B2. Experience Rating

Question 1

What is a mod factor

Answer 1

prospective measure of the loss potential of a single risk for the future exposure period

Question 2

What is experience rating

Answer 2

Application of a mod factor on top of the manual rates of a classification plan .

• corrects for different risks level within a class
• reflects actual experience from prior policy terms
• relates them to the premium for the current term

If no correlation between loss over time, experience rating would not be predictive or appropriate

Question 3

Difference between rate level and premium level

Answer 3

Rate level is a function of:

• manual rates
• it is prior to experience rating, schedule rating, retrospective rating, premium discount, dividend plans

Premium level is affected by:

• manual rates
• experience rating
• schedule rating
• retrospective rating
• premium discount
• dividend plans

**inadquate rate level may be partially corrected by experience rating and therefore still have adequate premium level

**rate level changes are offset by the off-balance factor and therefore may result in lower premium level changes

Question 4

Advantages of experience rating

why well suited for commercial lines

Answer 4

1. captures differences between risks within the same class
2. accounts for variables that are difficult to quantify/not captured in classification
3. further refinement of classification beyond manual rates

***well suited for commercial lines bc cie mng great deal control over company practices

Question 5

Why experience rating supports the principle that rates should not be unfairly discriminatory

Answer 5

• main goal is individual risk equity
• experience rating recognizes that each risk has different loss potential
• by modifying rates, expected profit potential for each risk can be made equal
• therefore rates are not unfairly disciminatory and achieve equity

Question 6

Why using full credibility conflicts with one goal of experience rating

Answer 6

Greater individual risk equity (predictive accuracy):

• giving full credibility experience would penalize for random losses
• but random losses do not reflect the true expected losses
• therefore it does NOT charge insured for the true potential loss cost

Question 7

Necessary condition for a plan using experience rating

Answer 7

-Credit and debit groups of risks should equally reproduce the PLR
-Each random subgroup of risks that is credible enough, should give the PLR
=>Therefore credit and debit risks are all equally desirable

Question 8

Why overall mod factor may be lower than 1

• Credit more frequent
• Off-balance is typically a slight credit

Answer 8

1. larger risks have relatively better experience , resulting in credit mods that get a lot of weight in the book, The book could have a lot of small policies not eligible for experience rating that have horrible experience.
2. manual rates are too high relative to expected cost => mod factor pushes down the off-balance
3. overall mod factor for industry is lower than 1 => insurer does no do anything special
4. underwriters have faulty understanding of mod factor => they refuse to renew risks with mod factor > 1

Question 9

In general, cannot determine whehter a risk is desirable from Mod only:

Answer 9

• debit mod could just mean risk a poor fit to manual rates

- debit mod could be due to any loss that is pure random chance

Question 10

Interpretation of off-balance in experience rating

Answer 10

• if off-balance > 1 => rates were inadequate
• if off-balance decrease (closer to 1) => rates are becoming more adequate

**In general, cannot determine whether rates are adequate from off-balance only

Question 11

Effect of off-balance on indicated rate level increases

Answer 11

• indicated rate level increases are calculated on standard premium assuming no change to the off-balance
• usually off-balance > 1, but the actual premium level increase will bring back the off-balance = 1 or lower
• therefore since the indication assumed no change to the off-balance, then indication < actual rate increase

Question 12

Credibility methods

Answer 12

1. classical
   - determines full credibility standard based on a given probability that observed will be within x% of the true mean
   - relies on normal distribution
   - limited fluctuation credibility
2. bayesian
   - updates prior hypothesis with new experience
   - relies on MCMC simulations
3. buhlmann
   - involves analysis of variance
   - used in experience rating
   - greatest accuracy or least squares credibility

Question 13

Credibility issues with Mod factor

Answer 13

To prevent random large losses not predictive of futur losses from having too much influence on the insured premium:

1. individual large loss can be capped by MSL
2. mod factor itself can be capped/limited to a range

Question 14

Differences between primary and excess layers in a split plan

Answer 14

Primary layer:

• reflects parameter risk
• related to the amount of frequency of many small claims
• receives the most weight

Excess layer:

• reflects process risk
• related to the volatility of severity of very few large claims
• receives less weight
• usually capped to prevent large losses not predictive of future losses from having too bug impact on insured prm

Question 15

Effect of inflation on split plan

Answer 15

Split point should increase to reflect inflation:

• helps maintain the same proportion of primary / XS losses
• otherwise Dratio decreases => expected XS losses increase => mod factor increase

Question 16

When to apply schedule rating on top of experience rating

Answer 16

To reflect individual risk characteristics that are:

1. not reflected in manual rates => due to less refined classification plan
2. not already reflected in experience rating => due to characteristic that was not inforce during experience period

• wrk compensation
• commercial line

Question 17

Discuss three considerations that would justify truncating of adjusted loss data at a certain $ value (e.g. 100K).

Answer 17

1. maximize reliance on reported data
2. keep enough data points above the truncation point to permit reasonable curve fitting
3. be a round number prior to data thinning out

Question 18

In addition to truncation, shifting, and normalizing, list three adj. that should be made to WC claims before fitting a severity distribution to the data.

Answer 18

1. trend
2. loss development
3. adj. to new benefit level

(1) and ( 2) because can vary by layer of loss and thus xs ratio on ultimate trended loss may be dirrefent than undeceloped and untrended loss. Since xs ratio use for pricing a future policy they should reflect the ult loss that could be covered
(3) to reflect the benefit level in the propspective period since xs ratio will be usee to price future policy

Question 19

Discuss Mahler’s approach for building a loss distribution model and his rationale for doing so

ILF THEORICAL METHOD ( CURVE FITTING) HOW TO AVOID UNDER/OVER FITTING AT DIFFERENT PART OF DISTRIBUTION

Answer 19

• Uses empirical data at less than 100K, then he blends exponential and pareto distributions at higher limits after truncating and shifting
• rely on actual experience to the extent possible at the lower limits while fitting a curve to make up for sparser data at higher limits, where experience may not be credible
• The pareto has a thick tail which makes it ideal at very high limits. Exponential works well just above the experience cut off pt.

avoids some arbitrary or judgmental division of claims between injury kind

Question 20

Is it reasonable to fit a single curve rather than multiple curves by HG?

Answer 20

reasonable if the shapes of the distributions are similar to diff. RGs after truncation and normalization

Question 21

With regard to experience rating, describe the relationship between variance of the hypothetical means and the credibility of individual risk experience.

Answer 21

The higher the VHM, the higher the credibility assigned to individual experience. The more varied the individual risks are in a class, the more valuable the individual experience becomes in determining a proper individual rate.

experience rating is more powerful when classification plan does not sufficiently explain variance in loss experience between risks

Question 22

split plan works better when

Answer 22

parameter risk can be separated from process risk

Question 23

Explanation why Mod may increase but ELR decrease

Answer 23

Probably and issue with the classification of the risk. May be a better fit in another class.

Question 24

Treatment of losses for Terrorism vs Worker compensation in experience rating

Answer 24

Capping :
Experience rating uses past losses to the extent that they are predictive of the future loss to improve individual risk equity. Large losses in WC are capped bc to some extent they are just bad luck.
Terrorism ratemaking is not interrested in individaual risk equity as much as spreading the cost of terrorism losses accross all insured. Capping losss may improve stability but may lead to inadequacy.

Put more weight to actual experience for larger risk :
The larger the risk, the more stable their expected losses are. However, due to the rarity and catastrophic nature of terrorism losses, it is unlikely that larger risks would have more stable losses than smaller risks.

Question 25

benefit of split plan

Answer 25

can give different amount of credivility for loss experience in the primary layer than or the excess layer. This give the plan more flexibility and can improve the plan’s performance for a line of business loke worker comp

Question 26

an effective plan should

Answer 26

1. identify risk difference ( upward trend in manual LR)

2. Correct for risk difference ( std LR equivalent accross quantile, small variance )

Question 27

argument against using latest 3 yrs past loss data to as variable in worker comp model

Answer 27

if use experience rating, historical loss experience already impacts premium through this , so should not be double counted

variable most likely be correlated with other variables which may lead to an unstable model. Multicolinearity and no convergence may happen

Small risk have volatile experience and incorporatign latest 3 yrs historical losses will cause fluctuations in their prm

last 3 yrs wont be fully developed si if reporting lag varies by company, it would be over or under preducting the loss experience.

would be very correlated with risk size since larger insured are more likely to have hifher historical losees so including the variable without stating it as a ratio to exposure or to prm would skew the result.

Question 28

overall inadequacy is best handled with manual rates of experience ratign ?

Answer 28

It’s better to correct with the manual rates, Experience mod plan is intended to adjust for individual cost differences.