On estimation of insurance risk parameters by combining local regression and distribution fitting ideas

The problem of premium estimation is an essential part of the insurance mathematics. Often the problem is divided into two parts: estimation of claim number (or frequency) and the estimation of individual claim amounts (severities). In this paper, we will focus on the former. More precisely, we are looking for certain semiparametric dynamic regression type model to avoid the "price shock" issue of static classification. We apply locally the regression method, use local maximum likelihood estimation for the parameters of the model and cross validation techniques to determine the optimal size of a neighborhood. A case study with real vehicle casco insurance dataset is included, the results obtained by proposed method are compared by the ones obtained by global regression and the classification and regression trees (C&RT) approach.