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13 Cards in this Set
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Required Surplus is different from Riskbased Capital. See detailed notes.
The Required Surplus depends on many characteristics of a company or product, including: 
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) 

SENSITIVITY ANALYSIS
Sensitivity analysis is useful for: 
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) 

RUIN THEORY
Description of the RuinTheoretic Model 
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 . 

Mathematical Technicalities of the RuinTheoretic Model

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. 

LIMITATIONS OF THE RUIN MODEL
Mathematical Limitations 
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. FullyInsured expense allocation method Reserve methods differ between LI and DI. For LTD, interest is important. Model assumes an infinite time horizon realistic for 20year 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 

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

Premium is true expected claims plus loading
“True expected claims” hard to predict because of: inflation outofdate 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 

DIFFICULTIES in COMPUTING the REQUIRED SURPLUS for SPECIFIC PRODUCTS
For Group Life Insurance 
The Distribution of Claims assumption
Large face amounts have big impact (include “shadow claims”) 

For Group AD&D Insurance

those above, and the following:
Lowfreq, highseverity Req Surp higher Accident probability (Doubleindemnity) key 

For Group LTD Insurance

Lowfreq, highseverity
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 (longterm), but model ignores it. RuinTheoretic 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. 

Results of Having Inversely Correlated Risks

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. 

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

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

Effect of Required Surplus on ROE Calculations

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. 

Different Sized Companies in the Group Insurance Marketplace

Jumbo and Large companies
Advantages: Reputation as leaders Great MIS Wellstaffed MediumSized 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 Closeknit team Info Systems good Disadvantages they suffer: Reinsurance needed One or two key people Done. 