Quantile Regression Analysis Of IBNR Reserving On Conditional Copulas

For an insurance company operating non-life insurance businesses,the non-life insurance reserve is the largest liability item on the balance sheet,so it is essential for this company to scientifically estimate non-life insurance reserves.Since the traditional chain ladder methods or separation methods have many defects,which lose a large amount of individual information.At present,many scholars have begun to study the individual claim reserve model,which comprehensively consider the individual's claim information,and overcome many defects of the traditional model.For IBNR individual reserve model based on Copulas,most scholars tend to focus on the estimation of insurance claims,and this article turns the focus to the relationship between the event occurrence time T and the reporting delay W.Because only the insurance company correctly estimates W,and further estimates the amount of the claim,the reserve can be reasonably allocated.On the one hand,the reserve of the insurance company is sufficient to pay the indemnity of all insurers in the current period,in the meantime increasing the solvency of the insurance company,reducing the operational risk,and improving the risk management level.On the other hand,insurance company can use the excess funds for investment,which may increase it's income and market competitiveness.The IBNR reserve quantile regression model established in this paper is based on the conditional Copula method.Both the occurrence time T and the reporting delay W of the event have a Cox structure,and a Copula function is used to describe the dependence relationship between them.In the past,when scholars estimated the individual reserve model,most of them assumed that the two variables were independent,which obviously did not match the facts.We all know that the traditional OLS(Ordinary Least Squares)method has many defects,especially when the data exists spikes or thick tails,and significant heteroscedasticity.So in this paper,we chooses the quantile regression method to build the model,which better use the various parts of the data features.In this paper,we consider the case that the data existing random right censored,and then give the censored weight expression,establishe the censored quantile regression model based on the condition Copula.In terms of parameter estimation,we use Monte Carlo simulation method to compare the estimated effect of interior point algorithm and MM(majorize-minimize algorithm)algorithm on two nonlinear models.The experimental results show that the MM algorithm still perform well on more complex nonlinear quantile model.So we choose MM algorithm to estimate our complicated censored quantile regression model.In order to verify the accuracy of the model,we make a numerical simulation in chapter 4.Firstly,we use the Copula sampling method to generate experimental data,propose a weighted MM algorithm to estimate the model parameters,and the specific implementation steps are listed,which is convenient for other scholars to test and learn from.Furthermore,we study the influence of the difference of the quantile level and the size of the sample on the parameter estimation.The results of the table verify the accuracy of the model.The chapter five gives the conclusions of this paper,and points out the shortcomings and the direction of future improvement.