STAM Formula Sheet

(1)

Exam STAM

Adapt to Your Exam

SEVERITY, FREQUENCY &

AGGREGATE MOD

AGGREGATE MODELSELS

Basic Basic

CDFs, Survival Functions, and Hazard Functions CDFs, Survival Functions, and Hazard Functions

(()) = = PrPr((   ≤ ≤ )) = = * * (())

_//

--

dd

(()) = = PrPr((  >

 > )) = = * * (())

_--

//

dd

ℎℎ(()) = =  (())

_{(())}

(()) = = * * ℎℎ(())

_//

--

d d = = −−lnln(()) ; ; (()) = = 

((--))

Moments Moments

EE[[((  )])] = = * * (())⋅ ⋅ (())

_//

//

dd

= * ′

= * ′(())⋅ ⋅ (())

_

//

dd



DD

raw moment: raw moment:



HH

= = EE[[  



]] ; ; 

HH

= = 



DD

central moment: central moment:





= = EE[([(  −

 −))



]]

VarVar[[  ]] = = 

MM

= = 

_MM

VarVar[[((  )])] = = EE[[((  ))

MM

]] − E − E[[((  )])]

MM

Covariance:

CovCov(( , ,)) = = EE[[  ]] − −EE[[  ]]EE[[]]

Coefficient of variation:  =

Coefficient of variation:  =  

Skewness =

Skewness =  

_

__

_{__}

_{; Kurtosis =}

_{; Kurtosis =  }

_



_

Moment and Probability Generating Functions Moment and Probability Generating Functions





(()) = = EE[[



]]



(())

((00)) = = EE[[  



]]

where where



(())

is the is the



DD

derivative derivative





(()) = = EE[[



]]



(())

((11)) = = EE[[  ((  − 1

 − 1))⋯⋯((  − 

 −  ++11)])]

where



(())

is the is the



DD

derivative derivative Conditional Distributions Conditional Distributions

PrPr((  ∣  ∣ )) = = Pr Pr((  ∩ 

_{PrPr(()) == Pr Pr(( ∣  ∣ ))PrPr((  ))}

 ∩ ))

_{PrPr(())}

 

∣

(()) = = 

_{PrPr((  <  <   < < )),where  <  < }



(())

,where  <  < 

Law of Total Probability Law of Total Probability

PrPr((  =

 = )) = = EE



[[PrPr((  =

 =   ∣ ∣ )])]

Law of Total Expectation Law of Total Expectation

EE



[[  ]] = = EE



EE



[[  ∣  ∣ ]]

Law of Total Variance Law of Total Variance

VarVar



[[  ]] = = EE



VarVar



[[   ∣ ∣ ]]+Var

+Var



EE



[[  ∣  ∣ ]]

Independence Independence For independent

For independent

 

andand



,, •

•

PrPr((   = = ,, =  = )) = = PrPr((   = = ))⋅ Pr⋅ Pr((  = = ))

•

EE[[((  )) ⋅ ℎ ⋅ ℎ(()])] = = EE[[((  )])] ⋅ E ⋅ E[[ℎℎ(()])]

Parametric Distributions

Parametric Distributions Special Distribution Shortcuts Special Distribution Shortcuts

 

 − 

−  ∣  ∣  > > 

Pareto

Pareto((,,)) Pareto

Pareto((,

, ++))

Exponential

Exponential(()) Exponential

_Uniform

_{Uniform((,,)) Uniform}

_{Uniform((0, − }

Exponential(())

_{0, − ))}

Zero-Truncated Distributions Zero-Truncated Distributions



áá

= = 111 −1 −

_

 



,,fofor  = 1

r  = 1,,2,⋯2,⋯

EE[([(

áá

))



]] = = 111 −1 −

_

E E[[



]]

Zero-Modified Distributions Zero-Modified Distributions



ää

= = 1 − 1 −

_{11− − }

ää

_

 



,,fofor  = 1

r  = 1,2,,2,⋯⋯

EE[([(

ää

))



]] = = 1 − 1 −

_{11− − }

ää

_

E E[[



]]

(,,0)

Class Property Class Property









= =  + +  ,,fofor  = 1

r  = 1,2,,2,⋯⋯

Mixtures and Splices Mixtures and Splices Bernoulli Shortcut Bernoulli Shortcut If

If

  == ã ã, , PrProbobababililitity y = = 

, , ProProbababibilility ty = = 1 1 −−

, then:, then:

VarVar[[  ]] = = ( ( − −))

MM

((1 −1 −))

Poisson-Gamma Mixture Poisson-Gamma Mixture If

If

  ∣  ∣  ∼ P∼ Poisson

oisson(())

where where

 ∼ Gamma

 ∼ Gamma((,,))

,, then

then

 ∼

 ∼ Neg.

Neg.Binomial

Binomial(( = , = 

 = , = ))

.. Frailty Models

Frailty Models

ℎℎ((  ∣ ∣ )) =  ⋅ 

=  ⋅ (())

(()) = = 

ôô

[[−−(()])],,whe

where re (()) = = * * (())

_//

--

dd

Insurance Applications Insurance Applications



öö

: payment per loss: payment per loss Policy Limits, Policy Limits,





öö

=  ∧  =

=  ∧  = ù ù , ,   < < 

_{, ,   ≥ ≥ }

EE[([(

öö

))



]] = = EE[([(  ∧ 

 ∧ ))



]]

= = * * 

üü



 (())



d d ++



⋅  ⋅ (())

= * 

üü



(())



dd

Increas

Increased Limit Fac

ed Limit Factor:

tor:  =

 = E E[[  ∧ 

_{EE[[  ∧ }

 ∧ ]]

_{ ∧ ]]}

•



: original limit: original limit •

•



: increased limit: increased limit Deductibles, Deductibles,



Ordinary deductible: Ordinary deductible:



öö

= = ( (  −

 −))

_••

= = ã ã 0 0, ,   < < 

_{ −}

_{ −, ,   ≥ ≥ }

EE[[

öö

]] = = EE[([(  − 

 − ))

_••

]] = = EE[[  ]] − E − E[[  ∧ 

 ∧ ]]

EE[([(

öö

))



]] = = EE[([(  −  −))

_••

]]

= = ** (( − −))

_¶¶

//



 (())

dd

= = * * (( − −))

_¶¶

//



(())

dd

Loss eliminiation ratio:  =

Loss eliminiation ratio:  = E E[[  ∧ 

 ∧ ]]

_{EE[[  ]]}

Franchise deductible: Franchise deductible:



öö

= = ã ã00, ,   < < 

_{, ,  ≥}

_{ ≥ }

EE[[

öö

]] = = EE[([(  − 

 − ))

_••

]] + + ⋅  ⋅ (())

Payment per Payment Payment per Payment



©©

: payment per payment: payment per payment

EE[[

©©

]] = = E E[[

_{(()) ; ; EE[[}

öö

]]

öö

]] = = EE[[

©©

]]⋅ ⋅ (())

With ordinary deductible With ordinary deductible



,,

[[

©©

]] = = (()) = = EE[[  −  −  ∣  ∣  > > ]] = = E E[([(  −  −))

_{(())}

••

]]

Special Shortcuts for Special Shortcuts for

(())

Exponential

Exponential(())



Uniform

Uniform((,,))

 −  − 22

Pareto

Pareto((,,))

 + +

_{ − −11}

S-P S-P

Pareto((,,))

Pareto

 − −11

The Ultimate Formula for Insurance The Ultimate Formula for Insurance

EE[[

öö

]] = = ((1 +1 +))™E´ ∧

™E´ ∧ 1 +1 +≠≠− E− EÆÆ  ∧  ∧ 1 +1 +ØØ

where where



: deductible (set to 0 if : deductible (set to 0 if not applicable)not applicable)



: policy limit (set to: policy limit (set to

∞∞

if not applicable) if not applicable)



: coinsurance (set to 1 if not applicable): coinsurance (set to 1 if not applicable)



: inflation rate (set to 0 if not applicable): inflation rate (set to 0 if not applicable)

: maximum covered loss,

: maximum covered loss,which equal

_{which equalss  + +}

Aggregate L

Aggregate Loss Modelsoss Models Collective Risk Model Collective Risk Model If

If

  == ∑ ∑ 

µµ¥∂¥∂

¥¥

for for independentindependent



and and

 

, then:, then: •

•

EE[[]] = = EE[[]]EE[[  ]]

•

VarVar[[]] = = EE[[]]VarVar[[  ]] + +VaVarr[[]]EE[[  ]]

MM

Impact of Deductibles on Claim Frequency Impact of Deductibles on Claim Frequency For For

 = Pr

 = Pr((  >

 > ))

,,

 ′′

Poisson Poisson

 

Binomial Binomial

,, ,

,

Neg. Neg. Binomial Binomial

,, ,

,

Negative Binomial/Exponential Compound Models Negative Binomial/Exponential Compound Models

ãã ∼ Neg.Binomial

 ∼ Neg.Binomial((,,))

_{ ∼ Exponential}

_{ ∼}

_{Exponential(()) ππ}

_⇕⇕

ªª  ∼ Binomial ™,

_{ ∼}

_{ ∼ Exponential}

 ∼ Binomial ™, 1 +1 +

_{Exponential(([[11+ + ])])ºº}

Compound Poisson Models Compound Poisson Models

A collective risk model where the frequency A collective risk model where the frequency follows a Poisson distribution.

follows a Poisson distribution.

SEVERITY, FREQUENCY

SEVERITY, FREQUENCY & AGGREGATE& AGGREGATE

MODELS

(2)

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Copyright © 2018 Coaching Actuaries. All Rights Reserved. 2

Risk Measures

Value-at-Risk (VaR)

VaR

æ

( ) = 

.I

()

Tail-Value-at-Risk (TVaR)

TVaR

æ

( ) = E  ∣  > VaR

æ

( )y

= VaR

æ

( ) +VaR

æ

( )y

TVaR

æ

( )

Normal

 + ¿¬

æ

√

1 − ƒ

Lognormal

E[ ] ⋅ ¿Φ¬ − 

æ

√

1 −  ƒ

Coherence

( )

is coherent if it satisfies the properties below: • Translation invariance:

(  + ) = ( )+

• Positive homogeneity:

() =  ⋅ ( )

• Subadditivity:

(  + ) ≤ ( )+()

• Monotonicity:

() ≤ ()

, if

Pr(  ≤ ) = 1

VaR is not coherent because it fails subaddivity. TVaR is coherent.

Tail Weight

1. Fewer positive raw moments

⟹

heavier tail 2. If

lim

-→



À

Ã

(-)

= ∞

or

-→

lim

Õ

À

Ã

(-)

= ∞

, then numerator has a heavier tail.

3.

ℎ()

decreases with

 ⟹

heavy tail 4.

()

increases with

⟹

heavy tail CONSTRUCTION AND SELECTION OF PARAMETRIC MODELS

Maximum Likelihood Estimators Steps to Calculating MLE

1.

() = ∏ ()

2.

() = ln()

3.



H

() =

–

–—

()

4.

Set 

H

() = 0

Incomplete Data Left-truncated at



() ()

⁄

Right-censored at



()

Grouped data on interval

(,]

Pr( <  ≤ )

Special Cases Distribution Shortcuts Gamma, fixed



” = ̅

Normal

̂ = ̅

÷



_{= ∑ }

g¥∂I

¥

 −̂



Lognormal

̂ = ∑ ln

¥

g¥∂I



÷



_{= ∑ (ln}

g¥∂I

_{ − ̂}

¥

)



Poisson

◊ = ̅

Binomial, fixed



÷ = ̅

Neg. Binomial, fixed



◊ = ̅

Zero-Truncated Distribution:

• Match

E[ 

á

]

to

̅

Zero-Modified Distribution:

• Match



Bä

to the proportion of zero observations • Match

E[ 

ä

]

to

̅

Uniform Distribution on

(0,)

: •

” = max(

I

,



,…,

g

)

Choosing from

(,,0)

Class

Two methods to fit data to an

(,,0)

class distributions:

• Method 1: Compare

̅

and





•

Method 2: Observe the slope of

Gg

‹

g

‹›À

Distribution Method 1 Method 2 Poisson

̅ = 



0 Binomial

̅ > 



Negative Neg. Binomial

̅ < 



Positive Variance of MLE Fisher’s Information One Parameter:

() = −E



[′′()]

Var”y = [()]

.I

Two Parameters:

(,) = −E



¿ 

_

_ﬁ,—

H

ﬁHH

(,) 

_{(,) }

ﬁ,—

H

_—HH

_{(,) ƒ}

(,)

[(,)]

.I

_{= ﬂ Var[÷] Cov÷,”y}

Cov÷,”y Var”y ‡

Delta Approximation One-Variable:

Var¬”√y ≈ Æ ()Ø



Var”y

Two-Variable:

Var¬÷,”√y ≈ (

ﬁH

)



Var[÷] +2

ﬁH



—H

Cov÷,”y

+(

—H

)



Var”y

Confidence Interval

” ±

(I•æ)/

‰ VarÂ ”y

Hypothesis Tests



B

: null hypothesis



I

: alternative hypothesis

Reject



B

when test statistic

>

critical value





is true



_

is false Reject



_

Type I Error Correct Decision Fail to reject





DecisionCorrect Type II Error Hypothesis Tests: Kolmogorov-Smirnov Empirical Distribution

Equal probability for each observation



g

() = # of observations ≤ 

_

Kolmogorov-Smirnov Test

Test statistic:  = max

_{ÍÎÎ }





y

where





= max¬Ï

g

¬



√−

∗

¬



√Ï,Ï

g

¬

.I

√− 

∗

¬



√Ï√

If data is truncated at



, then



∗

() = ()− ()

_{1 − () ,for  ≥ }

Kolmogorov-Smirnov Test Properties • Individual data only

• Continuous fit only

• Lower critical value for censored data • If parameters are estimated, critical value

should be adjusted

• Lower critical value if sample size is large • No discretion

• Uniform weight on all parts of distribution

()

Plot

Graph the difference between empirical CDF and fitted CDF

Peak:

() = 

g

¬



√− 

∗

¬



√

Valley:

() = 

_g

¬

_.I

√−

∗

¬

_

√



-



Plot

Coordinate: Ó

g

¬



√,

∗

¬



√Ô where 

g

¬



√ = 

_{ + 1}

Hypothesis Tests: Chi-Square Goodness-of-Fit Chi-Square Goodness-of-Fit Test

Test statistic:



_{= Ò¬}



− 

_



√





G

∂I

where

•



: # of groups

•





: expected # of observations in group



•





: actual # of observations in group



Degrees of freedom

=  − 1 −

where •



: # of estimated parameters

Chi-Square Goodness-of-Fit Test Properties • Individual and grouped data

• Continuous and discrete fit

• No adjustments to critical value for censored data

• If parameters are estimated, critical value is automatically adjusted via degrees of freedom • No change for critical value if s ample size is

large

• Data needs to be grouped according to





• More weights on intervals with poor fit Hypothesis Tests: Likelihood Ratio

Test statistic: = 2[(

I

) − (

B

)]

Degrees of freedom

= # of free parameters in 

I

− # of free parameters in 

B

Score-Based Approaches Two types of criteria:

• Schwarz Bayesian Criterion (SBC), a.k.a. Bayesian Information Criterion (BIC) • Akaike Information Criterion (AIC)

SBC/BIC

 − 2ln

AIC

 − 

where

:

log-likelihood

:# of estimated parameters

: sample size

Select model with the highest SBC or AIC value.

CONSTRUCTION AND SELECTION OF PARAMETRIC MODELS

(3)

CREDIBILITY Classical Credibility

a.k.a. Limited Fluctuation Credibility Full Credibility

# of exposures needed for full credibility,



ı

: Full credibility of aggregate claims:



ı

= ´

(•æ) ⁄

_{ ≠}



(



)

# of claims needed for ful l credibility,



ˆ

: Full credibility of aggregate claims:



ˆ

= ´

(•æ) ⁄

_{ ≠}



ﬂ

_

µ

_µ

+ 



‡

• Full credibility of claim frequency: set





= 0

•

Full credibility of claim severity: set

˜

¯Ã

˘

¯

= 0



ˆ

= 

ı

⋅ 

µ

; 

ı

= 

_

_µ

ˆ

Partial Credibility

Credibility premium: 

˙

= ̅ + (1 − )

_{=  + (̅ − )}

where



: manual premium



: credibility factor/credibility

Square Root Rule: = ¸ 

ı

= ¸ ′

ˆ

where



: actual # of exposures

′

: actual # of claims Bayesian Credibility Model Distribution

Distribution of model conditioned on a parameter Model density function:

( ∣ )

Prior Distribution

Initial distribution of the parameter Prior density function:

()

Posterior Distribution

Revised distribution of the parameter Posterior density function:

( ∣ data)

( ∣ data) = (data ∣ ) ⋅()

_{∫ (data ∣  ) ⋅ () d}

_//

Predictive Distribution

Revised unconditional distribution (w.r.t. model) of the model

Predictive density function:

( ∣ data)

Predictive Mean = Bayesian Premium

Bühlmann Credibility

Expected Hypothetical Mean (EHM):

 = EE[  ∣ ]

Expected Process Variance (EPV):

 = EVar[  ∣ ]

Variance of Hypothetical Mean (VHM):

 = VarE[  ∣ ]

Bühlmann :  = 

Bühlmann Credibility Factor: =  + 

Bühlmann Credibility Premium:



˙

= ̅ + (1 − )

_{=  + (̅ − )}

Bühlmann As Least Squares Estimate of Bayesian

Minimize

∑ ´

ÍÎÎ -

-

¬

-

− ”

-

√



≠

where



-

: Bayesian estimate given





= 

”

-

: Bühlmann estimate given





= 

Properties of a Bayesian/Bühlmann graph • Bühlmann estimates are on a straight line • Bayesian estimates are within the range of

hypothetical means

• There are Bayesian estimates above and below the Bühlmann line

• Bühlmann estimates are between the sample mean and theoretical mean

Conjugate Priors Poisson/Gamma • Model:

Poisson()

• Prior:

Gamma(,)

Posterior

( ∣ data) ∼ Gamma(

∗

,

∗

)

•



∗

=  + ∑ 

¥∂

¥

•



∗

= Ó

—

+ Ô



Predictive

Neg.Binomial( = 

∗

, = 

∗

)

Binomial/Beta • Model:

(  ∣ ) ∼ Binomial(,)

• Prior:

 ∼ Beta(,,1)

Posterior

( ∣ data) ∼ Beta(

∗

,

∗

,1)

•



∗

=  + ∑ 

¥∂

¥

•



∗

=  + [() − ∑ 

¥∂

¥

]

Predictive -Exponential/Inv. Gamma • Model:

(  ∣  ) ∼ Exponential()

• Prior:

 ∼ Inv.Gamma(,)

Posterior

( ∣ data) ∼ Inv.Gamma(

∗

,

∗

)

•



∗

=  + 

•



∗

=  + ∑ 

¥∂

¥

Predictive

Pareto( = 

∗

, = 

∗

)

Normal/Normal • Model:

(  ∣  ) ∼ Normal(,)

• Prior:

 ∼ Normal(,)

Posterior

( ∣ data) ∼ Normal(

∗

,

∗

)

•



∗

= ̅ + (1− )

•



∗

= (1− )

Predictive

Normal( = 

∗

,



=  + 

∗

)

Uniform/S-P Pareto • Model:

(  ∣  ) ∼ Uniform(0,)

• Prior:

 ∼

S-P Pareto

(,)

Posterior

( ∣ data) ∼

S-P Pareto

(

∗

,

∗

)

•



∗

=  + 

•



∗

= max(,



,…,



)

Predictive -Exact Credibility

Bayesian estimate = Bühlmann estimate

• Poisson/Gamma • Binomial/Beta

• Exponential/Inv. Gamma • Normal/Normal

Empirical Bayes Non-Parametric Methods Uniform Exposures

̂ = ∑ ∑ 

!

∂

¥

¥∂

_{ ⋅ }

÷ = ∑ ∑ ¬

!

∂

¥

− ̅

¥

√



¥∂

_{( − 1)}

÷ = ∑ (̅

!

¥

− ̅)



¥∂

_{ − 1 − ÷}

Non-uniform Exposures

̂ = ∑ ∑ 



"

¥



¥

∂

!

¥∂



÷ = ∑ ∑ 



"

¥

¬

¥

− ̅

¥

√



∂

!

¥∂

∑ (

!

¥

− 1)

¥∂

÷ = ∑ 

!

¥

(̅

¥

− ̅)



− ÷( − 1)

¥∂

_{ − }

_

_{∑ }

¥

!

¥∂

Balancing the Estimators

Estimate E

H

M as: ̂ = ∑ 

¥

̅

¥

!

¥∂

∑ 

!

¥

¥∂

Empirical Bayes Semi-Parametric Methods To estimate

÷

:

Model %

Poisson()

̅

Neg.Binomial(,) ̅(1 + )

Gamma(,)

̅

To estimate

̂

and

÷

, use the non-parametric method formulas shown above.

(4)

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

Expenses and Profit

Variable Expense Ratio:  = 

_

ä

Fixed Expense Ratio:  = 

_

ç

Permissible Loss Ratio: PLR = 1−  −

ë

,

where



ë

is the target profit and contingencies ratio Premium

Unearned premium for CY



:



Uí

= 

Uì

−

U

+

U\í

Extension of Exposures Method

Recalculates the premiums of historical policies under the current rate l evel Parallelogram Method

Calculates average factors to be a pplied to the aggregate historical premiums to make them on-level

Ratemaking Loss Ratio Method

Indicated Avg.Rate Change =  +

_{1 − − }

_ë

−1

Indicated Relativity

U

= Current Relativity

U

⋅ 



_òôöõ

U

Indicated Base Rate = Current Base Rate ⋅ 1+ Indicated Avg.Rate Change

_{Off-Balance Factor}

Off-Balance Factor = Indicated Avg.Relativity

_{Current Avg.Relativity}

Pure Premium Method

Indicated Avg.Rate = † +†

_{1 − − }

ç

_ë

Avg.Relativity

U

= Avg.Rate

Base Rate

U

_U

Adj.†

U

=

Avg.Relativity



U

_U

⋅ Exposure

_U

Indicated Relativity

U

= Adj.†

Adj.†

_òôöõ

U

Indicated Base Rate = Indicated Avg.Rate

_{Indicated Avg.Relativity}

Credibility-Weighted Relativities

New Relativity = (Indicated Relativity) +(1 −)(Current Relativity)

 = ()+

_{()+ }

ß

_®

•



: original limit •



: increased limit

Rate of policy variation with limit

 = 

ß

⋅ Indicated Base Rate

Loss Elimination Ratio



©

= ()− ()

̅ −()

•



: original deductible •



: increased deductible

Rate of policy variation with deductible

 = (1− 

©

)⋅ Indicated Base Rate

Insurance Coverages

Homeowners Coinsurance

Compensation:  = /min,  ⋅ 7,  < 

_{min(,),  ≥ }

Disappearing Deductible

Deductible decreases linearly over a specific range:

 =  ,  ≤ 

 −

_{ −7,  <  ≤ }

_{0,  > }

Claim Payment:

 =

⎩

0,

 ≤ 

 −,  <  ≤ 

 − −

_,

_{ − 7,  <  ≤ }

_{ > }

Loss Reserving

Expected Loss Ratio Method 1.

K

M.

= 



⋅

2.

 = K

M.

− 

S

Chain-Ladder Method

a.k.a. Loss Development Triangle Method 1.



UM.

= ∏ 

XWYZ[\

W

2.

K

UM.

= 

U,Z

⋅ 

UM.

3.

 = K

M.

−

S

Bornhuetter-Ferguson Method

 = K

M.

1 − 1 

_M.

7 where

•

K

M.

is calculated based on the expected loss ratio method •



M.

is calculated based on the c hain-ladder method

Alternatively,

 =  ⋅



+(1 −) ⋅ 



where  = 1 

M.

Frequency-Severity Method Alternate Method:

1. Apply the chain-ladder method to frequency and severity separately 2.

K

M.

= k

M.

⋅ K

M.

3.

 = K

M.

− 

S

Closure Method: Frequency 1.



U,W

=

k



,

q.



,

2.



U,W

= ̂

W

k

UM.

−

U,W\

z

Aggregate

1.

|

U,W

= 

U,W

⋅ 

U,W

2.

 = ∑ |

U[WÄ

U,W

, where



is the valuation CY Data Preparation

Losses

Incurred losses for CY



:



UÉ

= 

US

+ 

U

−

U\

where



U

is the reserves at the end of CY



Incurred losses for AY or PY



:



UÉ

= 

US

+ 

U

where



U

is the reserves as of the valuation date

† †

†

††

̅

SHORT-TERM INSURANCES Losses Projected Losses Aggregation

• Calendar Year (CY) • Accident Year (AY) • Policy Year (PY)

• Trend Period • Trend Factor • Loss Development Factors Develop to Ultimate Trending Premium

Premium at Current Rates

Aggregation Current Rate Level • Calendar Year (CY)

• Policy Year (PY)

• Extension of Exposures Method

(5)