PRESENT VALUES AND RESERVES WHAT IF WE PROJECT

I. N. A. I. L. Istituto Nazionale per le Assicurazioni contro gli Infortuni sul

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

WHY PROJECTED MORTALITY TABLES? Ø 1938 first INAIL tables based on the Italian population

WHY PROJECTED MORTALITY TABLES? • The current demographic panorama • The longevity risk •

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

WHY PROJECTED MORTALITY TABLES? Observed mortality table Reached age t 0 q(0, t) 1

WHY PROJECTED MORTALITY TABLES? Observed mortality table Projected mortality table YEARS OF PROJECTION Reached

THE NEW INAIL’S PROJECTED MORTALITY TABLES • The Lee-Carter model 9 Technical Seminar of

THE EVOLUTIONARY TREND OF THE SURVIVAL LAW WITHIN THE PROJECTION PERIOD DISABILITY FROM 11%

FIRST RESULTS HOW MUCH THE PROBABILITY OF DEATH WILL DECREASE? 11 Technical Seminar of

FIRST RESULTS DISABILITY FROM 11% TO 40% 12 Technical Seminar of the ISSA Technical

FIRST RESULTS DISABILITY FROM 11% TO 40% 13 Technical Seminar of the ISSA Technical

FIRST RESULTS DISABILITY FROM 11% TO 40% 14 Technical Seminar of the ISSA Technical

FIRST RESULTS DISABILITY FROM 11% TO 40% 15 Technical Seminar of the ISSA Technical

FIRST RESULTS DISABILITY FROM 11% TO 40% 16 Technical Seminar of the ISSA Technical

THE NEW PRESENT VALUES The present value structure depends on: • probability of death

THE NEW PRESENT VALUES Three steps: 1. update observed mortality tables (2004) 2. project

THE NEW PRESENT VALUES INDUSTRIAL SECTOR WORK INJURES AND OCCUPATIONAL DISEASES AVERAGE NUMBER OF

THE NEW PRESENT VALUES VS OLD PRESENT VALUES AT SOME AGES 20 Technical Seminar

THE NEW PRESENT VALUES VS OLD PRESENT VALUES AT SOME AGES 21 Technical Seminar

THE NEW PRESENT VALUES FIRST STEP: • UPDATED MORTALITY • NO PROJECTION • INTEREST

THE NEW PRESENT VALUES SECOND STEP: • UPDATED MORTALITY • PROJECTION • INTEREST RATE

THE NEW PRESENT VALUES THIRD STEP: • UPDATED MORTALITY • PROJECTION • INTEREST RATE

THE NEW PRESENT VALUES MAIN RESULTS 28 Technical Seminar of the ISSA Technical Commission

THE NEW PRESENT VALUES COMPOSITION OF THE DEMOGRAPHIC VARIATION 29 Technical Seminar of the

THE NEW PRESENT VALUES COMPOSITION OF THE TOTAL VARIATION 30 Technical Seminar of the

RESERVES INDUSTRIAL SECTOR WORK INJURES AND OCCUPATIONAL DISEASES RESERVES AMOUNT AT DEC 31 th

RESERVES INDUSTRIAL SECTOR WORK INJURES AND OCCUPATIONAL DISEASES 32 Technical Seminar of the ISSA

PRESENT VALUES AND RESERVES: WHAT IF WE PROJECT MORTALITY? THANK YOU FOR YOUR ATTENTION

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

I. N. A. I. L. Istituto Nazionale per le Assicurazioni contro gli Infortuni sul Lavoro (National Employment Accident Insurance Institute) 2 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. –April 27 -28, 2010

WHY PROJECTED MORTALITY TABLES? • INAIL’s disabled mortality tables: Normative Referencies A brief history 3 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. –April 27 -28, 2010

WHY PROJECTED MORTALITY TABLES? Ø 1938 first INAIL tables based on the Italian population … 24 years … Ø 1962 based on disabled workers population … 22 years … Ø 1984 … 16 years … Ø 2000 … 8 years … Ø 2008 disabled workers’ projected mortality tables 4 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. –April 27 -28, 2010

WHY PROJECTED MORTALITY TABLES? • The current demographic panorama • The longevity risk • The projected mortality tables 5 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. –April 27 -28, 2010

WHY PROJECTED MORTALITY TABLES? DISABLED WORKERS VS ITALIAN POPULATION MORTALITY RATES AT AGE 60 6 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. –April 27 -28, 2010

WHY PROJECTED MORTALITY TABLES? Observed mortality table Reached age t 0 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) 7 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. –April 27 -28, 2010

WHY PROJECTED MORTALITY TABLES? Observed mortality table Projected mortality table YEARS OF PROJECTION Reached age t t+1 t+2 … t+n-1 t+n 0 q(0, t) q(0, t+1) q(0, t+2) … q(0, t+n-1) q(0, t+n) 1 q(1, t) q(1, t+1) q(1, t+2) … q(1, t+n-1) q(1, t+n) 2 q(2, t) q(2, t+1) q(2, t+2) … q(2, t+n-1) q(2, t+n) … … … … x q(x, t) x+1 q(x+1, t) q(x, t+1) q(x, t+2) … q(x, t+n-1) q(x, t+n) x+2 q(x+2, t) 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) ω-2 q(ω-2, t) … … … ω-1 q(ω-1, t) 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) 8 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. –April 27 -28, 2010

THE NEW INAIL’S PROJECTED MORTALITY TABLES • The Lee-Carter model 9 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. –April 27 -28, 2010

THE EVOLUTIONARY TREND OF THE SURVIVAL LAW WITHIN THE PROJECTION PERIOD DISABILITY FROM 11% TO 40% 10 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. –April 27 -28, 2010

FIRST RESULTS HOW MUCH THE PROBABILITY OF DEATH WILL DECREASE? 11 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. –April 27 -28, 2010

FIRST RESULTS DISABILITY FROM 11% TO 40% 12 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. –April 27 -28, 2010

FIRST RESULTS DISABILITY FROM 11% TO 40% 13 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. –April 27 -28, 2010

FIRST RESULTS DISABILITY FROM 11% TO 40% 14 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. –April 27 -28, 2010

FIRST RESULTS DISABILITY FROM 11% TO 40% 15 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. –April 27 -28, 2010

FIRST RESULTS DISABILITY FROM 11% TO 40% 16 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. –April 27 -28, 2010

THE NEW PRESENT VALUES The present value structure depends on: • probability of death • rate of interest 17 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. –April 27 -28, 2010

THE NEW PRESENT VALUES Three steps: 1. update observed mortality tables (2004) 2. project mortality tables (2004 -2030) 3. change interest rate (from 4, 5% to 2, 5%) 18 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. –April 27 -28, 2010

THE NEW PRESENT VALUES INDUSTRIAL SECTOR WORK INJURES AND OCCUPATIONAL DISEASES AVERAGE NUMBER OF PENSIONS PAID MONTLY IN 2008 627. 493 PENSIONS TO WORKERS WITH DISABILITY BETWEEN 11% AND 40% 534. 810 PENSIONS TO WORKERS WITH DISABILITY OVER 40% 92. 683 >85% OF TOTAL INDUSTRIAL SECTOR PENSIONS 19 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. –April 27 -28, 2010

THE NEW PRESENT VALUES VS OLD PRESENT VALUES AT SOME AGES 20 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. –April 27 -28, 2010

THE NEW PRESENT VALUES VS OLD PRESENT VALUES AT SOME AGES 21 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. –April 27 -28, 2010

THE NEW PRESENT VALUES FIRST STEP: • UPDATED MORTALITY • NO PROJECTION • INTEREST RATE = 4, 5% 22 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. –April 27 -28, 2010

THE NEW PRESENT VALUES FIRST STEP: • UPDATED MORTALITY • NO PROJECTION • INTEREST RATE = 4, 5% 23 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. –April 27 -28, 2010

THE NEW PRESENT VALUES SECOND STEP: • UPDATED MORTALITY • PROJECTION • INTEREST RATE = 4, 5% 24 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. –April 27 -28, 2010

THE NEW PRESENT VALUES SECOND STEP: • UPDATED MORTALITY • PROJECTION • INTEREST RATE = 4, 5% 25 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. –April 27 -28, 2010

THE NEW PRESENT VALUES THIRD STEP: • UPDATED MORTALITY • PROJECTION • INTEREST RATE = 2, 5% 26 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. –April 27 -28, 2010

THE NEW PRESENT VALUES THIRD STEP: • UPDATED MORTALITY • PROJECTION • INTEREST RATE = 2, 5% 27 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. –April 27 -28, 2010

THE NEW PRESENT VALUES MAIN RESULTS 28 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. –April 27 -28, 2010

THE NEW PRESENT VALUES COMPOSITION OF THE DEMOGRAPHIC VARIATION 29 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. –April 27 -28, 2010

THE NEW PRESENT VALUES COMPOSITION OF THE TOTAL VARIATION 30 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. –April 27 -28, 2010

RESERVES INDUSTRIAL SECTOR WORK INJURES AND OCCUPATIONAL DISEASES RESERVES AMOUNT AT DEC 31 th 2008 15. 454 MILLION EURO RESERVES FOR ANNUITIES WITH DISABILITY BETWEEN 11% AND 40% 10. 015 MILLION EURO RESERVES FOR ANNUITIES WITH DISABILITY >40% 5. 439 ~ 65% 31 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. –April 27 -28, 2010

RESERVES INDUSTRIAL SECTOR WORK INJURES AND OCCUPATIONAL DISEASES 32 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. –April 27 -28, 2010

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 e-mail: r. marcelloni@inail. it 33 Technical Seminar of the ISSA Technical Commission of Statistical, Actuarial and Financial Studies Montevideo, Uruguay. –April 27 -28, 2010