Tia Brehm C.3 Part 1

Front 1

When implementing an Internal Risk Model, firms often underestimate what three things?

Back 1

• Resource Commitment - Staff, Systems, Software

• Timelines

• Organization impact

Front 2

When implementing an Internal Risk Model - Staff Considerations (6)

Back 2

• Reporting Lines should be clear

• Leader should have a reputation for Fairness

• Functions Represented: U/W, Planning, Finance,Actuarial, Risk

• Full Time Staff vs. Part Time Staff (also have day to day job)

• Permanent Staff vs. Temporary Staff (for implementation)

• think of IRM as a new compentency - need to staff

Front 3

Implementing IRM - Scope considerations? (4)

Back 3

• Underwriting Year

• Reserves

• Assets

• Low Detail on Company OR High Detail on pilot segment

Front 4

Parameter Estimation is difficult because: (4)

Back 4

• Low Data Quality

• Low Data Volume

• Unique Characteristics of Firm

• Differing Risk Attitudes

Front 5

Correlation Assessment in an IRM is difficult because: (4)

Back 5

• Lack of Data

• High Political Sensitivity

• spans Multiple Business Units

• Significant impact on Company Risk Profile and Capital

AllocationIRM team recommends correlation assumptionsOwned by CRO/CEO/CUO

Front 6

Why is Validation of an Internal Risk Model difficult?How can we Validate?

Back 6

• No current model to compare to

• Review a series of complementary variables over an extended period

Front 7

How should a Pilot Test be done for the implementation of an Internal Risk Model? (4)

Back 7

• Provide output in parallel to current decision metrics(allows user to get comfortable with new metrics)

• High Level of the Company OR Detail of a Pilot Segment

• Provide Education on New Metrics

• Each Quarter increase Weight that is given to new metrics

Front 8

Recommendations for Integration and Maintentance of an Internal Risk Model (4)

Back 8

• Integrate into the Corporate Calendar that already exists

• Major Updates - no more than twice a year

• Minor Updates - via scaling

• Input/Output - Ownership and Control must be very clear

Front 9

Formula for Coefficient of Variation (CV) of Losses

Back 9

CV^2 (S) = CV^2(N) + CV^2(X) / µN

Front 10

What is Superimposed Inflation

Back 10

Severity Trend less General Inflation

[Claim Severity Trend] =[General Inflation] + [Superimposed Inflation]

Front 11

For Projecting Annual Loss Trend, the author recommends an AR(1) processwith what parameters?

Back 11

rt+1 = m + α1 · (rt − m) + et+1

α1 = 80%

et+1 ∼ Normal(0, 2.5%)

Front 12

What is the preferred method to estimate parameters for Frequency andSeverity Distributions?

Back 12

Maximum Likelihood Estimator (MLE)

Among Unbiased estimators, it has the lowest Estimation Error (for large data sets)

Front 13

How do the authors recommend we model parameter estimates and theirdependencies

Back 13

Model the parameter estimates as Joint LogNormalwith correlations from the Information Matrix

Front 14

When Estimating Parameters how we can estimate correlations

Back 14

LL = Log Likelihood of the data set, Given a set ofparameters α

I = −∂ ^2 (LL) / ∂^2 α

Σ = I−1is the Covariance Matrix

Front 15

What is Model Risk

Back 15

Risk that the selected model is not the correct one

Front 16

Why do we prefer to use Joint LogNormal to model estimates of parameters

Back 16

• Removes Negative Values from possiblesimulated values

• Parameter Estimates have a heavy tail -LogNormal captures this

Front 17

A method to account for Model Risk

Back 17

When comparing different models use the HQIC tocompare them

• Hannan-Quinn Information Criterion (HQIC) is acompromise on the # of parameters penalty

• Multiple models can be chosen for a pool of possiblemodels

• For each simulation, draw one of these models, and thenparameters from that model

Front 18

When estimating parameters - we can calculate the Likelihood of the datagiven the selected parameters.

What does the slope of the Negative Log Likelihood tell us about ourestimate of the parameters?

Back 18

A steep slope tells us we are quite certain of our estimate ofthe parameters

A shallow slope tells us we are not certain of our estimate ofthe parameters

Front 19

Formula for Copula Density

Back 19

c(u, v) = ∂ ^C(u, v) / ∂u∂v

Front 20

Gumbel τ

Back 20

Gumbel τ = 1 −1/a

Front 21

HRT τ

Back 21

HRTτ =1/ ( 2a + 1)

Front 22

Frank τ

Back 22

FrankComplicated formula with an integral

Front 23

Normal τ

Back 23

Normalτ =2 · arcsin(a) / π