A Multivariate Evolutionary Generalised Linear Model Framework with Adaptive Estimation for Claims Reserving

36 Pages Posted: 2 Jul 2019 Last revised: 7 Jul 2019

See all articles by Benjamin Avanzi

Benjamin Avanzi

UNSW Australia Business School, School of Risk and Actuarial Studies

Greg Taylor

UNSW Australia Business School, School of Risk & Actuarial Studies

Phuong Anh Vu

UNSW Business School - School of Risk and Actuarial Studies; Université de Montréal - Département de mathématiques et de statistique

Bernard Wong

UNSW Australia Business School, School of Risk & Actuarial Studies

Date Written: July 1, 2019

Abstract

In this paper, we develop a multivariate evolutionary generalised linear model (GLM) framework for claims reserving, which allows for dynamic features of claims activity in conjunction with dependency across business lines to accurately assess claims reserves. We extend the traditional GLM reserving framework on two fronts: GLM fixed factors are allowed to evolve in a recursive manner, and dependence is incorporated in the specification of these factors using a common shock approach.

We consider factors that evolve across accident years in conjunction with factors that evolve across calendar years. This two-dimensional evolution of factors is unconventional as a traditional evolutionary model typically considers the evolution in one single time dimension. This creates challenges for the estimation process, which we tackle in this paper. We develop the formulation of a particle filtering algorithm with parameter learning procedure. This is an adaptive estimation approach which updates evolving factors of the framework recursively over time.

We implement and illustrate our model with a simulated data set, as well as a set of real data from a Canadian insurer.

Keywords: Claims Reserving, Evolutionary GLM, Adaptive Reserving, Particle Learning, Common Shock Models

JEL Classification: G22

Suggested Citation

Avanzi, Benjamin and Taylor, Greg and Vu, Phuong Anh and Wong, Bernard, A Multivariate Evolutionary Generalised Linear Model Framework with Adaptive Estimation for Claims Reserving (July 1, 2019). UNSW Business School Research Paper No. 2019ACTL03. Available at SSRN: https://ssrn.com/abstract=3413016 or http://dx.doi.org/10.2139/ssrn.3413016

Benjamin Avanzi

UNSW Australia Business School, School of Risk and Actuarial Studies ( email )

UNSW Sydney, NSW 2052
Australia

Greg Taylor

UNSW Australia Business School, School of Risk & Actuarial Studies ( email )

Level 6, East Lobby
UNSW Business School Building, UNSW
Sydney, NSW 2052
Australia
+61 421 338 448 (Phone)

Phuong Anh Vu (Contact Author)

UNSW Business School - School of Risk and Actuarial Studies ( email )

Sydney, NSW 2052
Australia

Université de Montréal - Département de mathématiques et de statistique ( email )

Montreal, Quebec H3C 3J7
Canada

Bernard Wong

UNSW Australia Business School, School of Risk & Actuarial Studies ( email )

Room 2058 South Wing 2nd Floor
Quadrangle building, Kensington Campus
Sydney, NSW 2052
Australia

Register to save articles to
your library

Register

Paper statistics

Downloads
13
Abstract Views
93
PlumX Metrics