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

IAAHS Colloquium 2004 IAAHS Colloquium 2004 Actuarial Foundations of Full Coverage with Ageing Reserves in Germany 29.04.2004 Heinz-Werner Richter 1

German Health Insurance (Full Coverage) Statutory Health Insurance Private Health Insurance 2002 IAAHS Colloquium 2004 2002 • 71 million insured • 8 million insured • premium income € 132 • premium income € 16 billion billion • premium income € 5 billion • 8 million insured with privat supplementary coverage 29.04.2004 Heinz-Werner Richter 2

German Health Insurance (Full Coverage) Insured Persons Private Health Insurance Statutory Health Insurance IAAHS Colloquium 2004 • employees with a salary • compulsory : employees exceeding a certain limit with a salary under a • pensioners certain limit • self-employed persons (€ 3825 in 2003) • civil servants • pensioners • their families • voluntary members • „once private, ever private“ • their families (if their (return only possible in income can be neglected) exceptional cases) 29.04.2004 Heinz-Werner Richter 3

German Health Insurance (Full Coverage) Main Requirements Statutory Health Insurance Private Health Insurance IAAHS Colloquium 2004 • non-standardized coverage • standardized coverage – „substitutive health insurance“ • acceptance of each = similarity to the statutory applicant insurance – different tariffs • possibility to change the – deductibles coverage by law • lifelong insurance guarantee • managed by about 400 • managed by about 50 health health insurance funds insurance companies, which (under public law) are either stock companies or mutuals 29.04.2004 Heinz-Werner Richter 4

German Health Insurance (Full Coverage) Contributions Private Health Insurance Statutory Health Insurance IAAHS Colloquium 2004 • premium depending on • percentage of the salary coverage (tariff), sex, entry respectively the social age and insurance pension (up to • physical condition at the time a certain limit) of application • contribution-free: family – extra premium or members – exclusion rider • one half by the employee, • one half by the employer (up to the defined limit) one half by the employer 29.04.2004 Heinz-Werner Richter 5

Statutory Health Insurance Premiums and Loss Expenses per Capita Source: Prof. Bernd Raffelhueschen (Universität Freiburg und Universität Bergen, Norwegen) IAAHS Colloquium 2004 29.04.2004 Heinz-Werner Richter 6

Private Health Insurance (Full Coverage) Further Requirements • Lifelong insurance garantee IAAHS Colloquium 2004 – 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 of health expenses – cautious calculation assumptions • The right of tariff switch • Equal bases of calculation for old and new customers 29.04.2004 Heinz-Werner Richter 7

Private Health Insurance (Full Coverage) Calculation Requirements • The premiums have to be calculated individually. IAAHS Colloquium 2004 • 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 – ... 29.04.2004 Heinz-Werner Richter 8

Private Health Insurance (Full Coverage) Calculation ? x age (end: ) IAAHS Colloquium 2004 i interest rate (max. 3.5 %) q x mortality rate w x lapse rate a x present value of an annuity − ? x 1 ∑ + = ⋅ x t a l v = ⋅ − − + l l ( 1 q w ) ⋅ x x t x l v + = x 1 x x x t 0 x − ? x 1 ∑ = 1 D = + v x t D + = t 0 1 i x 29.04.2004 Heinz-Werner Richter 9

Mortality Rates in Germany 0,300000 0,250000 IAAHS Colloquium 2004 0,200000 0,150000 0,100000 0,050000 0,000000 20 30 40 50 60 70 80 90 100 Age men women 29.04.2004 Heinz-Werner Richter 10

Average Lapse Rates in Germany (normal risks) 14,0000% 12,0000% IAAHS Colloquium 2004 10,0000% 8,0000% 6,0000% 4,0000% 2,0000% 0,0000% 20 30 40 50 60 70 80 90 100 Age men women 29.04.2004 Heinz-Werner Richter 11

Average Lapse Rates in Germany (civil servants) 7,0000% 6,0000% IAAHS Colloquium 2004 5,0000% 4,0000% 3,0000% 2,0000% 1,0000% 0,0000% 20 30 40 50 60 70 80 90 100 Age men women 29.04.2004 Heinz-Werner Richter 12

Private Health Insurance (Full Coverage) Calculation K x+t expected yearly loss expense at age x+t IAAHS Colloquium 2004 A x present value of loss expenses P x yearly net premium − ? x 1 ∑ + = ⋅ ⋅ x t A l v K A + + x x t x t ⋅ x P = l v x = t 0 x x − ? x a 1 ∑ = ⋅ D K x + + x t x t D = t 0 x 29.04.2004 Heinz-Werner Richter 13

Tariff with out- and inpatient medical treatment, dental care, drugs and appliances Expected Yearly Loss Expense for an Insured Person 9.000 8.000 IAAHS Colloquium 2004 7.000 6.000 5.000 € 4.000 3.000 2.000 1.000 0 20 30 40 50 60 70 80 90 100 Age men women 29.04.2004 Heinz-Werner Richter 14

Net premiums for the entry ages 21 and 40 Expected Yearly Loss Expense for an Insured Person 9.000 8.000 7.000 IAAHS Colloquium 2004 6.000 5.000 € 4.000 3.000 2.000 1.000 0 20 30 40 50 60 70 80 90 100 Age 29.04.2004 Heinz-Werner Richter 15

Private Health Insurance (Full Coverage) Calculation Loadings: IAAHS Colloquium 2004 • 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) 29.04.2004 Heinz-Werner Richter 16

Private Health Insurance (Full Coverage) The Reserve for Increasing Age IAAHS Colloquium 2004 = − ⋅ V A P a + + m x x m x x m [ ] = − ⋅ P P a + + x m x x m 29.04.2004 Heinz-Werner Richter 17

Ageeing reserves for the entry ages 21 and 40 80.000 70.000 IAAHS Colloquium 2004 60.000 50.000 € 40.000 30.000 20.000 10.000 0 20 30 40 50 60 70 80 90 100 Age 29.04.2004 Heinz-Werner Richter 18

Private Health Insurance (Full Coverage) Premium Adjustment • Yearly comparison of the assumed claims with the IAAHS Colloquium 2004 actually occured claims • Adjustment of the premiums, if deviation exceeds a certain limit. • Strongly regulated and supervised rules. 29.04.2004 Heinz-Werner Richter 19

Private Health Insurance (Full Coverage) Premium Adjustment „old“ / „new“ refer to the bases of calculation before IAAHS Colloquium 2004 and after a premium adjustment x+m age at the time of the adjustment [ ] 1 = + ⋅ − new new new old P P V V + x / x m x m x m x a + x m [ ] 1 = + ⋅ − ⋅ − − ⋅ new new new old old P ( P P ) a ( P P ) a + + + + x x m x x m x m x x m a + x m = + − old new old P P P + + x x m x m 29.04.2004 Heinz-Werner Richter 20

Private Health Insurance (Full Coverage) Premium Adjustment a rate of inflation of health expenses IAAHS Colloquium 2004 = + ⋅ ⇒ = + ⋅ new old new old K ( 1 a ) K P ( 1 a ) P + + x t x t x x = + − new old new old P P P P + + + x / x m x x m x m = + ⋅ old old P a P + x x m 29.04.2004 Heinz-Werner Richter 21

Private Health Insurance (Full Coverage) Usage of Profits • Reimbursement of at least 80% of the profits IAAHS Colloquium 2004 – 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 29.04.2004 Heinz-Werner Richter 22