CAS RPM SEMINARPrice Sophistication: from cost modelling to optimization…and beyond
by Yves ColombMarch 2015
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Ratemaking vs. Pricing
Actuarial Ratemaking
Pricing
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Actuarial Statement of Principles on Ratemaking:A rate is reasonable and not excessive, inadequate, or unfairly discriminatory if it is an actuarially sound estimate of the expected value of all future costsassociated with an individual risk transfer
Taking into account all factors, such as costs, regulatory constraints, business constraints (e.g. competitive constraints) and strategic constraints when setting actual price charged
Today is about pricing analytics
Traditionally, actuaries provide the actuarial indication which was an input into the pricing decision
Introduction: objectives, context & definitions
Objectives Price sophistication is a natural evolution Why this phenomenon will continue Prompt action
In the context of an insurance book
Price is defined as the sum of several components Loss estimate Expenses and other costs Profit margin
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A history of pricing approaches
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Agenda
Estimating costs
Estimating customer behavior
An integrated framework
Over and beyond …
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Estimating costs
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Estimating Loss Costs
The simplest of models is based on E(X)
Why not use it? Since we are at book level….
Because: Price is a signal… …leading to policyholder behavior… …because E(X) has no consideration for individual risk of loss
Need to modulate the signal sent to policyholders
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Estimating Loss Costs – with segmentation
Requirements Risk level information (observations, predictors) Model form?
More accurate modelling At granular level Not dramatically so at book level
The GLMs take over
Refinements Numerous possibilities accuracy and predictiveness
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Estimating Loss Costs – with segmentation & refinement
New predictors Clustering techniques Spatial smoothing to create territory definitions or vehicle symbols Interaction detection, saddles UBI score for auto, devices for property
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Interactions
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Spatial smoothing
Unsmoothed Smoothed
2%
4%
6%
8%
10%
12%
14%
16%
18%
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48
Data analysed Unseen data Frequency: data analysed Frequency: unseen data
x 4
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Analogous vehicle groupings techniques
Spatial Smoothing Factor
0.7
0.8
0.9
1
1.1
1.2
1.3
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200%
5%
10%
15%
20%
% Exposure Relativity Relativity + 2 SE Relativity - 2 SE
x 1.4
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Usage Based Insurance
0
200
400
600
800
1000
1200
1400
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Score
Device Rank
Device Score Distribution
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Estimating Loss Costs – with segmentation & refinement
What can this be used for? Indications (“CostPlus”) Subsidies Loss ratios, profit
A thought experiment: what if charged = indicated? Anti-selection remains Volume and performance are typically inferior
How is segmentation an improvement? Some consideration of individual risk of loss (expected value basis) Acknowledges price signal… Mitigates anti-selection through price signal
BUT some behaviors are left uncaptured (mix of business turn)© 2015 Towers Watson. All rights reserved. Proprietary and Confidential. For Towers Watson and Towers Watson client use only.
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Estimating customer behavior
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Estimating Customer Purchasing Behavior (‘Demand’)
More complex than estimating loss Multiple products/risks Closely linked to distribution e.g. intermediaries Multiple dimensions: quote conversion, acquisition, renewal, up-sell, cross-
sell
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Up-Sell / Cross-Sell
Customer Retention
Lead Acquisition
Lead Generation
Prospect Identification
Lead Generation Conversion Retention Propensity
Estimating Customer Purchasing Behavior (‘Demand’)
Binary choices not well processed by humans
Framing bias A deadly outbreak breaks in a town of 600 people. All 600 people in the
town are expected to die if you do nothing. Two different programs are designed to fight to the disease:– With Program 1: 200 people in the town will be saved– With Program 2: There is a 1/3rd probability that 600 people will be saved, and a
2/3rds probability that no people will be saved. In the study, 72 percent of the subjects picked Program 1. Now consider this other set of choices
– With Program 3: 400 people in the town will die– With Program 4: There is a 1/3rd probability that nobody will die, and a 2/3rds
probability that 600 people will die. In the study, 78 percent of the subjects picked Program 4 These are the same scenarii – just worded differently…
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Estimating Demand
Requirements Risk level information (observations, predictors) Model form?
The GLMs take over (again?) A natural choice GLMs are predictive and flexible R&D continues
Refinements Accuracy and predictiveness
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Estimating Demand
What can this be used for? Identify profiles and target/segment customer base Identify profiles and determine UW action
A prospective view
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Plot Loss RatioCase Study
Loss RatioHighLow
Profitable Unprofitable
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Plot DemandCase Study
Loss Ratio
Dem
and
HighLow
Low
Hig
h
Frequent Customers
Infrequent Customers
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Loss Ratio and Demand SimultaneouslyCase Study
Loss Ratio
Dem
and
HighLow
Low
Hig
h
Best Customer
Good Customer
Adverse Selection
Less desirable
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Loss Ratio and Demand Across Company
Best Customer
Good Customer Less desirable
Adverse Selection
71%
63%
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Predictive Modeling Marketing Application
Identifying Best AgentsSimultaneously plot loss ratio and demand across each agent separately
Case Study
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Agent 19 — Low Loss Ratio and High Demand
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Agent 19 — Low Loss Ratio and High Demand
Best Customer Adverse Selection
Good Customer
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Less desirable
Agent 2 — Low Loss Ratio and Low Demand
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Agent 2 — Low Loss Ratio and Low Demand
Adverse Selection
Best Customer
Good Customer
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Less desirable
Agent 13 — High Loss Ratio and High Demand
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Agent 13 — High Loss Ratio and High Demand
Adverse Selection
Best Customer
Good Customer
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Less desirable
Estimating Demand
How is demand modelling an improvement? Directly measures behavior Better acknowledges “power of price” (if price predictors are selected) Captures mix of business turn
BUT removed from original intent – “how to decide if the price is right” Presence of price information / predictors Not directly ‘pricing’
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An integrated framework
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How it works
Take a premium proposal Current Indicated Proposed
Take a set of risks In-force Quotes
Score loss and demand models Calculate expected future cash-flow and volume [Optional - Extrapolate over multiple years
Calculate expected Policy Lifetime Value (LV) Calculate expected Policy Life Expectancy (PLE)]
Analyze results Iterate?
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Calculation of a policy lifetime value
Revenue
$ LV
Premium
$$
$
Investmentincome
Expectedclaims cost
Acquisition cost
Profit
Futureprofits
Costs and Expenses
Modelling over time
Fixed expenses
TaxesCost ofcapital
Policy lifetimevalue
Commissions%
%%
Renewalprobability
*
=
Future Expected Profits
ILLUSTRATIVE
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Additional ingredients for estimating LV
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Integrated framework
Expected Profit
Renewal
Current Premiums
Expected Profit (T=1)
Renewal (T=1)
T=1 Premiums
T=1
Expected Profit (T=2)
Renewal (T=2)
T=2 Premiums
T=2
2-year Cumulative
Renewal
2-year Cumulative
Expected Profit
Distribution change
Ageing
Mask
Pricing Strategy
LV
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Integration
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Pricing Strategy
Profit
Volume
Price Integration quantifies chosen metrics for current
and proposed pricing strategies
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(multi-year) IntegratedFramework
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Volume
Profit
Segment A
Volume
Profit
Segment B
Volume
Profit
Overall
Modulating the book through manual premium setting
Volume
Profit
Segment A
Volume
Profit
Segment B
Volume
Profit
Overall
Trade-off
Improvement
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Automated approach
Pricing Strategy
Profit
Volume
Price Integration quantifies chosen metrics for current
and proposed pricing strategies
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(multi-year) IntegratedFramework
Search Algo
Price Optimization identifies pricing strategies with optimal outcomes
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More on this automated approach
Sound fundamentals are essential
A double-edged sword
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Integrated Framework
What can this be used for? Business planning and prospective testing Inform selections for PL Inform discretionary deviations in CL – inform UW
How is this integrated framework an improvement? Anticipates mix of business turn more accurately Acknowledges “power of price” even better and helps mitigate
naïve/penalizing decisions We are back in the “how to decide if the price is right” framework
BUT we rest on simplifying assumptions
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Over and beyond
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Advanced Uses
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Co-optimization
Optimal Growth
Incorporating reinsurance costs
Other metrics being used/considered
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A menu of possible investments
Confidence intervals
Confidence Intervals
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Confidence intervals
How far are we from current position?
Does risk increase? Quantify risk mitigation (reinsurance, securitization, etc.)
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Volume
Profit
Volume
Profit
A Menu of possible investments
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A menu of options
Assume Cost at $60 and Profit is “mobile” between $30 and $40
Standard = discount or not?
More than 2 ways to “invest” the $10
Give $10 discount today
Invest $10 for targeted marketing
Invest $10 for superior client service
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Satisfaction
Retention
Up/Cross Sell
Which (mix) is the highest return?
Co-optimization
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Co-optimization
What is it? Metric = F(price1, price2, etc.)
Several products
Up-sells
Several price structures for the same product (when permitted)
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Product Lifecycle – Standard Optimization
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A
None
A
None
Retention
Model
Conversion
Model
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A + B
A B
None
Product Lifecycle – Co-optimization
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A + B
A B
None
A + B
A B
None
(& vice versa with B)
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Other Thoughts
Multinomial models– or combination of binomial models for disjointed events
Four profiles now instead of two before Each has its own demand model Still one “black hole” profile but now 3 “live profiles” Makes for more complex expected profit calculation Even more if multi-year
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In Force
Renew
New Bus
Cancel
Renew Cancel
T=0
T=1
T=2
NA BA+B
NA BA+B
NA BA+B
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Optimal Growth
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Optimal Growth (Luyang Fu, Variance vol 6 issue 1)
High-level summary NB produces higher loss and expense ratios & lower retention than
renewals BUT high profits are required to add more NB
– Generate additional capital needed to support exposure growth How can we balance this?
Similar approach: Growth limit curve (CR declines with growth) Growth impact curve (CR increases with growth)
Optimal growth rate = maximizes the expected enterprise value over time Useful for strategic planning process Select a point on the frontier graph
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Incorporating Reinsurance Costs
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Standard Profit Calculation
Integration Losses Demand Premiums Expenses
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Premium Losses Expenses
ProfitDemand
Expected Profit
Profit = + Premium – Attritional Losses – Expenses
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Enhanced Profit Calculation
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Premium Losses Expenses
Gross ProfitDemand
Expected Profit
Reinsurance Profit
Net Profit
Ceded Losses RI cost
Reinsurance Program New Components:
Ceded Losses Reinsurance Cost
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Enhanced Profit Calculation
Low
Medium
High
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Other Metrics
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Advanced Uses: Multiple constraints & Alternative Metrics
Standard goal is to seek maximum profit given a set retention rate:
Other constraints can be added A wealth of alternative metrics: overall dislocation/impact,
competitive ratio, long-term profit, win rate, cross-subsidy, mix of business change speed
Helps to achieve a more refined selection
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Customer Satisfaction
Appealing but challenging Difficult to measure and hard to observe Costly Not clear how price influences customer satisfaction
other dimensions to customer service
2014 J.D. Power Reports: “Customers Switch Auto Insurers Because of Poor Service; However, Savings with New Carrier Often Isn't Enough to Fully Satisfy”
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