Multivariate Adaptive Regression Splines on Loss Reserve

• Main Authors: Yi-Chen Chang, 張益城
• Other Authors: Chang-Hsien Wei
• Format: Others
• Language: zh-TW
• Published: 2015
• Online Access: http://ndltd.ncl.edu.tw/handle/73009419260625267884

碩士 === 東吳大學 === 財務工程與精算數學系 === 104 === Loss reserve is the insurer’s estimated total financial obligation for the claims that have not yet been paid, claims from policies written in the past. Estimate the loss reserve is one of the most important tasks for actuaries. Most popular methods in non-life loss reserving are Chain Ladder (CL) method, Expected Claims (EC) method, Bornhuetter-Ferguson (BF) method and Cape Cod (CC) method. These method not only easy to understand, has the beauty of simplicity, but also includes actuaries own experience. These methods are good for stable and short tailed type insurance, unknown for unstable and long tailed type contract. In this study we propose to use Multivariate Adaptive Regression Splines (MARS) to estimate the Loss Reserve. A set of real data is used. It is the claim data of general liability from one of Taiwan’s general insurance companies. General liability insurance covers variety of claims and, as result, severity is highly uncertain. We use this data to demonstrate the method of MARS estimation and verify tit’s accuracy. This data contains 20 accident quarters’ quarterly paid data for 20 development quarters, along with the earned premium. The 20 by 20 data are divided into two parts; the upper triangle is used for modeling purpose and the lower triangle for out-sample checking. We assume that the ultimate loss can be obtained by the fifth developing year, and calculate the severity at the end of fifth development year via MARS and four methods mentioned previously. Comparisons of the loss reserving and the actual severity are given: (1) MARS and CC methods are overestimate, slightly overestimate for the former and highly overestimate for the later method. (2) Other three methods are under estimate; BF method is slightly under estimate, results from EC and CL method are close, and CL method is the least favorable method. (3) In view of loss reserve should sufficient, but should not over conservative, for general liability insurance, we recommend MARS method over the other methods.