1 Insurance Premium Increase Optimization: Case Study Charles Pollack B.Ec F.I.A.A.
2 Agenda Introduction Business Rules CART analysis to identify customer groups Elasticity modelling for each group Setting optimal levels of capping Model Validation Conclusion
3 Introduction Business Background Property Insurance (Auto and Home) Australia s 2 nd biggest Insurer Result of merger between 2 companies 2 million customers for auto/home Project to bring pricing structures in to line Some premiums increase, others decrease Want to minimise cost of transition to new pricing structures.
4 Introduction Retention Rate drops whether premiums go up or down. Difference between New and Old Premiums % 90% % 70% Number % 50% 40% Retention Rate 30% % 10% $ Price Change 0% Number Offered Retention Rate
5 Introduction Usual response is to limit premium increases to maximise customer renewal rates. Known as Capping increases Legacy systems traditionally constrain business in application of the capping limit. Eg One % based limit for all customers.
6 Introduction Opportunity to break free of old legacy constraints and start afresh with a blank sheet of paper Combination of $ and % capping limits Limits able to be varied by customer groups. But how do we define those customer groups?
7 Business Rules The business managers wanted 3 groups of customers uncapped, irrespective of their elasticity or other characteristics. Customers making claims Customers changing their risk profile Customers on risk for less than 1 full year. Customers not in the groups above are candidates for capping.
8 Business Rules All Customers No Capping Yes Claim? No Capping Yes No Risk Profile Change? No Business Rules No Capping Yes Short-term policy? No Customers to limit price increases.
9 CART Analysis Use CART to identify different groups of customers. 12 months of renewal offers Take out records falling in to the 3 business rule groups. Split 2:1 (Train:Test) Model Renewed Yes/No.
10 CART Analysis Model variables include: Age of insured Other product holdings Length of time with organisation Distribution channel Geographic Location Age of vehicle/house Method of Payment (Monthly/Annual) Level of No Claims Bonus Value of vehicle/house Level of Deductible
11 CART Analysis Price NOT a model variable. When included in models, this variable is a very strong predictor of retention. A number of key customer attributes are also factors in the premium calculation. These variables come out as strong surrogates when price is a splitter. Exact splitting points using Premium are difficult to use when applying the model in practice due to premium inflation and competitor movements.
12 CART Analysis Assume: price change in the data used is randomly spread across all customer profiles. elasticity curves for each customer group are convex. Assumptions imply that nodes created by CART have Different intercept for the same elasticity curve shape Different shape of curve for a given intercept Or, A combination of the above.
13 CART Analysis Validating the random-price-change assumption. Use CART to build several models using same data. Very Large increase (Yes/No) Very Large decrease (Yes/No) Price Change within $5 (Yes/No) Seek a no split tree as the optimal tree on the test file to confirm assumption is valid.
14 CART Analysis Build main model tree(s) using training data. Standard settings except minchild increase to avoid excessively large trees. Compare impact of splitting methods (gini, sym gini, twoing) Select optimal tree using test data. Further prune tree if it is too big for business managers to cope with.
15 CART Analysis
16 CART Analysis NCD Step Back? Group 1 Endorsement? Business Rules Group 2 Multi-Product Holdings? Group 3 Group 4 NCD Level < 40%? Group 5 Risk added mid term? (Renewal term different from last term) Group 6 Annual Number of previous renewals > 4? NSW, QLD Premium Payment Frequency State Monthly Group 14 Other NCD < 40%? Group 15 CTP Discount? Vehicle Age < 8? Group 7 Number of Previous Renewals < 1? Group 11 Driver age < 49? Group 12 Group 13 Group 8 Driver age < 42? Group 9 Group 10
17 CART Analysis Variable importance differed somewhat from business expectations Notable absence of age of insured high in tree. Length of time with company of lower order importance than business normally assumes. Some variables were important, however in a different way to expected behaviour (eg multiproduct holdings customers).
18 CART Analysis The convexity or elasticity curves assumption was confirmed post-modelling. Charts of observed elasticity by terminal node analysed.
19 Elasticity Modelling Logistic Regression Price change by Customer Group Use 100% of data that was previously split 2:1 for CART modelling. Separate models for $ and % price change Fit polynomial curves Review curves for reasonableness
20 Elasticity Modelling Example of curves fit to observed retention.
21 Setting Optimal Capping Levels Charging less than book premium on renewal (capping) is like a discount. The cost of capping Balance this cost with the cost of replacing the lost customer with a new one on full rates. Optimise (minimise) the following equation: Predicted retention x (cost of capping + admin cost of renewing) + (1 predicted retention) x admin cost of acquiring a new customer Simulation Exercise Recalculate new and old premiums for each customer in existing portfolio. Difference is raw price change on renewal. Resolve above equation for each level of capping, by customer group. Select optimal capping level for each customer group.
22 Setting Optimal Capping Levels Even with extremely high cost of new business acquisition, the optimal result is achieved with no capping.
23 Model Validation Used a 3 month period after the initial 12 month data period in the earlier modelling. Predict retention, on observed price changes, and compare to actual retention. Very close match. <==== 12 months of renewal offers ====> <= 3 months => CART Model Training Validation Period CART Model Testing
24 Conclusion CART is very useful for determining customer groups with no-preconceptions. Tree easily explained to management and can be grafted on to business rules Business myths can be confirmed or denied Can also be used to review important modelling assumptions (such as randomness) When combined with Logistic Regression, forms a powerful elasticity modelling tool. Validation of model performance on an independent data set is always sensible to ensure veracity of the model.
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