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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Main Authors: Alessandro G. Laporta, Susanna Levantesi, Lea Petrella
Format: Article
Language:English
Published: MDPI AG 2025-04-01
Series:Risks
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Online Access:https://www.mdpi.com/2227-9091/13/5/82
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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.
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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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