IAAHS Colloquium 2004actuaries.org/IAAHS/Colloquia/Dresden/Richter presentation.pdf29.04.2004...

29.04.2004 Heinz-Werner Richter 1

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IAAHS Colloquium 2004

Actuarial Foundationsof Full Coverage with Ageing Reserves in

Germany


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4German Health Insurance (Full Coverage)

Statutory Health Insurance

2002• 71 million insured• premium income € 132

billion

• 8 million insured with privat supplementary coverage

Private Health Insurance

2002• 8 million insured• premium income € 16 billion

• premium income € 5 billion


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Insured Persons


• compulsory: employees with a salary under a certain limit(€ 3825 in 2003)

• pensioners• voluntary members• their families (if their

income can be neglected)


• employees with a salary exceeding a certain limit

• pensioners• self-employed persons• civil servants• their families• „once private, ever private“

(return only possible in exceptional cases)


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Main Requirements


• standardized coverage• acceptance of each

applicant• possibility to change the

coverage by law• managed by about 400

health insurance funds (under public law)


• non-standardized coverage– „substitutive health insurance“

= similarity to the statutory insurance

– different tariffs– deductibles

• lifelong insurance guarantee• managed by about 50 health

insurance companies, which are either stock companies or mutuals


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Contributions


• percentage of the salary respectively the social insurance pension (up to a certain limit)

• contribution-free: family members

• one half by the employee, one half by the employer


• premium depending on coverage (tariff), sex, entry age and

• physical condition at the time of application– extra premium or– exclusion rider

• one half by the employer (up to the defined limit)


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4Statutory Health Insurance

Premiums and Loss Expenses per CapitaSource: Prof. Bernd Raffelhueschen (Universität Freiburg und Universität Bergen, Norwegen)


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Private Health Insurance (Full Coverage)Further Requirements

• Lifelong insurance garantee– no end of insurance

• if a certain age is reached• if a certain sickness occurs• if high costs emerge

– no right of the insurer• to cancel the contract provided the premium is paid• to reduce the coverage

– premium adjustments according to the general increaseof health expenses

– cautious calculation assumptions• The right of tariff switch• Equal bases of calculation for old and new customers


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Private Health Insurance (Full Coverage)Calculation Requirements

• The premiums have to be calculated individually.• The premium rates must not increase because of

increasing age.• The technical basis is similar to that of life insurance.• A surrender value is not paid. • There are a lot of further requirements, defined by the

legislator.– safety: all values have to be set cautiously– in addition: contingency margin of at least 5% of the

premium– ...


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Private Health Insurance (Full Coverage)Calculation

x age (end: )i interest rate (max. 3.5 %)qx mortality ratewx lapse rateax present value of an annuity

)wq1(ll xxx1x −−⋅=+

i11

v+

=

?

∑

∑−

=+

−

=

++

=

⋅⋅

=

x?

0ttx

x

x?

0t

txtxx

xx

DD1

vlvl

1a


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Mortality Rates in Germany

0,000000

0,050000

0,100000

0,150000

0,200000

0,250000

0,300000

20 30 40 50 60 70 80 90 100

Age

men women


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Average Lapse Rates in Germany(normal risks)

0,0000%

2,0000%

4,0000%

6,0000%

8,0000%

10,0000%

12,0000%

14,0000%

20 30 40 50 60 70 80 90 100

Age

men women


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Average Lapse Rates in Germany(civil servants)

0,0000%

1,0000%

2,0000%

3,0000%

4,0000%

5,0000%

6,0000%

7,0000%

20 30 40 50 60 70 80 90 100

Age

men women


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Kx+t expected yearly loss expense at age x+tAx present value of loss expensesPx yearly net premium

∑

∑−

=++

−

=+

++

⋅=

⋅⋅⋅

=

x?

0ttxtx

x

x?

0ttx

txtxx

xx

KDD1

Kvlvl

1A

x

xx a

AP =


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Expected Yearly Loss Expense for an Insured Person

0

1.000

2.000

3.000

4.000

5.000

6.000

7.000

8.000

9.000

20 30 40 50 60 70 80 90 100

Age

€

men women

Tariff with out- and inpatient medical treatment, dental care, drugs and appliances


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Expected Yearly Loss Expense for an Insured Person

0

1.000

2.000

3.000

4.000

5.000

6.000

7.000

8.000

9.000

20 30 40 50 60 70 80 90 100

Age

€

Net premiums for the entry ages 21 and 40


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Loadings:

• administration expenses• initial expenses (acquisition commission etc.)• contingency margin• „10%-Loading“: up to the age of 60 (used to reduce

premium rises in old age)


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Private Health Insurance (Full Coverage)The Reserve for Increasing Age

[ ] mxxmx

mxxmxxm

aPP

aPAV

++

++

⋅−=

⋅−=


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4Ageeing reserves for the entry ages 21 and 40

0

10.000

20.000

30.000

40.000

50.000

60.000

70.000

80.000

20 30 40 50 60 70 80 90 100

Age

€


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Private Health Insurance (Full Coverage)Premium Adjustment

• Yearly comparison of the assumed claims with theactually occured claims

• Adjustment of the premiums, if deviation exceeds a certain limit.

• Strongly regulated and supervised rules.


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„old“ / „new“ refer to the bases of calculation beforeand after a premium adjustment

x+m age at the time of the adjustment

[ ]

[ ]old

mxnew

mxoldx

mxoldx

oldmxmx

newx

newmx

mx

newx

oldxm

newxm

mx

newx

newmx/x

PPP

a)PP(a)PP(a

1P

VVa

1PP

++

+++++

++

−+=

⋅−−⋅−⋅+=

−⋅+=


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a rate of inflation of health expenses

oldx

newx

oldtx

newtx P)a1(PK)a1(K ⋅+=⇒⋅+= ++

oldmx

oldx

oldmx

newmx

oldx

newmx/x

PaP

PPPP

+

+++

⋅+=

−+=


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Private Health Insurance (Full Coverage)Usage of Profits

• Reimbursement of at least 80% of the profits– refund of premium (persons without claims)– mitigation of premium rises

• Reimbursement of 90% of the difference between calculated and occured interest rate– mitigation of premium rises in old age

IAAHS Colloquium 2004actuaries.org/IAAHS/Colloquia/Dresden/Richter presentation.pdf29.04.2004...

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