A Micro-Level Claim Count Model with Overdispersion and Reporting Delays

24 Pages Posted: 2 Jan 2016

See all articles by Benjamin Avanzi

Benjamin Avanzi

UNSW Australia Business School, School of Risk and Actuarial Studies

Bernard Wong

UNSW Australia Business School, School of Risk & Actuarial Studies

Xinda Yang

University of New South Wales (UNSW) - School of Actuarial Studies

Date Written: December 31, 2015

Abstract

The accurate estimation of outstanding liabilities of an insurance company is an essential task. This is to meet regulatory requirements, but also to achieve efficient internal capital management. Over the recent years, there has been increasing interest in the utilisation of insurance data at a more granular level, and to model claims using stochastic processes. So far, this so-called 'micro-level reserving' approach has mainly focused on the Poisson process.

In this paper, we propose and apply a Cox process approach to model the arrival process and reporting pattern of insurance claims. This allows for over-dispersion and serial dependency in claim counts, which are typical features in real data. We explicitly consider risk exposure and reporting delays, and show how to use our model to predict the numbers of Incurred-But-Not-Reported (IBNR) claims. The model is calibrated and illustrated using real data from the AUSI data set.

Keywords: Cox process, Shot noise, Insurance claims counts, Markov Chain Monte Carlo, Filtering

JEL Classification: C51, C53, C55, G22

Suggested Citation

Avanzi, Benjamin and Wong, Bernard and Yang, Xinda, A Micro-Level Claim Count Model with Overdispersion and Reporting Delays (December 31, 2015). UNSW Business School Research Paper No. 2015ACTL25. Available at SSRN: https://ssrn.com/abstract=2705241 or http://dx.doi.org/10.2139/ssrn.2705241

Benjamin Avanzi

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

UNSW Sydney, NSW 2052
Australia

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

Xinda Yang (Contact Author)

University of New South Wales (UNSW) - School of Actuarial Studies ( email )

Sydney, NSW 2052
Australia

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