Evaluation Model Of Liability Reserve With Dependent Risk Structure

Liability reserve, the most important liabilities item of non-life insurance company, determines the future solvency and profitability of insurance company. Calculated non-life insurance liability reserves by reasonable evaluation method can increase the accuracy of assessing non-life insurance liability reserve, thereby to enhance the ability of property insurance to perform insurance claim. In the traditional models of assessing liability reserve, no matter the chain ladder method, B-F method, Bayesian method under aggregated data or the models under individual data, they all assume that the claim happens in each accident year or different insurance policies caused claims are mutually independent. However, there are a lot of insurance occasions in real life, making a certain dependency exist between all kinds of claims. This paper assumes that there are a certain random common effect between the claims caused by different insurance policies and different accident years, establishes the liability reserve models of aggregated data and individual data and discusses the statistical properties of assessing liability reserve. On the one hand the paper establishes the liability reserve model of random common effect under aggregated data and uses the methods of credibility theory to get liability reserve estimation, the consistency of verification the estimates of reserve and other statistical properties. On the other hand, under individual data model, the paper establishes the random common effect model of RBNS.Thus the hierarchical Bayesian models are derived for individual reserves. Compared with aggregated data model, individual data models have smaller error of mean square and get the estimation of structural parameter by using empirical Bayesian method. Finnally the paper summarizes the full paper and puts forward the future research direction.