[PPT] - IAAHS Colloquium 2004 IAAHS Colloquium 2004 Actuarial Foundations PowerPoint Presentation

SLIDE 1

29.04.2004 Heinz-Werner Richter 1

IAAHS Colloquium 2004

IAAHS Colloquium 2004 Actuarial Foundations

f Full Coverage with

Ageing Reserves in Germany

SLIDE 2

29.04.2004 Heinz-Werner Richter 2

IAAHS Colloquium 2004

German 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

SLIDE 3

29.04.2004 Heinz-Werner Richter 3

IAAHS Colloquium 2004

German Health Insurance (Full Coverage) Insured Persons

Statutory Health Insurance

compulsory: employees

with a salary under a certain limit

(€ 3825 in 2003)

pensioners
voluntary members
their families (if their

income can be neglected) Private Health Insurance

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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29.04.2004 Heinz-Werner Richter 4

IAAHS Colloquium 2004

German Health Insurance (Full Coverage) Main Requirements

Statutory Health Insurance

standardized coverage
acceptance of each

applicant

possibility to change the

coverage by law

managed by about 400

health insurance funds (under public law) Private Health Insurance

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

r mutuals

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29.04.2004 Heinz-Werner Richter 5

IAAHS Colloquium 2004

German Health Insurance (Full Coverage) Contributions

Statutory Health Insurance

percentage of the salary

respectively the social insurance pension (up to a certain limit)

contribution-free: family

members

one half by the employee,
ne half by the employer

Private Health Insurance

premium depending on

coverage (tariff), sex, entry age and

physical condition at the time
f application

– extra premium or – exclusion rider

one half by the employer (up

to the defined limit)

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29.04.2004 Heinz-Werner Richter 6

IAAHS Colloquium 2004

Statutory Health Insurance Premiums and Loss Expenses per Capita

Source: Prof. Bernd Raffelhueschen (Universität Freiburg und Universität Bergen, Norwegen)

SLIDE 7

29.04.2004 Heinz-Werner Richter 7

IAAHS Colloquium 2004

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 increase

f health expenses

– cautious calculation assumptions

The right of tariff switch
Equal bases of calculation for old and new customers

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29.04.2004 Heinz-Werner Richter 8

IAAHS Colloquium 2004

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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29.04.2004 Heinz-Werner Richter 9

IAAHS Colloquium 2004

Private Health Insurance (Full Coverage) Calculation

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

) w q 1 ( l l

x x x 1 x

− − ⋅ =

+

i 1 1 v + = ?

∑ ∑

− = + − = + +

= ⋅ ⋅ =

x ? t t x x x ? t t x t x x x x

D D 1 v l v l 1 a

SLIDE 10

29.04.2004 Heinz-Werner Richter 10

IAAHS Colloquium 2004

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

SLIDE 11

29.04.2004 Heinz-Werner Richter 11

IAAHS Colloquium 2004

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

SLIDE 12

29.04.2004 Heinz-Werner Richter 12

IAAHS Colloquium 2004

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

SLIDE 13

29.04.2004 Heinz-Werner Richter 13

IAAHS Colloquium 2004

Private Health Insurance (Full Coverage) Calculation

Kx+t expected yearly loss expense at age x+t Ax present value of loss expenses Px yearly net premium

∑ ∑

− = + + − = + + +

⋅ = ⋅ ⋅ ⋅ =

x ? t t x t x x x ? t t x t x t x x x x

K D D 1 K v l v l 1 A

x x x

a A P =

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29.04.2004 Heinz-Werner Richter 14

IAAHS Colloquium 2004

Expected Yearly Loss Expense for an Insured Person

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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29.04.2004 Heinz-Werner Richter 15

IAAHS Colloquium 2004

Expected Yearly Loss Expense for an Insured Person

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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29.04.2004 Heinz-Werner Richter 16

IAAHS Colloquium 2004

Private Health Insurance (Full Coverage) Calculation

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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29.04.2004 Heinz-Werner Richter 17

IAAHS Colloquium 2004

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

[ ]

m x x m x m x x m x x m

a P P a P A V

+ + + +

⋅ − = ⋅ − =

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29.04.2004 Heinz-Werner Richter 18

IAAHS Colloquium 2004

Ageeing reserves for the entry ages 21 and 40

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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29.04.2004 Heinz-Werner Richter 19

IAAHS Colloquium 2004

Private Health Insurance (Full Coverage) Premium Adjustment

Yearly comparison of the assumed claims with the

actually occured claims

Adjustment of the premiums, if deviation exceeds a

certain limit.

Strongly regulated and supervised rules.

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29.04.2004 Heinz-Werner Richter 20

IAAHS Colloquium 2004

Private Health Insurance (Full Coverage) Premium Adjustment

„old“ / „new“ refer to the bases of calculation before and after a premium adjustment x+m age at the time of the adjustment

[ ] [ ]

ld

m x new m x

ld

x m x

ld

x

ld

m x m x new x new m x m x new x

ld

x m new x m m x new x new m x / x

P P P a ) P P ( a ) P P ( a 1 P V V a 1 P P

+ + + + + + + + +

− + = ⋅ − − ⋅ − ⋅ + = − ⋅ + =

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29.04.2004 Heinz-Werner Richter 21

IAAHS Colloquium 2004

Private Health Insurance (Full Coverage) Premium Adjustment

a rate of inflation of health expenses

ld

x new x

ld

t x new t x

P ) a 1 ( P K ) a 1 ( K ⋅ + = ⇒ ⋅ + =

+ +

ld

m x

ld

x

ld

m x new m x

ld

x new m x / x

P a P P P P P

+ + + +

⋅ + = − + =

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29.04.2004 Heinz-Werner Richter 22

IAAHS Colloquium 2004

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