Gaussian Mixture Regression Model with Sparsity for Clustering of Territory Risk in Auto Insurance
-
Shengkun Xie
,
Chong Gan
Abstract
Insurance rating territory design and accurate estimation of territory risk relativities are fundamental aspects of auto insurance rate regulation. It is crucial to develop methodologies that can facilitate the effective design of rating territories and their risk relativities estimate, as they directly impact the rate filing and the decision support of the rate change review process. This article proposes a Gaussian Mixture Regression model clustering approach for territory design. The proposed method incorporates a linear regression model, taking spatial location as model covariates, which helps estimate the cluster mean more accurately. Also, to further enhance the estimation of territory risk relativities, we impose sparsity through sparse matrix decomposition of the membership coefficient matrix obtained from the Gaussian Mixture Regression model. By transitioning from the current hard clustering method to a soft approach, our methodology could improve the evaluation of territory risk for rate-making purposes. Moreover, using non-negative sparse matrix approximation ensures that the estimation of risk relativities for basic rating units remains smooth, effectively eliminating data noise from the territory risk relativity estimate. Overall, our novel methodology aims to significantly enhance the accuracy and reliability of risk analysis in auto insurance. Furthermore, the proposed method exhibits potential for extension to various other domains that involve spatial clustering of data, thereby broadening its applicability and expanding its usefulness beyond auto insurance rate regulation.
The first 40 rows of the FSA data, sorted in descending order by ‘exposures’. This data is given as an example of input data for Gaussian mixture regression clustering.
| FSA | Loss cost | Exposures | Latitude | Longitude |
|---|---|---|---|---|
| L5N | 1,519 | 46,127 | 43.58701 | −79.75656 |
| L5M | 2,070 | 45,842 | 43.56732 | −79.71608 |
| L4C | 1,801 | 36,837 | 43.87009 | −79.43920 |
| L4J | 2,110 | 36,284 | 43.81237 | −79.44938 |
| L3R | 1,591 | 34,114 | 43.84944 | −79.32583 |
| L6A | 2,423 | 33,640 | 43.85930 | −79.51554 |
| L4L | 1,678 | 33,347 | 43.79339 | −79.57974 |
| L6Y | 2,749 | 30,515 | 43.65887 | −79.75180 |
| L6R | 3,667 | 30,459 | 43.75530 | −79.75334 |
| L7A | 3,008 | 28,507 | 43.70264 | −79.82300 |
| L6S | 2,445 | 27,688 | 43.73340 | −79.73314 |
| L3T | 1,671 | 26,799 | 43.82198 | −79.39453 |
| M2N | 1,737 | 26,124 | 43.76766 | −79.40879 |
| L4H | 2,473 | 25,288 | 43.82593 | −79.58696 |
| L3S | 3,187 | 24,838 | 43.84275 | −79.27094 |
| L5L | 1,498 | 24,822 | 43.53743 | −79.69186 |
| L5B | 2,272 | 24,542 | 43.57746 | −79.63006 |
| M1B | 4,082 | 24,415 | 43.80588 | −79.20751 |
| M5C | 141 | 23,987 | 43.65710 | −79.38253 |
| L6X | 2,457 | 23,027 | 43.68150 | −79.78490 |
| L3P | 980 | 22,967 | 43.88057 | −79.26391 |
| L5V | 2,428 | 22,696 | 43.59532 | −79.69070 |
| L6P | 3,738 | 22,376 | 43.78321 | −79.70193 |
| M1V | 2,662 | 21,966 | 43.81752 | −79.28170 |
| L4E | 1,675 | 21,150 | 43.94182 | −79.45497 |
| L5A | 2,390 | 20,852 | 43.58620 | −79.61031 |
| M2J | 2,092 | 20,369 | 43.77962 | −79.34920 |
| M1W | 2,140 | 19,943 | 43.79816 | −79.32107 |
| L6C | 1,332 | 19,729 | 43.89046 | −79.33551 |
| L4B | 1,608 | 19,701 | 43.85529 | −79.40083 |
| L6V | 3,110 | 19,248 | 43.70306 | −79.76144 |
| M9C | 1,360 | 18,714 | 43.64486 | −79.57317 |
| L4Z | 2,046 | 18,168 | 43.61335 | −79.64676 |
| M1C | 1,242 | 18,057 | 43.78708 | −79.15529 |
| L5R | 2,546 | 17,854 | 43.60404 | −79.66888 |
| M1E | 2,568 | 17,669 | 43.76557 | −79.19081 |
| M9W | 3,123 | 17,441 | 43.71797 | −79.58034 |
| L6T | 2,677 | 17,042 | 43.71664 | −79.70027 |
| L6Z | 1,770 | 16,999 | 43.72642 | −79.79354 |
| L4S | 1,677 | 16,638 | 43.89404 | −79.42243 |
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Articles in the same Issue
- Frontmatter
- Featured Articles (Research Paper)
- Evaluating the Efficiency of Capital Enhancement and Investment Constraints in Life Insurance Supervision
- The Impact of the Social Insurance System on Chinese Adults’ Subjective Well-Being
- Financial Sustainability of Social Insurance: The Case of Korean Workers’ Compensation Insurance and Possibility of Triple Moral Hazard
- Gaussian Mixture Regression Model with Sparsity for Clustering of Territory Risk in Auto Insurance
Articles in the same Issue
- Frontmatter
- Featured Articles (Research Paper)
- Evaluating the Efficiency of Capital Enhancement and Investment Constraints in Life Insurance Supervision
- The Impact of the Social Insurance System on Chinese Adults’ Subjective Well-Being
- Financial Sustainability of Social Insurance: The Case of Korean Workers’ Compensation Insurance and Possibility of Triple Moral Hazard
- Gaussian Mixture Regression Model with Sparsity for Clustering of Territory Risk in Auto Insurance
