State‐space models for predicting IBNR reserve in row‐wise ordered runoff triangles: Calendar year IBNR reserves & tail effects

• Author: Adrian Pizzinga,Leonardo Costa
• Published date: 01 April 2020
• Date: 01 April 2020
• DOI: http://doi.org/10.1002/for.2638

RESEARCH ARTICLE

State-space models for predicting IBNR reserve in row-wise

ordered runoff triangles: Calendar year IBNR reserves & tail

effects

Leonardo Costa

1

| Adrian Pizzinga

2

1

Institute of Applied Social Sciences,

Alfenas Federal University (UNIFAL),

Brazil

2

Institute of Mathematics and Statistics,

Fluminense Federal University (UFF), S~

ao

Domingos, Niteroi, Rio de Janeiro, Brazil

Correspondence

Adrian Pizzinga, Institute of Mathematics

and Statistics, Fluminense Federal

University (UFF), Rua Professor Marcos

Waldemar de Freitas Reis s/n, Bloco G,

S~

ao Domingos, CEP 24210-201, Niteroi.

Rio de Janeiro, Brazil.

Email: adrianhpster@gmail.com

Funding information

CAPES,, Grant/Award Number: PNPD

scholarship - Finance Code 001; Funenseg;

IAPUC; Icatu Hartford Seguros S.A.;

PROPPI; aforementioned institutions

Abstract

The issue of modeling and forecasting IBNR (incurred but not reported) actu-

arial reserve under Kalman filter techniques and extensions, using data

arranged in a runoff triangle, is a frequent theme in the literature. One quite

recent approach is to order the runoff triangle under a row-wise fashion and

use linear state-space models for the resulting data set. To allow new possibili-

ties for short-term IBNR reserves as well as to mitigate insolvency risk, in this

paper we extend such a state-space method by: (i) a calendar year IBNR

reserve prediction; and (ii) a tail effect for the row-wise ordered triangle. The

extension is implemented with a real runoff triangle and compared with some

traditional IBNR predictors. Empirical results indicate that the approach of

this paper outperforms the competing methods in terms of out-of-sample com-

parisons and gives more conservative IBNR reserves than the original state-

space method.

KEYWORDS

calendar year IBNR reserve, Kalman filter, linear state-space model, runoff triangle, tail effect

1|INTRODUCTION

According to Taylor (2000), Wüthrich and Merz (2008),

and Costa, Pizzinga, and Atherino (2016), nonlife insur-

ances are financial contracts between the insurance com-

pany and the insured involving some different lines of

business, such as motor/car insurance, marine insurance,

and property insurance. By such contracts, the insurance

company receives from the insured a premium (fixed

amount of money) for providing financial coverage

against the random occurrence of well-specified events,

or accidents. The right of the insured to such financial

coverage constitutes a claim.

Not infrequently, there is a delay between the claim

occurrence date and the claim reporting date. During this

period, the insurance company remains unaware of the

accidents. This is precisely the case of an incurred but not

reported (IBNR) claim. To manage this specific risk, the

insurance company has to make IBNR reserves

(cf. Atherino, Pizzinga, & Fernandes, 2010; Costa et al.,

2016; de Jong & Zehnwirth, 1983; England & Verrall,

2002; Grize, 2015; Kaas, Goovaerts, Dhaene, & Denuit,

2009; Kremer, 1982; Taylor, 2000). Since IBNR accidents

become known only in the future, efforts at a given pre-

sent time must be towards the forecasting of the

corresponding financial coverage, which are taken as the

IBNR reserves.

This article focuses on improving the paradigm pro-

posed by Atherino et al. (2010) for dealing with IBNR

data. Basically, the methodology of Atherino et al. con-

sists of row-wise ordering the runoff triangle (which is

the traditional arrangement of IBNR reserve data) and,

with the reordered data set (which has many missing

values), considering an appropriate linear state model

Received: 20 July 2019 Revised: 13 September 2019 Accepted: 25 November 2019

DOI: 10.1002/for.2638

438 © 2019 John Wiley & Sons, Ltd. Journal of Forecasting. 2020;39:438–448.wileyonlinelibrary.com/journal/for