Insurance Premium Increase
Optimization:
Case Study
Agenda
• Introduction
• Business Rules
• CART analysis to identify customer groups • Elasticity modelling for each group
• Setting optimal levels of capping • Model Validation
Introduction
• Business Background
– Property Insurance (Auto and Home) – Australia’s 2nd 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.
Introduction
• Retention Rate drops whether premiums go up or down.
Difference between New and Old Premiums
0 5000 10000 15000 20000 25000 -300 -270 -240 -210 -180 -150 -120 -90 -60 -30 0 30 60 90 120 150 180 210 240 270 300 $ Price Change Number 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Retention Rate
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.
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?
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.
Business Rules
All Customers Claim? Yes No Capping No Business Rules YesRisk Profile Change? No Capping
No
Short-term policy?
No Capping Yes
No
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)
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 • …
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.
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
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.
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.
CART Analysis
NCD Step Back?
Group 1 Endorsement?
Group 2 Risk added mid term?
(Renewal term different from last term)
Group 3 Premium Payment Frequency Group 14 NCD < 40%? Group 15 Multi-Product Holdings? Group 4 NCD Level < 40%? Monthly Group 5 Annual Number of previous renewals > 4? Group 6 State Vehicle Age < 8? Group 11 Other Driver age < 49? Group 12 Group 13 CTP Discount? NSW, QLD Group 7 Number of Previous Renewals < 1?
Group 8 Driver age < 42?
Group 10 Group 9
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 multi-product holdings customers).
CART Analysis
• The convexity or elasticity curves assumption was
confirmed post-modelling. • Charts of observed
elasticity by terminal node analysed.
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
Elasticity Modelling
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.
Setting Optimal Capping Levels
• Even with extremely high cost of new business acquisition, the optimal result is achieved with ‘no capping’.
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.
<==== ====> <= 3 months =>
CART Model Training
Validation Period CART Model Testing
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.
