cas rpm seminar · 2021. 3. 13. · estimating loss costs – with segmentation & refinement...

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


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


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


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


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


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


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


Advanced Uses

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Co-optimization

Optimal Growth

Incorporating reinsurance costs

Other metrics being used/considered


A menu of possible investments

Confidence intervals

Confidence Intervals


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


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


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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A + B

A B

None

Product Lifecycle – Co-optimization


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


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


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


Standard Profit Calculation

Integration Losses Demand Premiums Expenses


Premium Losses Expenses

ProfitDemand

Expected Profit

Profit = + Premium – Attritional Losses – Expenses

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Enhanced Profit Calculation


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


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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cas rpm seminar · 2021. 3. 13. · estimating loss costs – with segmentation & refinement...

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