Outstanding Loss Reserve Estimation Method Comparison Study

This paper is concerned with the situation that occurs in claims reserving when there are negative values in the development triangle of incremental claim amounts. Typically these negative values will be the result of salvage recoveries, payments from third parties, total or partial cancellation of outstanding claims due to initial overestimation of the loss or to a possible favorable jury decision in favor of the insurer, rejection by the insurer, or just plain errors. Some of the traditional methods of claims reserving, such as the chain-ladder technique, may produce estimates of the reserves even when there are negative values. However, many methods can break down in the presence of enough (in number and/or size) negative incremental claims if certain constraints are not met. Historically the chain-ladder method has been used as a gold standard (benchmark) because of its generalized use and ease of application. A method that improves on the gold standard is one that can handle situations where there are many negative incremental claims and/ or some of these are large. This paper presents a Bayesian model to consider negative incremental values, based on a three-parameter log-normal distribution. The model presented here allows the actuary to provide point estimates and measures of dispersion, as well as the complete distribution for outstanding claims from which the reserves can be derived. It is concluded that the method has a clear advantage over other existing methods. A Markov chain Monte Carlo simulation is applied using the package WinBUGS.The full text of a total of five parts. The first part of introduction, the topics introduced in this paper background, as well as domestic and foreign literature of this research ideas and research restrictions. The second part, on the basis of this paper on the analysis of some major awards, including outstanding for the classification, outstanding claims reserve estimation methods of the classification, comparison and choice, and the estimated traffic triangle theory, lead to incremental payments for the negative , the chain ladder of outstanding claims reserve on the specific process and the estimated proved. The third part, chain ladder of stochastic model introduced to Mack and super-Poisson distribution model as an example, identify the flow triangle in the existence of a large number Award incremental negative, can still effective estimated outstanding claims reserve Chain staircase law stochastic model, comparative analysis and empirical analysis in this paper was the basis of reference. Part IV, hierarchical Bayesian estimation and MCMC simulation of the three-parameter lognormal distribution model introduction, and on how to use the three-parameter model of normality, and how to use hierarchical Bayesian estimation and MCMC simulation and the parameters obtained estimated outstanding claims reserve and its posterior distribution of the specific process were introduced. The fifth part, the application of the model, the Mack model, super-Poisson distribution, the three-parameter lognormal distribution model of profile likelihood estimation, hierarchical Bayesian estimation and MCMC simulation of the three-parameter lognormal distribution model, contains a lot of a group of incremental amount paid to the observation of negative value is estimated that the outstanding claims reserve estimates, and the estimated accuracy of their comparisons. Also presented by the three-parameter lognormal distribution model MCMC simulation was outstanding claims reserve posterior distribution map, the performance of its more intuitive data features.