance applications. The Poisson center process which expresses arrival times of claims, triggers off cluster member processes which correspond to number or amount of payments. The cluster member process is an additive process. Given the past observations of the process we consider expected values of future increments and their mean squared errors, aiming the application in claims reserving problems. Our proposed process can cope with non-homogeneous observations such as the seasonality of claims arrival or the reducing property of payment processes, which are unavailable in the former models where both center and member processes are time homogeneous. Hence results presented in this paper are significant extensions toward applications. We also give numerical examples to show how non-homogeneity appears in predictions.