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Statistical Learning Algorithms Applied to Automobile Insurance Ratemaking

Statistical Learning Algorithms Applied to Automobile Insurance Ratemaking. CAS Seminar on Ratemaking San Antonio, TX, March 27th, 2003 Charles Dugas, M.Sc.A., A.S.A. Apstat Technologies Inc. and University of Montr éal. Outline. Assume n criteria (30-50)

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Statistical Learning Algorithms Applied to Automobile Insurance Ratemaking

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  1. Statistical Learning Algorithms Applied to Automobile Insurance Ratemaking CAS Seminar on Ratemaking San Antonio, TX, March 27th, 2003 Charles Dugas, M.Sc.A., A.S.A. Apstat Technologies Inc. and University of Montréal

  2. Outline

  3. Assume n criteria (30-50) nh hidden units or neurons (10-20) Step 0: Initialize weights to pseudo random values Step 1: Forward propagation Step 1.1: Compute nh linear combinations Training an ANN

  4. Training an ANN (cont’d) • Step 1.2: Apply nonlinear transfer function to each of the linear combinations • Step 1.3: Compute linear combination of hidden units

  5. Outline

  6. Training an ANN (cont’d) • Step 2: Compute approximation error • Step 3: Backpropagate error and update weights

  7. Training an ANN (cont’d) • Epoch: Repeat Steps 1,2 and 3 for each record in the database (100K - 1M). • Whole training: multiple epochs (10,100,1000).

  8. Nonlinear Transfer Function • Finite range output : [-1,1] or [0,1] • “Integrate and fire” neural computation • Continuous function allows computation of derivatives • Detect directions of interest • Otherwise similar to Linear Regression

  9. Pros and Cons • Performance • successful in multiple industries : banking, pharma, navigation, terrorism (e.g. HNC/FICO) • Computationally demanding • no analytical solution • need to use optimization algorithms • multiple passes (epochs) through entire dataset • exponential function is slow • Black boxes…

  10. The Black Box Argument Can not associate a specific meaning to each of the parameters • Explain differences between premiums • gain&loss analysis • small program on laptop or PDA • amount for variables • amount for most important correlations • residual amount for high-level correlations • Control over possible outcomes • neural networks lead to infinite number of premiums • commonly stated figure of 2:1 worst to best premium • Explanation • actuarial end, not a business end • gain knowledge • Legislation…

  11. Challenge of Model Selection

  12. Methodology for Model Selection

  13. Credibility and Model Selection

  14. Numerical ResultsMean-Squared Error

  15. Numerical ResultsRisk Sharing Pool

  16. Conclusions • Neural Nets need to be adapted for large claims • Black box argument s/b put in perspective • Model Selection is the counterpart to Credibility • MSE Numerical results not as convining as RSP results • ANNs should be adopted over the next few years

  17. About Apstat • Research contract • 4 Founders: Advisor with 3 PhD students • Former employers : AT&T, Bell Labs, DoD, FICO, Hydro-Québec, Lucent, MIT, Microsoft, NEC, Nortel, Swiss Re, W.M. Mercer • insurance analytics (fraud detection, ratemaking, risk sharing pools, customer lifetime value) • www.apstat.com • dugas@apstat.com

  18. Insurance Analytics:CRM CRM: Customer Relationship Management • market for profit, not numbers • include CLV (customer lifetime value) • need to merge efforts from marketing & actuarial • relationship marketing • traditional product-driven mass & and target marketing: • move on to customer-centric relationship marketing to maximize each customer’s value • cross-selling (could ING direct databases be used to target market insurance ?) • customer retention, behavior prediction, channel optimization, personalization

  19. Insurance Analytics: Core Actuarial Underwriting, Ratemaking • highly regulated • strategic concerns Reinsurance • mainly market-driven, results from negotiations • marginal role for analytics • what is the probability of another WTC next year ?

  20. Insurance Analytics: Fraud “Detection is Prevention” • 10% of claims in P&C insurance industry • analytics for fast track • increase adjusters’ containment of build-up • analytics for adjusters’ referrals to SIUs • increase investigator’s hit rate • analytics for fraud rings • deterrence measures (e.g. visit top 10% therapists)

  21. Insurance Analytics: Fraud

  22. Insurance Analytics: Risk Sharing Pools • purely analytical • legislation is looser • marketing not involved • business case is quick and easy • point of entry for new technologies in the industry. • can’t be used for strategic purposes, theoretically…

  23. Québec 10% of volume B.I. not included (SAAQ) facility within RSP exp. ratio: 25% fixed 100% ceeded Ontario 5% of units (car years) B.I. included facility apart from RSP exp. ratio: 30% max. 85% ceeded RSP: Technicalities

  24. RSP:Methodology and Hypotheses

  25. RSP: Analysis of Numerical Results • system recommends ceeding the full 10% of volume • true if LR > 60% • prior knowledge of LR (adjusted severity, frequency ca.17%) • simulated underwriting (15%, 30%:1M$ PF) • 100M$ volume • LR = 65%

  26. Conclusions • RSP & PRR as testbeds for new technologies • potential source of important profits • NNs can reliably identify GLM weaknesses • ad hoc reductions are RSP-costly • pressure on analytics (direct, kanetix) • analytics should merge • hard markets: use fraud patterns to pullout • soft markets: market with CLV

  27. Outline • Introduction to Neural Networks • Pros and Cons • The Black Box Argument • Model Selection and Credibility • Performance on Ratemaking • Other applications • Conclusions

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