price optimisation for personal lines insurance 26 june 2013 richard brookes
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Price optimisation for personal lines insurance
26 June 2013
Richard Brookes
© Taylor Fry Pty Ltd 2
Price optimisation
Basic principle
• How do we calculate profit?
– Conventional solution is as a constant proportion of cost (profit margin), but
– By varying the profit margin for different customer segments we can take advantage of how they react to different price levels/changes
– This can improve the average profit margin by around 3% of cost whilst retaining the same business volume
Cost(risk, expenses etc)
Profit
X%
of
cost
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Optimisation set-up
• Maximise– Average profit margin
• By varying– Individual policy premiums
• Subject to– A global constraint of the number of policies in force, and– Individual profit margin constraints for each policy, say the interval [-
$50, $50] around a “technical” profit margin
• To do this we need a relationship between policy price and the number of risks in force
Price optimisation
© Taylor Fry Pty Ltd 4
Price optimisation
Demand model
• Logistic regression model of renewal rate
– Policy characteristics just before renewal notice is sent out• Tenure, socio-demographic
information• Behavioural indicators
– Premium related predictors• Premium increase since last
renewal• Premium in relation to
competitor premia
© Taylor Fry Pty Ltd 5
Individual demand curves
• Combine the objective function, constraints, demand model and an optimisation algorithm
Renewal curves for two policies
92%
93%
94%
95%
96%
97%
98%
99%
-30% -20% -10% 0% 10% 20% 30%
Price change from current price ($)
Ren
ewal
rat
e (%
)
Policy 1 Current price Policy 2
Competitor price
Competitor price
Competitor price
Price optimisation
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Portfolio results
Insurance profit vs Renewal rate
Current
0
5,000,000
10,000,000
15,000,000
20,000,000
25,000,000
87% 88% 89% 90% 91% 92%
Renewal rate
Insu
ran
ce p
rofi
t ($
)
$4M (30%)
1½%
Price optimisation
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Distribution of price adjustments
• Caution required - this can lead to a deterioration in the portfolio over time
Frequency of price adjustment
0%
10%
20%
30%
40%
50%
60%
70%
80%
-50 -40 -30 -20 -10 0 10 20 30 40 50
Price adjustment
Pro
po
rtio
n o
f p
oli
cies
Tend to be less elastic
These policies move to a competitor price
or a point of slope change in the
demand functionTend to be more elastic
Price optimisation
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Optimisation cycle
Demandmodelling
Projection and
optimisation
Datacollection
Ongoing data collection:
• Renewal rates and quote strike rates
• Price flexing
• Competitor rates
• Customer characteristics
Statistical models predicting how renewal and strike rates will change in response to price changes
Projections of portfolio volume given price changes
Optimal price changes to maximise profit at given portfolio volumes
Price optimisation
© Taylor Fry Pty Ltd 9
The leading edge
• The best basic optimisation uses– Price testing and/or competitor rate
deconstructions– Hold out segments to assess ongoing
effectiveness– Accurate, up to date demand and risk
cost models• Monitoring and recalibration of
these models is important• Demand models must address
slope and level
• Leading edge optimisation extends to:
– Real time optimisation of new business quotes
– Taking into account extra dimensions of behaviour (see diagram to the right)
Optimisation taking into account each
customer’s multiple product holdings
Optimisation taking into account of the multiple brands offered to each
customer
Optimising over the full expected lifetime of
each customer i.e. multi-year optimisation
Price optimisation
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