  For a typical insurance portfolio, the claims process for a short period,
typically one year, is characterized by observing frequency of claims together
with the associated claims severities. The collective risk model describes this
portfolio as a random sum of the aggregation of the claim amounts. In the
classical framework, for simplicity, the claim frequency and claim severities
are assumed to be mutually independent. However, there is a growing interest in
relaxing this independence assumption which is more realistic and useful for
the practical insurance ratemaking. While the common thread has been capturing
the dependence between frequency and aggregate severity within a single period,
the work of Oh et al. (2020a) provides an interesting extension to the addition
of capturing dependence among individual severities. In this paper, we extend
these works within a framework where we have a portfolio of microlevel
frequencies and severities for multiple years. This allows us to develop a
factor copula model framework that captures various types of dependence between
claim frequencies and claim severities over multiple years. It is therefore a
clear extension of earlier works on one-year dependent frequency-severity
models and on random effects model for capturing serial dependence of claims.
We focus on the results using a family of elliptical copulas to model the
dependence. The paper further describes how to calibrate the proposed model
using illustrative claims data arising from a Singapore insurance company. The
estimated results provide strong evidence of all forms of dependencies captured
by our model.
