Individual Claims Development with Machine Learning ASTIN Working Party Individual Claims Development with Machine Learning Bor Harej Zavarovalnica Triglav, d.d. Slovenia bor.harej@triglav.si

Bor Harej Slovenia Roman Gächter Australia Salma Jamal France Alexander Schaeper Germany Alexandre Boumezoued Andrew McGuinness UK Erik Gustafsson Sweden Frank Cuypers Switzerland Greg Taylor Ivan Valdes Klaus Krøier Denmark Maria Inês Silva Portugal Mario V. Wüthrich Martin Cairns Niels Rietdorf Peter England Rocco Roberto Cerchiara Italy Sabine Betz Stefan Mueck Tetiana Korzhynska Tom van den Vorst Netherlands Vittorio Magatti

Working party ACKNOWLEDGEMENT: Frank Cuypers Greg Taylor Authors of report Core working group Wider brainstorming group ASTIN Lisbon Colloquia 2016 Regular conference calls Slack to share research Individual research Report ACKNOWLEDGEMENT: Frank Cuypers Greg Taylor

Agenda Claim process and reserving Machine learning Synthetic data Average claim development Aggregate vs individual reserving approach Individual claim development Machine learning Synthetic data Data samples Adjustments and calibration Results Sample 1&2 Sample 3 Sample 4 Sample 5 Summary & further research

Claim process and reserving € Ultimate claim amount IBNR Case reserves Our goal: estimation of IBNR! Payment Claim event Partial payment Final payment Reporting date Correction of case reserves Claim closed

Average claim development Segments with „similar“ developments: Homogeneous groups Learning from past developments: underlying pattern is not changing

Aggregate vs individual reserving approach DY AY individual claims annual aggregate loss

Individual claim development

Machine learning Analysis can be done analyticaly, but it takes time … We used neural networks Model arhitecture Number of layers Number of neurons Activation functions Learning algorithm …

Synthetic data Generate individual claims with probability distributions of Severity: ultimate 𝑈~𝐿𝑁 𝜇,𝜎 Development patterns: age-to-ultimate 𝐹 𝑡 ~𝐿𝑁 𝜇 𝑡 , 𝜎 𝑡 Components Paid 𝑃 𝑡 =𝑈⋅ 𝐹 𝑃 𝑡 Outstanding 𝑂 𝑡 =𝑈⋅ 𝐹 𝑂 𝑡 Incurred 𝐼 𝑡 =𝑃 𝑡 +𝑂 𝑡 Patterns 𝐹 𝑃 𝑡 : 𝜇 𝑡 = 1− 𝑒 − 𝑡−𝜏 𝜆 𝛼 𝐹 𝑂 𝑡 : 𝜇 𝑡 =𝛼 𝑒 − 𝑡−𝜏 𝜆 2 Dependence Frank Copula 𝐹 𝑃 𝑡 ⋈ 𝐹 𝑂 𝑡 for each 𝑡

Data samples 4000 claims 6000 claims Sample 1 Sample 2 Sample 3

Adjustments and calibration paid claims paid and outstanding claims Input data cumulative numbers transformation of amounts into ratios Input form simple - one hidden layer with 2 neurons complex - more than 2 neurons per one or two hidden layers Architecture of neural network

Results Individual estimations Sum of squared errors of ultimates Total reserve estimations Compare results from: Chain-Ladder method, Different architectures of neural networks

Sample 1 Sample 2

Sample 3

Sample 4 High error of Chain- Ladder estimate! NN methods make better prediction Not black magic! Could be done analytically

Sample 5

Summary & further research Same cascading approach Real data Wider granularity Optimal architecture Different model Parametric curve Covariates Model free approach Different algorithm Random forest Combination of methods Working party Claim process and methodology Neural networks Illustrative data samples Usage of NNs Data adjustments Calibration of NN Comparison of Chain-Ladder and NNs Individual and total reserves Changing pattern becomes a problem NN seems to perform better

Thank you for your attention! Questions? Bor Harej, Zavarovalnica Triglav, d.d. Slovenia bor.harej@triglav.si Thank you for your attention!