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Rate Competitiveness & Rate Stability with Rating TiersA Case Study for Personal Automobile Insurance

CAS Spring MeetingMay 2010

Outline

Introduction 3

Model Design Discussion 6

Personal Auto Case Study 12

Conclusion 31

Q&A 33

Appendix 34

Introduction

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GLMs have gained traction as powerful modeling tools to enhance the insurance rating plan and improve the accuracy of rating factors

IntroductionGeneralized Linear Models (GLMs) as a Standard Tool for Rating Plan Development

GLMs Enhanced Usage Challenges

Race in developing new and more complex insurance pricing models

¡ In the 1990s, Generalized Linear Models (GLM) were introduced to actuaries for developing personal automobile pricing

¡ Now, GLMs are used as a standard powerful modeling tool to enhance the insurance rating plan and improve the accuracy of rating factors

¡ Personal line industry has embraced more complex rating plans, such as adding new variables or including interaction terms

¡ Increases insurance companies’ competiveness in the market place

¡ Assists avoidance of adverse selection

However, GLMs caused challenges for the industry, especially on rate stability and regulatory compliance

¡ Frequent change of rating plans invites multiple rating products to be in production

¡ Price disruption on renewal business by new and more complicated products

¡ Resources and efforts needed to manage several different versions of a given rating plan is a significant challenge to insurance companies

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One approach for maintaining rate stability is to divide the entire rating plan into two parts; an underlying base class plan and a rating tier on top of the base class plan

IntroductionMaintaining a Consistent Base Plan using Tier Rating

• New or non-traditional rating variables (e.g., occupation, education, prior BI limit, etc.)

• Variables restricted by certain states, but not by others (e.g., credit score, not-at-fault accidents, etc.)

RatingTier

• Standard rating variables (e.g., territories, drivers, vehicles, coverage, discounts, etc.)

• Common across states

• Potential interactions (e.g., gender and age, driver age and mileage, etc.)

BaseClass Plan

One major advantage of separating the base class plan and the rating tier is the efficiency in managing the rating plan changes and price disruption for individual risks.

Model Design Discussion

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Two different modeling approaches can be employed for the rating tier creation: Frequency-Severity vs. Pure Premium

Model Design DiscussionFrequency-Severity Models vs. Pure Premium Models

1) Determine Modeled Frequency Estimate

• Frequency = Claim Count / Exposure

2) Determine Modeled Severity Estimate

• Severity = Loss ($’s) / Claim Count

3) Estimate Pure Premium by Combining

Estimates

• Pure Premium = Frequency * Severity

Frequency-Severity Approach

¡ Advantage associated with the frequency-severity modeling approach is the detailed insight available of the distinct loss cost drivers between frequency and severity

1) Determine Pure Premium Estimate Directly

• Pure Premium = Loss($’s) / Exposure

Pure Premium Approach

¡ The pure premium approach directly uses pure premium as the target variable for the estimate

The Frequency-Severity approach prescribes the product of two models, while the Pure Premium approach requires one model.

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The pure premium approach is our preferred methodology for the development of rating tiers because the frequency-severity approach has the following issues

Model Design DiscussionFrequency-Severity Models vs. Pure Premium Models

The above issues regarding the Frequency/Severity approach lead us to believe that the Pure Premium approach1 is a preferred approach for the rating tier development.

More Effort and Less Efficient• Need to double the number of models

Data Credibility• For example, liability coverage might lack data volume for its severity models

Model Disconnect• Do both models have the same variables?• Do both models treat a given variable in similar fashion?

• Does severity distribution vary among segments of the book?

Difficulty in Splitting Class Plan Factors Between Frequency and Severity Effects• How to split the resulting class plan factors between the frequency and severity contributions when evaluating rating factors?

Frequency-Severity Approach Issues

1 - For the pure premium approach, the Tweedier distribution, a compound distribution of Gamma and dispersed Poisson, is the standard distribution assumption. The Tweedie distribution is part of the GLM and the Exponential family distributions, and is currently available in many modeling software applications.

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The pure premium distribution is assumed to follow the Tweedie Distribution

Model Design DiscussionSetting up the Pure Premium Distribution

Pure Premium Distribution

¡ Claim count is Poisson distributed

¡ Size-of-Loss is Gamma distributed

¡ Since Pure Premium equals Frequency * Severity, the resulting distribution is a Gamma-Poisson distribution (i.e., the Tweedie Distribution)

¡ Therefore, the Tweedie Distribution harmonizes the compound effect of the Gamma Severity and Poisson Frequency distributions

¡ The Tweedie Distribution belongs to the Exponential Family of Distributions, where:

oVar(PP) = φµp

§φ is a scale parameter

§µ is the expected value of PP

§p є (1,2) Øp is a free parameter – must be supplied by the modelerØAs p à 1: Pure Premium approaches the Over-Dispersed Poisson ØAs p à 2: Pure Premium approaches the Gamma

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We select the “p value” parameter which corresponds to the maximum log-likelihood

Model Design DiscussionSelecting the “p value” for the Tweedier Model

¡ In determining the optimal result, we run a series of models with a changing “p value” (ceteris paribus) for determining the Tweedie distribution “p value” assumption

¡ The log-likelihood function exhibits a smooth inverse “U” shape

¡ The optimal “p value” selected corresponds to the model with the highest log-likelihood

Observations

Poisson GammaPP Model Approaches

Max Log-Likelihood at p=1.45

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It is to our knowledge that the policy level tiers are more popular in the industry

Model Design DiscussionVehicle Level Tiers vs. Policy Level Tiers

Vehicle Level Design Policy Level Design

Policy #: 00001

DriverAge

VehicleID

Vehicle Tier Assignment

Policy #: 00001

DriverAge

Vehicle ID

Policy Tier Assignment

Aggregate

75

38

19

AVG{75,38,19}

=44

1

0

2

2

¡ Able to use both vehicle level and police level variables

¡ In theory, vehicle level tiers are more accurate because it allows different tier rates for each vehicle on a policy, while policy level tiers assign the same tier rate for all vehicles on the policy

¡ While detailed vehicle level variables are available, some policy level variable do exhibit correlation across all vehicles on a policy (e.g., prior claims on other vehicles within policy)

¡ Efficiency gained by a policy level design typically outweighs the marginal compromise of accuracy from a vehicle level design

¡ Easily extended and integrated into other applications (e.g., Underwriting and Marketing purposes)

Personal Auto Case Study

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The data used in the study is a subset of actual industry data and contains the following specifications

Personal Auto Case StudyData Details

Component Detail

Line of Business Private Passenger Auto

Coverages (1) Personal Injury Protection (PIP)(2) Collision (COLL)

Policy Year 2005

Term Annual Policies

Single Car Policies 40,628

Multi Car Policies 48,353

Vehicles Level Records on All Policies 175,004

71% of vehicles purchase both coverages

29% of vehicles purchase PIP only

Source: Deloitte Research

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The rating variables used in the study

Personal Auto Case StudyData Details (continued)

Variable Target or Base/Tier Values

Territory Base {T1, T2, T3, T4, T5}

Type of Policy (TYPE) Base {M,S} S – Single Car, M – Multi Car

Driver Age Group Base {Youthful, Mature, Senior}

Vehicle Use Base {P, W}, P – Pleasure Use, W – Others

Vehicle Age Group Base {1, 2, 3, 4, 5}, the higher, the older

COLL Deductible Base {<=250, 500, >=1000}

Vehicle Symbol Group Base {1, 2, 3, 4, 5}

At Fault Accidents (AFA) Base {0, 1, 2+}

Credit Score Group Tier {0, 1, 2, 3, 4}, the higher, the better

Vehicle Level Not At Fault Accidents (NAFA) Tier {0, 1, 2+}

Policy Level Not At Fault Accidents (NAFA_POL) Tier {0, 1, 2+}


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The first step is to select a subset of variables (five for PIP, and eight for COLL) for the base class plan and estimate the associated class plan factors for each coverage using pure premium Tweedie approach)

Personal Auto Case Study Developing the Base Class Plan

Variable Value PIP Rating Factor(Tweedie P=1.45)

COLL Rating Factor(Tweedie P = 1.25)

Territory

T1 0.771 0.845T2 0.768 0.904T3 0.577 0.858T4 0.887 0.901T5 1.000 1.000

Driver AgeYoung 1.294 1.327Senior 1.020 1.067Mature 1.000 1.000

Vehicle Use P (Pleasure) 0.870 0.944W (Other) 1.000 1.000

Type M (Multi Car) 0.705 0.965S (Single Car) 1.000 1.000

AFA0 0.778 0.8681 0.709 0.9292 1.000 1.000

Vehicle AgeGroup

1 2.9902 3.0223 2.3944 1.8795 1.000

Symbol

1 0.7322 0.8243 0.9154 0.9805 1.000

Deductible250 1.354500 1.2531000 1.000

Observations

¡ We recognize the reversal in the at-fault accident (AFA) factors between 0 and 1 for PIP, as well as in the Vehicle Age factors between 0 and 1, however, these results are from the natural volatility of the data as well as model indications


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As an aside, the class plan factors in the previous slide are the optimized result by applying the GLM Tweedie assumption to the data


Log-LikelihoodsTweedier

p PIP COLL1.10 -781.3 -12728.21.15 -713.6 -12494.71.20 -660.4 -12338.81.25 -619.1 -12262.31.30 -588.1 -12269.21.35 -566.0 -12367.11.40 -552.1 -12567.11.45 -546.1 -12886.61.50 -548.0 -13351.11.55 -558.8 -13998.81.60 -579.9 -14888.81.65 -614.3 -16114.91.70 -667.3 -17835.01.75 -748.4 -20334.91.80 -877.6 -24187.61.85 -1101.4 -30732.11.90 -1559.6 -43987.4

¡ In determining the optimal result, we try a series of “p” values for the Tweedie distribution assumption

¡ For each coverage, 17 models were constructed by changing the “p” parameter from 1.10 to 1.90 in 0.05 increments

¡ The table shows the log likelihoods for the PIP and COLL models are “U-shaped” with an increasing “p” parameter

The optimal “p” value was identified to be 1.45 for the PIP model and 1.25 for the COLL model. PIP has a higher “p” value that COLL because it is more severity driven.

Observations


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After determining the class plan factors, we derive the base premium by achieving premium neutral between the actual premium and the new modeled premium


Base Premium

PIP COLL

$466.78 $211.31

Sum of Actual

Premium

Sum of Modeled Premium

¡ Need to determine a new base premium so that the sum of modeled premium equals the sum of actual premium


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The purpose of tier rating is to select a new subset of variables, most likely exclusive of those in the base class plan, to sit on top of the base class plan. We will use two variables, Not At Fault Accidents and Credit Score, for the rating tier design

Personal Auto Case Study Tier Rating Model Design

Not At Fault Accidents (NAFA)

Credit Score

Policy #: 00001

NAFA (Vehicle Level)

Vehicle

0

1

NAFA(Vehicle Level)

0

1

NAFA_POL(Policy Level)

1

1

¡ Credit score has proven to strongly correlate with auto losses

¡ Some states ban credit scores, therefore, using credit score as a tier factor allows rating flexibility between different states

¡ For NAFA_POL, the blue car will indicate one not at fault accident due to the NAFA experienced by the red car because NAFA_POL looks across all vehicles on a policy

¡ NAFA has proven to correlate with loss and there is a trend of using NAFA as a tier factor

Modeling Variables

The rating tier will be built at policy level, therefore NAFA_POL and Credit Score will be used.


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The model below indicates the specifications for a pure premium coverage specific model for PIP

Personal Auto Case Study Tier Rating Model Design Based on Pure Premium Approach

XEE pip ⋅+== β)factorpip_class_log())exposure_pip

pip_loss(log())PP(log(

¡ The model is coverage specific, and the equation above illustrates the PIP coverage model

¡ The target is the pure premium, which is the loss over the exposure for the given record and the given coverage

¡ The pip_class_factor reflects the combined effect of the class plan for PIP, i.e., territory, driver age, multi-car policy indicator, vehicle type, and at-fault accidents (AFA)

¡ X is the vector composed with the two tier elements: Credit Score and NAFA_POL Placeholder

¡ The theoretical distribution assumed is a Tweedier Distribution

¡ Used a Tweedier “P” value of 1.45

¡ Assume the class plan is multiplicative, therefore the “log” link function is used

¡ Use an offset of Log(pip_factor)

¡ Use weight of pip_exposure (in this case since the case study only uses annual term policies, all of the weights = 1)

Model #1

¡ PIP_Class_Factorsused as the “offset” term


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The model below indicates the specifications for a loss ratio coverage specific model for PIP

Personal Auto Case Study Tier Rating Model Design Based on Loss Ratio Approach

XEE pip ⋅=×= β))factorpip_class_

1repip_exposu

pip_loss(log())LR(log(

Multiplicative result of exposure and class factor is essentially the same as premium.

Therefore, the model essentially becomes a loss ratio model (i.e., loss over premium)

Model #2

¡ Coverage: PIP

¡ Target Variable: Loss ratio

¡ X (or Predictive Variables): Credit Score and NAFA

¡ Theoretical Distribution: Tweedier

¡ Tweedier P: 1.45

¡ Link Function: Log

¡ Weight: PIP Premium

¡ Offset: None

A pure premium model with offsetting base class plan factors is the same as a loss ratio model. With the loss ratio as the target variable, the above model no longer needs the offset mechanism


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The table below illustrates the parameter estimation difference between the pure premium and loss ratio coverage specific models

Personal Auto Case Study Tier Rating Model Result

Model 1: Pure Premium Model Model 2: Loss Ratio Model

Variable ValueParameter Estimate

Rating Factor Parameter Estimate

Rating Factor

PIP Results: P value = 1.45 P value = 1.45Credit Score 0 1.002 2.724 1.011 2.749

1 1.049 2.855 1.026 2.7892 0.395 1.484 0.396 1.4863 0.194 1.214 0.196 1.2174 0.000 1.000 0.000 1.000

NAFA_POL 0 -0.249 0.780 -0.308 0.7351 -0.834 0.434 -0.867 0.4202 0.000 1.000 0.000 1.000

COLL Results: P value = 1.25 P value = 1.30Credit Score 0 0.371 1.449 0.370 1.447

1 0.249 1.282 0.244 1.2762 0.161 1.174 0.153 1.1653 0.171 1.187 0.167 1.1824 0.000 1.000 0.000 1.000

NAFA_POL 0 -0.317 0.728 -0.319 0.7271 -0.255 0.775 -0.255 0.7752 0.000 1.000 0.000 1.000

Observations

¡ In general and as expected, the optimal p values for the tier models are the same as, or close to, the base class plan models

¡ The maximum likelihood estimates calculated by the two generalized linear models are not exactly the same, but remain very close

¡ Parameters for both credit score and not-at-fault accidents are significant, suggesting that they can further segment the risk beyond the underlying base class plan

The results given above demonstrate how we can remove the underlying class plan effect in establishing the rating tier factors via the use of premium for the loss ratio approach and the combined class plan factor for the pure premium approach.

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The model below indicates the specifications for a loss ratio all coverages combined model

Personal Auto Case Study Tier Rating Model Design

The all coverages combined option is not valid for the pure premium model design since we cannot add exposure or combine the class plan factors across different coverages.

Model #3

¡ Coverage: PIP and COLL

¡ Target Variable: Loss ratio

¡ X (or Predictive Variables): Credit Score and NAFA_POL

¡ Theoretical Distribution: Tweedier

¡ Tweedier P: 1.35

¡ Link Function: Log

¡ Weight: Total Premium

¡ Offset: None

XEE total ⋅== β))iumtotal_prem

total_loss(log())LR(log(


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The parameter estimates and optimal p value resulting from the all-coverages-combined model fall between the coverage specific model estimates

Personal Auto Case Study Tier Rating Model Result

Coverage Specific: PIP(Optimal P Value = 1.45)

All Coverages Combined(P Value = 1.35)

Coverage Specific: COLL(Optimal P Value = 1.30)

Variable Value Parameter Estimate Rating Factor Parameter

Estimate Rating Factor Parameter Estimate Rating Factor

Credit_Score 0 1.011 2.749 0.561 1.752 0.370 1.447

Credit_Score 1 1.026 2.789 0.492 1.636 0.244 1.276

Credit_Score 2 0.396 1.486 0.220 1.246 0.153 1.165

Credit_Score 3 0.196 1.217 0.175 1.191 0.167 1.182

Credit_Score 4 0.000 1.000 0.000 1.000 0.000 1.000

NAFA_POL 0 -0.308 0.735 -0.320 0.726 -0.319 0.727

NAFA_POL 1 -0.867 0.420 -0.405 0.667 -0.255 0.775

NAFA_POL 2 0.000 1.000 0.000 1.000 0.000 1.000

The combined coverages parameter estimates and the optimal p value fall between the by-coverage results. Since COLL has more premium than PIP, the combined

estimates are slightly closer to the COLL estimates than the PIP estimates.


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The selected model design for which we will build tier rating scores from is the loss ratio all-coverages-combined model (i.e., Model 3)

¡ Take the results from Model 3 and apply the tier rating factors to each of the risks. (Note: only the tier rating factors are applied, i.e., they are not combined with the base plan factors)

¡ After applying the tier rating factors, each risk will receive a “tier rating score”

¡ Next, we will group the risks into four rating tiers based on their tier rating score

Personal Auto Case Study Rating Tier Creation

Model #1

• Pure Premium Target

• Coverage Specific

Model #2

• Loss Ratio Target

• Coverage Specific

Model #3

• Loss Ratio Target

• All Coverages Combined

Model #3: All Coverages Combined

(P Value = 1.35)

Variable Value Parameter Estimate

Rating Factor

CreditScore 0 0.561 1.752





NAFAPOL 0 -0.320 0.726

NAFAPOL 1 -0.405 0.667

NAFAPOL 2 0.000 1.000

Policy Model Score

Tier Assignment

001 0.561 4

002 0.172 3

003 -0.185 1

004 0 2

005 -0.23 1

… … …

Tier Assignment

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The table below shows the final distribution of premium, loss, and loss ratio by rating tier and coverage, after grouping the risks into one of four rating tier based on their tier rating score


Policy Level

Rating Tier

PIPPremium

COLL Premium

PIP Loss

COLL Loss

PIP Loss Ratio

COLL Loss Ratio

PIP Tier

Factor

COLL Tier

Factor

1 7,196,865 11,700,975 1,566,394 5,197,147 21.8% 44.4% 0.355 0.678

2 15,464,220 25,384,564 4,725,373 13,132,471 30.6% 51.7% 0.498 0.789

3 6,549,586 10,508,607 3,870,624 6,076,159 59.1% 57.8% 0.964 0.882

4 7,680,868 10,614,534 4,709,582 6,957,082 61.3% 65.5% 1.000 1.000

Total 36,891,539 58,208,680 14,871,972 31,362,859 40.3% 53.9%

Observations

¡ The indicated tier relativity are located in the last two columns. For example, if we use Tier 4 as the base (poor experience) tier, we indicate a 32% (i.e., 1-0.678), 21%, and 12% discount to tier 1, 2, and 3 risks, respectively, for their COLL premium

¡ The number of tier groups and the distribution of the risks can vary from one company to another, and is dependent on each company’s business objectives. The “indicated” tier factors will depend on the selected tier group number, as well as the distribution of risks

¡ The “final selected” tier factors for premium adjustment is also dependent on each company’s objectives


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A premium neutral result can be achieved by rebasing the tier factors


Policy Level

Rating Tier

PIPPremium

COLL Premium

Initial PIP Tier Factor

Initial COLL Tier Factor

Final PIP Tier Factor

Final COLL Tier Factor

1 7,196,865 11,700,975 0.355 0.678 0.540 0.824

2 15,464,220 25,384,564 0.498 0.789 0.758 0.960

3 6,549,586 10,508,607 0.964 0.882 1.466 1.073

4 7,680,868 10,614,534 1.000 1.000 1.521 1.216

Total 36,891,539 58,208,680 0.657 0.822 1.000 1.000

By achieving the premium neutral, there will be no premium gain or loss due to the introduction of the rating tier.

¡ A tier 1 policy will receive a 46% (i.e., 1 - 0.54) and 17.6% (i.e., 1 - 0.824) premium deduction for PIP and COLL respectively

Observations


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The table below exhibits vehicle level tier factor estimates that would’ve resulted had we used a vehicle level dataset, and compares it to the policy level tier factor estimates


Policy Level Vehicle Level

Variable ValueParameter Estimate Rating Factor Variable Value

Parameter Estimate Rating Factor

Credit_Score 0 0.561 1.752 Credit_Score 0 0.566 1.762Credit_Score 1 0.492 1.636 Credit_Score 1 0.495 1.641Credit_Score 2 0.220 1.246 Credit_Score 2 0.225 1.252Credit_Score 3 0.175 1.191 Credit_Score 3 0.176 1.193Credit_Score 4 0.000 1.000 Credit_Score 4 0.000 1.000NAFA_POL 0 -0.320 0.726 NAFA 0 -0.220 0.803NAFA_POL 1 -0.405 0.667 NAFA 1 -0.033 0.967NAFA_POL 2 0.000 1.000 NAFA 2 0.000 1.000

¡ The indicated parameters for NAFA_POL are much stronger than the parameters for NAFA (vehicle level), suggesting a vehicle on a multi-car policy with accidents of “other” vehicles on the same policy are correlated with the vehicle’s future losses. This is why policy and family account level variables are being used in rating these days

¡ Another difference between policy level rating tiers and vehicle level rating tiers is that for the vehicle level tier rating, it is possible that different vehicles on a policy can be assigned to different tiers. Our study further indicates that for the 48,353 multi-cars policies, 6.9% of the policies will have different tier assignments among the vehicles within the given policy. Since the real word rating tiers typically contain more variables, the percentage should go up even more in practice

Observations


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Analyzing and controlling premium disruption is a very critical step in implementing any rating plan changes, with particular respect to regulation requirements

Personal Auto Case Study Premium Disruption


RatingTier

CreditScore NAFA

Premium Change

PIP COLL Total

1 4 1 -46% -18% -28%1 4 0 -46% -18% -28%1 3 1 -46% -18% -28%2 2 1 -24% -4% -12%2 3 0 -24% -4% -12%2 2 0 -24% -4% -12%

33

41

21

47%47%

7%7%

22%22%

3 0 1 47% 7% 22%

33

13

02

47%47%

7%7%

22%22%

4 2 2 52% 22% 34%4 0 0 52% 22% 34%4 1 2 52% 22% 34%4 0 2 52% 22% 34%

Total 0% 0% 0%

¡ Since the premium impact associated with the rating tier approach is completely isolated within the rating tier assignments and associated factors, the premium disruption can be quickly analyzed and understood

¡ Since the premium impact is isolated within the rating tier assignments and the associated tier factors, we can control and manage the disruption more efficiently by changing either the factors or establishing additional tier assignment rules

Observations

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The table below compares PIP’s original base class plan (i.e., excluding a rating tier) with PIP’s completely revised class plan with the inclusion of the rating tier factors

Personal Auto Case StudyPremium Disruption


Variable Value Base Class Plan, PIP Complete Class Plan, PIP

Base Premium $466.78 $263.08 Territory T1 0.7711 0.8008

T2 0.7675 0.7197T3 0.5765 0.5791T4 0.8873 0.8904T5 1.0000 1.0000

Driver Age Yng 1.2941 1.2971Senr 1.0203 1.4511Matr 1.0000 1.0000

Vehicle Use P 0.8701 0.9388W 1.0000 1.0000

Type M 0.7045 0.6884S 1.0000 1.0000

AFA 0 0.7776 0.86861 0.7094 0.83352 1.0000 1.0000

Credit Score 0 3.10121 3.32182 1.67063 1.29594 1.0000

NAFA_POL 0 0.75131 0.42692 1.0000

Observations

¡ The revised class plan for PIP includes NAFA_POL and credit score in the class plan

¡ The table indicates that all the base class plan factors have changed, and some of them have a fairly large change, such as AFA and senior driver factor

¡ Such significant change in class factors lead to increased difficulty in managing premium disruption

¡ The significant change in class factors require more effort for implementation on filing and system programming

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The rating tier design provides insurance companies an excellent approach in managing an insurance book with respect to rate distribution, rate disruption, and risk segmentation

Personal Auto Case StudyPractical Considerations


¡ It is fairly easy to manage the rate distribution for the book using the rating tier approach. For example, we can simply adjust the score cutoff to achieve different tier distributions.

¡ If the premium disruption is capped within a certain range due to business or regulatory reasons, we can simply change the final selected factors to be in compliance with the capped range

• For example, if a state restricts premium change to +/- 20%, we can change the final selected factors to 0.80 for Tier 1 and 1.20 for Tier 4 in Table 4 for the state.

• Another example is that we can add a business rule so that if the premium disruption exceeds a certain threshold for a risk, we can cap the change within the tier, such as Tier 2 to Tier 3, instead of to Tier 4

¡ Rating tiers allow a quick introduction of new variables if the variables have proven correlation with insurance loss

• Rating tiers approach will not affect the underlying base class plan factors, there is no need to file a new class plan. This will avoid multiple versions of class plans if certain factors, such as credit score, are allowed in some states, but not in others

Conclusion

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The preferred model design in this case study is at the policy level, using a loss ratio target, with the GLM Tweedier assumptions

Conclusion


¡ Rating tier is an excellent pricing design to help insurance companies achieve a balance in rate stability and rate complexity

¡ There are two approaches to develop rating tiers – pure premium modeling with an offset of base plan factor or loss ratio modeling. Both modeling will use GLM Tweedier assumption

¡ There are two different designs – policy level or vehicle level. It is more popular and more efficient to use policy level rating tier design

¡ The case study given in the paper is somewhat ideal and simplified. The real world applications will require considerable additional amount of work, especially on data preparation and data adjustments.

• For example, for loss ratio modeling, the premium re-rate could be much more complicated. For loss, we need to develop it to ultimate level and trend it to be consistent with on level premium period

§ We can develop an additional underwriting tier with the same methodology, by maintaining flexibility to implement the rating tier and the underwriting tier in different fashions

§ Add the rating tier into the existing rating plan using the underwriting tier for company placement

§ Combine the rating tier and the underwriting tier for underwriting purposes

Appendix

— 35 — Tier

Rat

ing

Cas

e S

tudy

v6.

ppt

Tier rating can be expanded to Underwriting applications, thereby increasing efficiency in predictive modeling efforts

AppendixExpanding the Application


Maintain the current class plan structure and class rating factors with no change

Generate the first level tier only using rating variables

Generate the second level tier using non-rating underwriting variables in tandem with the first tier

Predictive Modeling Efficiency

Implementation Options

Option 1 Option 2

§ Add the first level tier to the current class plan for rating§ Using the second level tier for

underwriting§ Company Placement§ Risk Selection

§ Use level one and level two tiers simultaneously for underwriting

new rate competitiveness & rate stability with rating tiers a case … · 2020. 10. 5. · race...

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