A Neural Network Approach for Pricing Correlated Health Risks
In recent years, the actuarial literature involving machine learning in insurance pricing has flourished. However, most actuarial machine learning research focuses on property and casualty insurance, while using such techniques in health insurance is yet to be explored. In this paper, we discuss the...
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MDPI AG
2025-04-01
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| author | Alessandro G. Laporta Susanna Levantesi Lea Petrella |
| author_facet | Alessandro G. Laporta Susanna Levantesi Lea Petrella |
| author_sort | Alessandro G. Laporta |
| collection | DOAJ |
| description | In recent years, the actuarial literature involving machine learning in insurance pricing has flourished. However, most actuarial machine learning research focuses on property and casualty insurance, while using such techniques in health insurance is yet to be explored. In this paper, we discuss the use of neural networks to set the price of health insurance coverage following the structure of a classical frequency-severity model. In particular, we propose negative multinomial neural networks to jointly model the frequency of possibly correlated medical claims and Gamma neural networks to estimate the expected claim severity. Using a case study based on real-world health insurance data, we highlight the overall better performance of the neural network models with respect to more established regression models, both in terms of accuracy (frequency models achieve an average out-of-sample deviance of 8.54 compared to 8.61 for classical regressions) and risk diversification, as indicated by the ABC lift metric, which is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>5.62</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></semantics></math></inline-formula> for neural networks versus <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>8.27</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></semantics></math></inline-formula> for traditional models. |
| format | Article |
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| institution | OA Journals |
| issn | 2227-9091 |
| language | English |
| publishDate | 2025-04-01 |
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| series | Risks |
| spelling | doaj-art-d1a4f839b19048dbbdbdacad6e8b09ea2025-08-20T02:33:58ZengMDPI AGRisks2227-90912025-04-011358210.3390/risks13050082A Neural Network Approach for Pricing Correlated Health RisksAlessandro G. Laporta0Susanna Levantesi1Lea Petrella2Department of Statistics, Sapienza University of Rome, 00185 Roma, ItalyDepartment of Statistics, Sapienza University of Rome, 00185 Roma, ItalyMEMOTEF Department, Sapienza University of Rome, 00185 Roma, ItalyIn recent years, the actuarial literature involving machine learning in insurance pricing has flourished. However, most actuarial machine learning research focuses on property and casualty insurance, while using such techniques in health insurance is yet to be explored. In this paper, we discuss the use of neural networks to set the price of health insurance coverage following the structure of a classical frequency-severity model. In particular, we propose negative multinomial neural networks to jointly model the frequency of possibly correlated medical claims and Gamma neural networks to estimate the expected claim severity. Using a case study based on real-world health insurance data, we highlight the overall better performance of the neural network models with respect to more established regression models, both in terms of accuracy (frequency models achieve an average out-of-sample deviance of 8.54 compared to 8.61 for classical regressions) and risk diversification, as indicated by the ABC lift metric, which is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>5.62</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></semantics></math></inline-formula> for neural networks versus <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>8.27</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></semantics></math></inline-formula> for traditional models.https://www.mdpi.com/2227-9091/13/5/82health insurance pricingneural networksmultinomial distributiongamma distribution |
| spellingShingle | Alessandro G. Laporta Susanna Levantesi Lea Petrella A Neural Network Approach for Pricing Correlated Health Risks Risks health insurance pricing neural networks multinomial distribution gamma distribution |
| title | A Neural Network Approach for Pricing Correlated Health Risks |
| title_full | A Neural Network Approach for Pricing Correlated Health Risks |
| title_fullStr | A Neural Network Approach for Pricing Correlated Health Risks |
| title_full_unstemmed | A Neural Network Approach for Pricing Correlated Health Risks |
| title_short | A Neural Network Approach for Pricing Correlated Health Risks |
| title_sort | neural network approach for pricing correlated health risks |
| topic | health insurance pricing neural networks multinomial distribution gamma distribution |
| url | https://www.mdpi.com/2227-9091/13/5/82 |
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