Stochastic Method Of Estimation Of IBNR Reserves

There is delay in the occurrence, report, and setting-up of claims. On the date of valuation, the insurers not only have to estimate reserves for reported claims, but also have to make capital preparation for those incurred but not reported claims, that is IBNR reserve, which is the vital part of loss reserve. When the insurers refer to IBNR reserve, they always mean more than pure IBNR reserve. The prudent way of calculation IBNR reserve has great impact on the insurers' liability valuation, solvency and performance assessment.Since IBNR provision has no case information to rely on directly, it is with the most uncertainty and assessment difficulty. Till now, many researches can be done since there are no publicly accepted techniques and models in both theory and practice. In our country, with more and more long-tail businesses insured, IBNR reserve is changing from "not more than 4 percent of actual paid losses that year" to "at lease prudently estimating IBNR in two ways such as chain ladder, payments per claim, reserve development and B-F method" , which is much closer to international criterion.A single value can be calculated through those methods mentioned above. However it is difficult to say how accurate the value is. Since IBNR reserve is a random variable, stochastic models can be set up to estimate its expected value, variance and confidence interval. The result can be more acceptable.In this paper, there are four parts. Firstly, the paper introduced the background of the issue. Section II gave the definition of IBNR reserve, told why need to estimate IBNR separately, and briefly introduced valuation method. Section III designed a time-series model to estimate the number of IBNR claims. Section IV is an example to illustrate the method mentioned in Section III. The innovation of this paper is using time series method to estimate the number of IBNR, and adjusting result with quadratic programming and truncated normal distribution.