1. PRESENT VALUES AND RESERVES: WHAT IF WE PROJECT MORTALITY?
Raffaello Marcelloni

2. Assicurazioni contro gli Infortuni sul Lavoro
I.N.A.I.L.
Istituto
Nazionale per le
Assicurazioni contro gli
Infortuni sul
Lavoro
(National Employment Accident Insurance Institute)

3. INAIL’s disabled mortality tables:
WHY PROJECTED MORTALITY TABLES?
INAIL’s disabled mortality tables:
Normative Referencies
A brief history

4. 1938 first INAIL tables based on the Italian population
WHY PROJECTED MORTALITY TABLES?
1938 first INAIL tables based on the Italian population
… 24 years …
1962 based on disabled workers population
… 22 years …
1984
… 16 years …
2000
… 8 years …
2008 disabled workers’ projected mortality tables

5. The current demographic panorama The longevity risk
WHY PROJECTED MORTALITY TABLES?
The current demographic panorama
The longevity risk
The projected mortality tables

6. DISABLED WORKERS VS ITALIAN POPULATION
WHY PROJECTED MORTALITY TABLES?
DISABLED WORKERS VS ITALIAN POPULATION
MORTALITY RATES AT AGE 60

7. WHY PROJECTED MORTALITY TABLES?
Observed mortality table
Reached age t
q(0,t) 1
q(1,t) 2
q(2,t) … x
q(x,t)
x+1
q(x+1,t)
x+2
q(x+2,t)
ω-2
q(ω-2,t)
ω-1
q(ω-1,t)

8. WHY PROJECTED MORTALITY TABLES?
Observed mortality table
Projected mortality table
Reached age t
q(0,t) 1
q(1,t) 2
q(2,t) … x
q(x,t)
x+1
q(x+1,t)
x+2
q(x+2,t)
ω-2
q(ω-2,t)
ω-1
q(ω-1,t)
YEARS OF PROJECTION
t+1
t+2 …
t+n-1
t+n
q(0,t+1)
q(0,t+2)
q(0,t+n-1)
q(0,t+n)
q(1,t+1)
q(1,t+2)
q(1,t+n-1)
q(1,t+n)
q(2,t+1)
q(2,t+2)
q(2,t+n-1)
q(2,t+n)
q(x,t+1)
q(x,t+2)
q(x,t+n-1)
q(x,t+n)
q(x+1,t+1)
q(x+1,t+2)
q(x+1,t+n-1)
q(x+1,t+n)
q(x+2,t+1)
q(x+2,t+2)
q(x+2,t+n-1)
q(x+2,t+n)
q(ω-2,t+1)
q(ω-2,t+2)
q(ω-2,t+n-1)
q(ω-2,t+n)
q(ω-1,t+1)
q(ω-1,t+2)
q(ω-1,t+n-1)
q(ω-1,t+n)

9. THE NEW INAIL’S PROJECTED MORTALITY TABLES
The Lee-Carter model

10. THE EVOLUTIONARY TREND OF THE SURVIVAL LAW
WITHIN THE PROJECTION PERIOD
DISABILITY FROM 11% TO 40%

11. HOW MUCH THE PROBABILITY OF DEATH
FIRST RESULTS
HOW MUCH THE PROBABILITY OF DEATH
WILL DECREASE?

12. FIRST RESULTS
DISABILITY FROM 11% TO 40%

13. FIRST RESULTS
DISABILITY FROM 11% TO 40%

14. FIRST RESULTS
DISABILITY FROM 11% TO 40%

15. FIRST RESULTS
DISABILITY FROM 11% TO 40%

16. FIRST RESULTS
DISABILITY FROM 11% TO 40%

17. The present value structure depends on: probability of death
THE NEW PRESENT VALUES
The present value structure depends on:
probability of death
rate of interest

18. update observed mortality tables (2004)
THE NEW PRESENT VALUES
Three steps:
update observed mortality tables (2004)
project mortality tables ( )
change interest rate (from 4,5% to 2,5%)

19. INDUSTRIAL SECTOR >85%
THE NEW PRESENT VALUES
INDUSTRIAL SECTOR
WORK INJURES AND OCCUPATIONAL DISEASES
AVERAGE NUMBER OF PENSIONS PAID MONTLY IN 2008
PENSIONS TO WORKERS WITH
DISABILITY
OVER 40%
92.683
PENSIONS TO WORKERS WITH
DISABILITY BETWEEN
11% AND 40%
>85%
OF TOTAL INDUSTRIAL SECTOR PENSIONS

20. OLD PRESENT VALUES AT SOME AGES
THE NEW PRESENT VALUES
NEW PRESENT VALUES VS
OLD PRESENT VALUES AT SOME AGES

21. OLD PRESENT VALUES AT SOME AGES
THE NEW PRESENT VALUES
NEW PRESENT VALUES VS
OLD PRESENT VALUES AT SOME AGES

22. THE NEW PRESENT VALUES UPDATED MORTALITY FIRST STEP: NO PROJECTION
INTEREST RATE = 4,5%

23. THE NEW PRESENT VALUES UPDATED MORTALITY FIRST STEP: NO PROJECTION
INTEREST RATE = 4,5%

24. THE NEW PRESENT VALUES PROJECTION SECOND STEP: UPDATED MORTALITY
INTEREST RATE = 4,5%

25. THE NEW PRESENT VALUES PROJECTION SECOND STEP: UPDATED MORTALITY
INTEREST RATE = 4,5%

26. THE NEW PRESENT VALUES INTEREST RATE = 2,5% THIRD STEP:
UPDATED MORTALITY
PROJECTION
INTEREST RATE = 2,5%

27. THE NEW PRESENT VALUES INTEREST RATE = 2,5% THIRD STEP:
UPDATED MORTALITY
PROJECTION
INTEREST RATE = 2,5%

28. THE NEW PRESENT VALUES
MAIN RESULTS

29. COMPOSITION OF THE DEMOGRAPHIC VARIATION
THE NEW PRESENT VALUES
COMPOSITION OF THE DEMOGRAPHIC VARIATION

30. COMPOSITION OF THE TOTAL VARIATION
THE NEW PRESENT VALUES
COMPOSITION OF THE TOTAL VARIATION

31. RESERVES INDUSTRIAL SECTOR ~ 65%
WORK INJURES AND OCCUPATIONAL DISEASES
RESERVES AMOUNT AT DEC 31th 2008
MILLION EURO
RESERVES FOR ANNUITIES WITH DISABILITY
>40%
5.439
RESERVES FOR ANNUITIES WITH DISABILITY BETWEEN
11% AND 40%
MILLION EURO
~ 65%

32. WORK INJURES AND OCCUPATIONAL DISEASES
RESERVES
INDUSTRIAL SECTOR
WORK INJURES AND OCCUPATIONAL DISEASES

33. PRESENT VALUES AND RESERVES: WHAT IF WE PROJECT MORTALITY?
THANK YOU FOR YOUR ATTENTION
Raffaello Marcelloni
Actuary
Statistical and Actuarial Department
Istituto Nazionale per le Assicurazioni contro gli Infortuni sul Lavoro
I.N.A.I.L. - ITALY