Tsa 36 Required Surplus For The Ins. Risk For Grp Ins.

Front 1

Required Surplus is different from Risk-based Capital. See detailed notes.

The Required Surplus depends on many characteristics of a company or product, including:

Back 1

 Frequency, Severity, and “Contagion” of expected claims
 Large Claims
 Face Amount Distribution (LI)
 Age/Sex of insureds
 Premium adequacy
 loadings
 credibility of data used in ratesetting
 Guarantees (renewability)
 Regulations (community rating)
 Retention Limit (RL)
 Req Surplus is only sensitive to RL if face amounts are close to the RL.
 Net Amount at Risk (NAR)
 the Economy
 inflation and utilization changes
 Time Horizon
 Size of company
 Lawsuit risk / malpractice risk
 Reinsurance Use (lowers Req Surp)

From GI 41:
 “vitality surplus” needed for corporate objectives
 the rating desired (e.g. AAA)

Front 2

SENSITIVITY ANALYSIS
Sensitivity analysis is useful for:

Back 2

 Understanding relative importance of the above factors
 Pricing decisions
 Estimate a product’s riskiness
 Withdraw a product if price to produce Req Surp is too high.

 Managing the portfolio of business:
 growth
 changing composition
 Risk Management (e.g. through Reinsurance)

Front 3

RUIN THEORY
Description of the Ruin-Theoretic Model

Back 3

 initial surplus U.
 Premiums & claims based on an assumed distribution
 If surplus ever falls below 0, the company is “ruined”.

“Ruin” means Agg Claims > Initial Surplus + Premiums

 given , find U() such that the probability of ruin is less than .

Front 4

Mathematical Technicalities of the Ruin-Theoretic Model

Back 4

 The surplus U() necessary to keep the probability of ruin less than  is:

U() = – 1 ln()
R

 R is the adjustment coefficient. The key factor.
 R can be determined in 2 ways:
a) Poisson model
b) Negative Binomial model

 These probability models include the following parameters:
 claim frequency, severity
 contagion
 claim “uncertainty”
 net premium and loading
 premiums are assumed to be equal to true expected claims plus the loading.

 If surplus is doubled, P(ruin) is squared.

The study note presents a lot of formulas and details about the effects of different parameter choices on R. I have chosen to focus on the major concepts instead.

Front 5

LIMITATIONS OF THE RUIN MODEL
Mathematical Limitations

Back 5

 The model ignores Commissions, Reserves, Interest, Taxes, and Expenses.

Mnemonic: ignores a lot of CRITEria.

Ignoring These Items is a Problem because:
 Expense risk varies by cpy
 ASO vs. Fully-Insured
 expense allocation method
 Reserve methods differ between LI and DI.
 For LTD, interest is important.

 Model assumes an infinite time horizon
 realistic for 20-year LI, but not for MI or DI.
 adds conservatism

 Poisson Model assumes the claims are independent

 It’s Difficult to model Dynamic Portfolios
 business portfolio grows, and face amounts change.
 Growth increases the required surplus
 Growth strain vs. new business strain
 age/health distribution changes
 Inflation  face amounts increase

Front 6

Assumption and Knowledge Limitations (preventing accurate use of the model)

Back 6

 Premium is true expected claims plus loading
 “True expected claims” hard to predict because of:
 inflation
 out-of-date experience studies
 volatility
 The frequency, severity, and contagion parameters used are guesses
 Effect of Retrospective Experience Rating
 Ruin Model implicitly assumes surpluses and deficits will offset
 Realities:
 Groups might terminate while in deficit
 dividend payouts may exceed expectations.

Solutions:
 Increase the loading
 Adjust for dividend payouts.

 No guidance as to an appropriate choice of 
 Surplus can be expressed in different ways
and not all of them are easy to model.

 Dollar amount
 % of premiums (Group Ins)
 % of claims (poor, since req surp not proportional to claims)

Moral: Required Surplus must be recalculated periodically

Front 7

DIFFICULTIES in COMPUTING the REQUIRED SURPLUS for SPECIFIC PRODUCTS
For Group Life Insurance

Back 7

 The Distribution of Claims assumption
 Large face amounts have big impact (include “shadow claims”)

Front 8

For Group AD&D Insurance

Back 8

 those above, and the following:
 Low-freq, high-severity
 Req Surp higher
 Accident probability (Double-indemnity) key

Front 9

For Group LTD Insurance

Back 9

 Low-freq, high-severity
 F and S are affected by external variables (unemployment, waiting period length)
 Claim amount not known at issue
 A new variable, continuance
 Interest is important (long-term), but model ignores it.
 Ruin-Theoretic model for LTD is complex
 two separate required surpluses: one for claim Incidence and one for Continuance.
 Analyze like two separate companies. Add req surps together.

Front 10

Results of Having Inversely Correlated Risks

Back 10

 The required composite surplus will be less than the sum of the surpluses for each part
 Pricing may be inaccurate
 A company should have a “combined profit / risk management center”, rather than analyze each of its products in isolation.

Front 11

Risks that Aren’t Covered by the Traditional Required Surplus Formula

Back 11

 Catastrophes
 Statistical fluctuation (affects small companies the most)
 Management risks / pricing errors
 Lawsuits
 Governmental policy changes

Front 12

Effect of Required Surplus on ROE Calculations

Back 12

 ROE = Earnings / Required Surplus
Because Required Surplus is in the denominator:
 The formula for Req. Surp. must be easy to calculate, so that ROE can be determined
 The formula should not vary significantly over time
 Group Insurance co’s need to be segmented by size, because their risks are different.
 they are subject to different required surplus risks;
 market forces affect different size companies differently.

Front 13

Different Sized Companies in the Group Insurance Marketplace

Back 13

Jumbo and Large companies
Advantages:
 Reputation as leaders
 Great MIS
 Well-staffed

Medium-Sized companies
Advantages they have:
 Can compete with the large companies


Disadvantages they suffer:
 understaffed
 MIS poor

Small companies
Advantages they have:
 Senior management is deeply involved
 Close-knit team
 Info Systems good

Disadvantages they suffer:
 Reinsurance needed
 One or two key people



Done.