On robust credibility models for premiums, including weighted regression.

摘要

In Chapter one we introduce the fundamental notions of credibility estimation theory for the classical and the regression case, review the literature as well as give the outline of the thesis.; In the first part of Chapter two we summarize the classical model of Buhlmann & Straub (1970) and Kunsch (1992) robust model for the classical credibility case. In the second part we define the robust weighted credibility model based on Kunsch's method and we present numerical illustration of the models.; In the first section of Chapter three we present Hachemeister's regression credibility model. In the following sections we propose credibility premium estimation using influence functions based on Hampel's and Cook's approach, respectively. We extend our models to the weighted regression case and present two methods of credibility estimation; the portfolio unbiased robust regression credibility estimation and the pure robust regression credibility one.; In Chapter four we introduce Bickel's pseudo-observations and present optimal solutions for credibility estimators based on De Vylder's results. Implementation to a data set and numerical results are also presented.; In Chapter five we present robust empirical Bayes credibility estimation, asymptotic properties and prove optimality of robust credibility estimation.