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

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)

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

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

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

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

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)

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)

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

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

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

FIRST RESULTS DISABILITY FROM 11% TO 40%

FIRST RESULTS DISABILITY FROM 11% TO 40%

FIRST RESULTS DISABILITY FROM 11% TO 40%

FIRST RESULTS DISABILITY FROM 11% TO 40%

FIRST RESULTS DISABILITY FROM 11% TO 40%

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

update observed mortality tables (2004) THE NEW PRESENT VALUES Three steps: update observed mortality tables (2004) project mortality tables (2004-2030) change interest rate (from 4,5% to 2,5%)

INDUSTRIAL SECTOR >85% 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 OVER 40% 92.683 PENSIONS TO WORKERS WITH DISABILITY BETWEEN 11% AND 40% 534.810 >85% OF TOTAL INDUSTRIAL SECTOR PENSIONS

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

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

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

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

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

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

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

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

THE NEW PRESENT VALUES MAIN RESULTS

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

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

RESERVES INDUSTRIAL SECTOR ~ 65% WORK INJURES AND OCCUPATIONAL DISEASES RESERVES AMOUNT AT DEC 31th 2008 15.454 MILLION EURO RESERVES FOR ANNUITIES WITH DISABILITY >40% 5.439 RESERVES FOR ANNUITIES WITH DISABILITY BETWEEN 11% AND 40% 10.015 MILLION EURO ~ 65%

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

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