Claims Reserving with a Stochastic Vector Projection

North American Actuarial Journal, Volume 22, Issue 1, pp. 22-39, March 2018, DOI 10.1080/10920277.2017.1353429

30 Pages Posted: 21 Aug 2016 Last revised: 20 Mar 2018

See all articles by Luis Portugal

Luis Portugal

Department of Mathematical Sciences, University of Liverpool

Athanasios A. Pantelous

Monash University - Department of Econometrics & Business Statistics

Hirbod Assa

University of Liverpool

Date Written: June 2, 2017

Abstract

In the last three decades, a variety of stochastic reserving models has been proposed in the general insurance literature mainly using (or reproducing) the eminent Chain-Ladder claims reserving estimates. In practice, when the data doesn’t satisfy the Chain-Ladder assumptions, high prediction errors might occur. Thus, in this paper, a combined methodology is proposed which is based on the stochastic vector projection method and uses the regression through the origin approach of Murphy (1994), but with heteroscedastic errors instead, and different to those that used by Mack (1993, 1994). Furthermore, the Mack (1993) distribution-free model appears to have higher prediction errors when it is compared with the pro-posed one, particularly, for data sets with increasing (regular) trends. Finally, three empirical examples with irregular and regular data sets illustrate the theoretical findings, and the concepts of best estimate and risk margin are reported.

Keywords: Stochastic Reserving, Chain-Ladder Distribution-Free, Vector Projection, Best Estimate, Risk Margin, Link Ratios, Loss Development Factors, Homoscedastic and Heteroscedastic Errors, Prediction Errors

JEL Classification: G22, C13, C18, C35

Suggested Citation

Portugal, Luis and Pantelous, Athanasios A. and Assa, Hirbod, Claims Reserving with a Stochastic Vector Projection (June 2, 2017). North American Actuarial Journal, Volume 22, Issue 1, pp. 22-39, March 2018, DOI 10.1080/10920277.2017.1353429 . Available at SSRN: https://ssrn.com/abstract=2824912 or http://dx.doi.org/10.2139/ssrn.2824912

Luis Portugal

Department of Mathematical Sciences, University of Liverpool ( email )

Chatham Street
Liverpool, L69 7ZA
United Kingdom

Athanasios A. Pantelous (Contact Author)

Monash University - Department of Econometrics & Business Statistics ( email )

Wellington Road
Clayton, Victoria 3168
Australia

Hirbod Assa

University of Liverpool ( email )

Institute for Financial and Actuarial Mathematics,
Liverpool, L18 8BF
United Kingdom
447522173132 (Phone)

HOME PAGE: http://sites.google.com/site/assahirbod/

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