| In the data age,the amount of informat,ion that can be reflected by a regres-sion line obtained by mean regression is very limited.As a feature number that,characterizes the position of the data,the quantile can mine a richer amount of information,by measuring the independent variable versus the dependent variable.The marginal influence of each particular quantile makes the quantile regression ef-fectively characterize the tail features of the data distribution.Since the insurance data is often robust,there are some outliers with strong influences.The classical reliability model can not effectively use the data information of these outliers,and the quantile method can solve this well.This paper introduces the idea of quantile into the credibility theory,and inno-vates the classical credibility model according to the actual economic life.On the one hand,we consider extending the independent hypothesis between policy risks to a special dependent risk structure,and establishing quantile credibility model with dependent structure;On the other hand,we comprehensively consider the positive safety load of premiums and the impact of inflation on premiums,and extend the classical regression credibility model to the quantile regression credibility model with inflation factor under the balance loss function,so as to adapt to the development of our country insurance actuarial systems internal economic laws and model features.The main research contents are as follows:1.Aiming at the independence hypothesis of policy risk in the classical Buhlmann credibility model,we find that policy risk often presents a certain dependence or spe-cific effect in non-life insurance practice applications,so we comprehensively consid-er the robustness of insurance data and the risk of policy.Combining the quantile credibility model proposed by Pitselis with the credibility model under the common effect established by Limin Wen et al,we establish quantile credibility model under the common effect structure.2.According to Yi Zhang et al,we extend the common effect to a more gen-eral risk-dependent situation,and study the quantile credibility model with risk-dependent structure.The results show that the common effect structure is a special case of risk-dependent structure.3.The classical regression credibility model is to solve the optimization problem under the mean square loss to obtain the future credibility premium estimate.On the one hand,considering the particularity of the mean square loss,the premium does not have a positive safety load,which brings risks to the insurance company.On the other hand,considering the price fluctuations caused by inflation will have a trending effect on the claim data.We use the balance loss instead of the mean square loss,and use the inflat,ion factor to reflect the impact of inflation on future premiums.Based on the quantile regression credibility model proposed by Pit:elis:a single contract and multi-contract balanced quantile regression credibility model with inflation factor is established. |
