Application Of Kalman Filter In Non-life Outstanding Claims Reserving

The outstanding claim reserve is the most important part of reserves. The actuaries in the insurance companies pay most time in estimating the outstanding claim reserves. The accuracy of the estimated outstanding claim reserve significantly affects insurance companies'moderate operations. But under the current circumstances of China insurance industry, most insurance companies have not enough historical data or the existing data are lack of reliability. So the traditional reserving methods produced not accurate outstanding claim reserves in non-life insurance companies.Considered practice claim characters in no-life insurance companies, this paper uses state-space model to describe two factors which affecting frequencies and severities of claims respectively. The two factors are: the claim process makes frequency and severity of claim developing under any certain trend; and, the stochastical changes of claims also make frequencies and severities random. By using state-space to describe the process of no-life claims and Kalman filter to estimate the conversion parameters of state-space, this article forecasts the severities and frequencies of claims respectively and then gets the reserves of the outstanding claims. The method in this paper not only is responsive to the trends but also to the stochastical changes of claims. The empirical results show us that this method is effective in developing the estimation of outstanding claims reserves. Also this method can be used freely when there are some err data, it can amend the wrong data automatically below a certain degree, and eliminate the effects of historical data to outstanding claims reserve estimation. So this method provides a more accuracy estimate of outstanding claims reserve for domestic non-life insurance companies.