  In this article, we apply non-convex regularization methods in order to
obtain stable estimation of loss development factors in insurance claims
reserving. Among the non-convex regularization methods, we focus on the use of
the log-adjusted absolute deviation (LAAD) penalty and provide discussion on
optimization of LAAD penalized regression model, which we prove to converge
with a coordinate descent algorithm under mild conditions. This has the
advantage of obtaining a consistent estimator for the regression coefficients
while allowing for the variable selection, which is linked to the stable
estimation of loss development factors. We calibrate our proposed model using a
multi-line insurance dataset from a property and casualty insurer where we
observed reported aggregate loss along accident years and development periods.
When compared to other regression models, our LAAD penalized regression model
provides very promising results.
