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
Date Written: June 2, 2017
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: Suggested Citation