The Use of GAMLSS in Assessing the Distribution of Unpaid Claims Reserves

Regression modeling through generalized linear models (GLM) has known increasing popularity in last decades after milestone papers published in actuarial literature, representing one of the most used tools to assess the variability of unpaid claims reserve. Generalized additive models for location scale and shape (GAMLSS)represent an extension of classical GLM framework allowing not only the location parameters but also shape and scale parameters of a relevant number of distributions to be modeled as function of dependent variable like accident and development years. The paper applies GAMLSS to triangles coming from NAIC loss triangle databases in order to assess the distribution of unpaid loss reserve in term of best estimate as well as distributional form. The results of GAMLSS are critically compared with those of classical stochastic reserving approach. All the analyses will be performed using R statistical software