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In this article, we apply non-convex regularization methods in order toobtain stable estimation of loss development factors in insurance claimsreserving. Among the non-convex regularization methods, we focus on the use ofthe log-adjusted absolute deviation (LAAD) penalty and provide discussion onoptimization of LAAD penalized regression model, which we prove to convergewith a coordinate descent algorithm under mild conditions. This has theadvantage of obtaining a consistent estimator for the regression coefficientswhile allowing for the variable selection, which is linked to the stableestimation of loss development factors. We calibrate our proposed model using amulti-line insurance dataset from a property and casualty insurer where weobserved reported aggregate loss along accident years and development periods.When compared to other regression models, our LAAD penalized regression modelprovides very promising results.

A non-convex regularization approach for stable estimation of loss development factors