Price optimisation for personal lines insurance

26 June 2013

Richard Brookes

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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

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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

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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

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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