Actuarial analysis in Social Security by Hikmet TAGIYEV

1. Azerbaijan Republic
Khazar University
MBA THESIS
“Actuarial analysis in social security”
MBA Thesis Presentation for the Master Degree at Khazar University, on 14th December
School : Economics & Management
Student: Hikmet Tagiyev Sakhavet
Supervisor : Dr.Oktay Ibrahimov Vahib
Baku 2007

2. Research Objectives
 Theoretical:
- To identify economic criteria for analyzing social security systems and
pension reform, in the context of population aging
 Empirical:
- To quantify the effects of demography + pension systems + pension
reforms on future poverty + inequality, for aging countries
- To develop simulation tool for theory validation and policy making

3. Aging
• Population Aging = lower mortality + lower fertility + higher life
expectancy
• By 2050, in EU:
 proportion of +65 projected to double
 average projected increase in dependency ratios (Old /
Young, Pensioners / Workers) from 24% to 49%
 average projected increase in retirement years
 average projected increase in pension expenditure by 3-5 %

4. What Future ?
• Future welfare of pensioners will depend on complex interactions
between Demography + Labour + Pension System.
– Aging can affect sustainability / efficiency of a Pension
System
– Pension System can also induce behavioural changes e.g.
increased retirement age which can counterbalance
demographic effects
• Economic consequences of Aging and Pension System need to be
analysed together  net effects.
• We need a model for net effects  what pension system is better
to address consequences of aging?

5. Our Questions…
1. How much protection can be provided with a given level of financial
resources?
2. What financial resources are necessary to provide given level of
protection?
3. Who will be covered? (Legal versus actual coverage)
4. What kind of benefit will be provided? (Benefit provisions )
5. What part of workers’ earnings will be subject to contributions and
used to compute benefits? (This refers to the floor and ceiling of
earnings adopted for the scheme.
6. What should be the earnings replacement rate in computing benefits?
7. Should the scheme allow for cross-subsidization between income
groups through the benefit formula?
8. What will be the required period of contribution as regards eligibility
for the various benefits?
9. What is the normal retirement age?
10. How should benefits be indexed?
11. Who pays and how much ? (Financing provisions)

6. What is an Actuary?
Better Definitions
• “One who analyzes the current financial implications of
future contingent events”
• “Actuaries put a price tag on future risks. They have
been called financial architects and social
mathematicians, because their unique combination of
analytical and business skills is helping to solve a
growing variety of financial and social problems.”

7. The Actuarial Science
Research Triangle
Mathematics
Fuzzy Set Stochastic Calculus /
Theory Ito’s Lemma
Markov Chain Financial Mathematics
Monte Carlo Theory Interest
of Risk Theory
Chaos Theory /
Fractals
Dynamic Interest
Financial Rate
Actuarial Analysis Modeling
Finance
Science Portfolio Contingent
Theory Claims
Analysis

8. Principles and techniques of actuarial analysis
1 –The projection technique - The actuarial analysis starts with a
comparison of the scheme’s actual demographic and financial
experience against the projections.
2 –The present value technique - This technique considers one cohort
of insured persons at a time and computes the probable present values of
the future insured salaries, on the one hand and of the pension benefits
payable to the members of the cohort and to their survivors, on the other.

9. The demographic projection technique (1)
The first step in the projection technique is the demographic projections, production
of estimates of numbers of individuals in each of the principal population subgroups
(active insured persons -A(t), retirees-R(t), invalids-I(t), widows/widowers- W(t),
orphans –O(t) at discrete time-points (t=1,2,..),starting from given initial values (at t=0).
The demographic projection procedure can be regarded as the iteration of a matrix
multiplication operation, typified as follows :
nt = nt −1 ⋅ Qt −1
in which is a row vector whose elements represent the demographic projection values
at time t and is a square matrix of transition probabilities for the interval (t-1, t) which
take the form:
 p (aa) q (ar) q (ai) q (aw) q (ao) 
 (rr) 
0 p 0 q (rw) q (ro) 
nt = [ A(t) R(t) I(t) W(t) O(t)] Qt = 0 0 p (ii) q (iw) q (io) 
 
0 0 0 p (ww)
0 
 (oo)

0
 0 0 0 p 


10. The demographic projection technique (2)
The elements of the matrix and the symbols have the following significance:
p (aa) , p (rr) ,... denotes the probability of remaining in the same r;
q (ar) , q (ai) , q (aw) , q (ao) ,... denotes the probability of transition from status a to
status r, i, w, o ;
a, r , i , w and o respectively represent active lives , retirees, invalids,
widows/widowers and orphans .

11. The demographic projection technique (3)
For carrying out the demographic projections it is necessary to adopt an actuarial basis, consisting
of the elements listed below:
The active table : a
lx , b ≤ x ≤ r
where b is the youngest entry age and the r the highest retirement age. The associated dependent
a
rates of decrement are denoted by q x (mortality) and ix (invalidity). Retirement is assumed to take
place at exact integral ages, just before each birthday, rx denoting the proportion retiring at age x.
The following expressions for the age and sex – specific one year transition probabilities are based
on the rules of addition and multiplication of probabilities:
a) Active to active : p (aa) = (1 - q a - i x ) ⋅ (1 - rx +1 )
x x
b) Active to retiree q (ar) = (1 - q a - i x ) ⋅ rx +1
x x
c) Active to invalid q (ai) = (1 - 0,5 ⋅ q ix ) ⋅ i x
x

12. The demographic projection technique (4)
We can also analyze below tables:
• The life table for invalids lx , b ≤ x < D
i
• The life table for retired persons l xp , r ≤ x < D
• The table for widows/widowers l y , y* ≤ y ≤ D
w
• The table for orphans l zo , 0 ≤ z ≤ z *
where b is the youngest entry age ; r the highest retirement age; D the death
age; y* the lowest age of a widow /widower ; z* the age limit for orphans’
pensions

13. The demographic projection technique (5)
Starting from the population data on the date of the valuation (t=0), the transition probabilities are
applied to successive projections by sex and age. The projection formula for the active insured
populations are given below, the method of projecting the beneficiary populations is illustrated with
reference retirement pensioners.
• Act(x, s, t) – denotes the active population aged x nearest birthday , with curtate past service duration s
years at time t ;
• Ac(x, t),Re(x, t) –denotes the active and beneficiary population aged x nearest birthday at
time t
• A(t), R(t) – denotes the total active and beneficiary population at time t
The projection of the total active and beneficiary populations from time t-1 to time t is expressed by
the equation:
r
A(t ) = ∑∑ Act ( x, s, t ) + Act ( x-1,s-1,t-1) ⋅ ( p (aa) − q xar ) − q xai ) − q xaw) − q x )
x-1
( ( ( a
x =b s > 0
D
R (t ) = ∑ Ac(x − 1,t − 1) ⋅ q (ar) + Re(x − 1,t − 1) ⋅ (p (rr) − q x )
x −1 x −1
r
x=r

14. The financial projection technique (1)
The basis for the financial projections would comprise assumptions in regard to
the following elements. They are specified as functions of age or time, the age
related elements should be understood to be sex specific and may be further
varied over time, if necessary.
• ss(x,t) : The age –related salary scale function aged x at time t
• b(x,t) : The factor average per capita pension amount of the pensioners aged
x at time t
• γt: The rate of salary escalation (increase) in each projection year
• β : The rate of pension indexation in each projection year
t
• dc(x) : The contribution density, that is, the fraction of the year during which
contributions are effectively payable

15. The financial projection technique (2)
The average salary at age x in projection year t is then computed by the formula
∑ ∑ Ac(y,t)
r −1 r −1
s(y,t −1) ⋅ Ac(y,t −1)
s(x,t) = ss(x,t) ⋅(1 +γ ) ⋅ b
⋅ b
∑ ∑ Ac(y,t −1)
t r −1 r −1
b
ss(y,t) ⋅ Ac(y,t) b
The total insured salary bill at time t would be estimated as:
S (t ) = ∑ Ac( x, t ) ⋅ s ( x, t ) ⋅ dc( x)
x
The total pension amount at time t would be estimated as:
P (t ) = ∑ Re( x, t ) ⋅ b( x − 1, t − 1) ⋅ (1 + β t )
x
where Ac(x,t) and Re(x,t) denotes the projected active and beneficiary population
aged x at time t.

16. The present value technique
• This technique considers one cohort of insured persons at a time and computes
the probable present values of the future insured salaries, on the one hand and of
the pension benefits payable to the members of the cohort and to their survivors,
on the other.
• The present value formulae will be developed for the simple case where the
pension accrues at 1percent of the final salary per year of service.
• A series (sex-specific) special commutation functions are needed for applying
the present value technique. Functions based on the Life table will be computed
at interest rate i, while those based on the other tables will be computed at rate j.
• A life table is a mathematical construction that shows the number of people
alive (based on the assumptions used to build the table) at a given age, or other
probabilities associated with such a construct.

17. Life Table based actuarial calculations
i = 12%
Age(x) lx qx px dx Vx Dx Nx Sx Cx Mx äx Ax
1/(1+i)x x
V * lx DX NX
x+1
V * dx CX Nx/Dx Mx/Dx
0 100 000 0,028500 0,971500 2 850 1,000000 100000,0 582 185,56 3 462 212,27 2 375,00 2 969,07 5,82 0,05
1 97 150 0,002386 0,997614 232 0,833333 80958,3 482 185,56 2 880 026,71 160,99 594,07 5,96 0,03
2 96 918 0,002386 0,997614 231 0,694444 67304,3 401 227,22 2 397 841,15 133,84 433,08 5,96 0,02
18 95 755 0,000619 0,999381 59 0,037561 3596,7 21 469,75 127 772,27 1,85 18,37 5,97 0,05
19 95 696 0,000689 0,999311 66 0,031301 2995,4 17 873,09 106 302,52 1,72 16,52 5,97 0,05
20 95 630 0,000759 0,999241 73 0,026084 2494,4 14 877,72 88 429,44 1,58 14,80 5,96 0,06
60 78 273 0,018944 0,981056 1 483 0,000018 1,4 7,34 37,16 0,02 0,17 5,28 0,82
99 940,2 0,288432 0,711568 271 0,000000 0,0 0,00 0,01 0,00 0,00 66,84 76,43
100 669 1,000000 0,000000 669 0,000000 0,0 0,00 0,01 0,00 0,00 113,71 149,49
: is the number of people alive, relative to an original cohort, at age x.
: shows the number of people who die between age x and age x + 1
: is the probability of death between the ages of x and age x + 1.
: is the probability of a life age x surviving to age x + 1.
: is a discount factor used to obtain the amount of money that must be
invested now in order to have a given amount of money in the future. For example if
you need 1 in one year then the amount of money you need now is: If you need
25 in 5 years the amount of money you need now is:

18. Life Table based actuarial calculations
i = 12%
Age(x) lx qx px dx Vx Dx Nx Sx Cx Mx äx Ax
1/(1+i)x x
V * lx DX NX
x+1
V * dx CX Nx/Dx Mx/Dx
0 100 000 0,028500 0,971500 2 850 1,000000 100000,0 582 185,56 3 462 212,27 2 375,00 2 969,07 5,82 0,05
1 97 150 0,002386 0,997614 232 0,833333 80958,3 482 185,56 2 880 026,71 160,99 594,07 5,96 0,03
2 96 918 0,002386 0,997614 231 0,694444 67304,3 401 227,22 2 397 841,15 133,84 433,08 5,96 0,02
18 95 755 0,000619 0,999381 59 0,037561 3596,7 21 469,75 127 772,27 1,85 18,37 5,97 0,05
19 95 696 0,000689 0,999311 66 0,031301 2995,4 17 873,09 106 302,52 1,72 16,52 5,97 0,05
20 95 630 0,000759 0,999241 73 0,026084 2494,4 14 877,72 88 429,44 1,58 14,80 5,96 0,06
60 78 273 0,018944 0,981056 1 483 0,000018 1,4 7,34 37,16 0,02 0,17 5,28 0,82
99 940,2 0,288432 0,711568 271 0,000000 0,0 0,00 0,01 0,00 0,00 66,84 76,43
100 669 1,000000 0,000000 669 0,000000 0,0 0,00 0,01 0,00 0,00 113,71 149,49
Special commutation functions based on the active and retirees table
D x = x ⋅v x
a
la Dxp = l xp ⋅ v x
∑
D
D x =D x ⋅s x
as a
− p Dtp + Dtp 1
+
Nx = t =r
− as D as
+ D as
− p
2
Dx = x x+ 1
− p
2 Nx
− as r−1 − ax =
D xp
N x =∑D
t=x
t
as
where b is the youngest entry age ; r the highest retirement age;sx the age related
salary scale function; .. indicates a life insurance benefit of 1 payable at the end
of the year of death; a x indicates an annuity of 1 unit per year payable at the start of
each year until death to someone currently age x .

19. Present values of insured salaries and benefits
• Present value of insured salaries ( b ≤ x < r )
− as − as
N x −N r
PVS(x) = as
Dx
• Present value of retirement pensions
Dras _p
PVR(x) = p (r , x) as a r
Dx
where p (r, x) denotes the retirement pension of the cohort aged x as a
proportion of the final salary.

20. Macro-economic parameters in
actuarial calculations
The economic variables necessary to develop a suitable macroeconomic frame include :
• economic growth
• the separation of GDP between remuneration of workers and broadly, remuneration of
capital
• labour force, employment and unemployment
• wages
• inflation
• bank (interest) rate
• taxes and other consideritions.

21. The general frame for macroeconomic projections
Fertility
Initial general Projected general
Mortality
population population
Migration
Initial labor Future evaluation of Projected labor
force the participation rate force
Projected active Projected inactive
population population
Future evaluation
of GDP
Historical
•GDP Projected Projected
•Employment employment unemployment
•productivity
Future productivity
Source: International Labor Organization (2002).

22. Macro-economic parameters in
actuarial calculations
The financial projections of a social security scheme depend on:
• the number of people who will pay contributions to the scheme ;
• the average earnings of these contributors ;
• the number of people who will receive benefits;
• the amount of benefits that will be paid, related to past earnings and
possibly indexed;
• the investment earnings on the reserve.

23. Determination of the average wage in the economy
Labor force supply model
(projected active population)
Historical
•GDP
•Employment Future productivity
•productivity
Projected Projected
employment unemployment
Future evaluation
of GDP
Historical share
of wages in GDP
Projected total Projected
remuneration Average wage
Projected share
of wages in GDP
Historical total
remuneration
Source: International Labor Organization (2002).
 Wage distribution assumptions are needed to simulate the possible impact of the social
protection system on the distribution of income, for example, through minimum and maximum
pension provisions.
 Assumptions on the differentiation of wages by age and sex must then be established, as
well as assumptions on the dispersion of wages between income groups.

24. Types of Pension Systems
• Pension Pillars = Public + Private
• Each Pillar can vary in:
– Type of Benefit: Defined Benefit vs. Defined Contribution
– Degree of Actuarial Fairness: Non-Actuarial (DB) vs. Actuarial (DC)
– Type of Financing: Funded vs. Unfunded (Pay-as-you-go)
• A Pension System consists of a given combination along these 3 dimensions
• Pension Reform usually entails moving along any of these dimensions.
• Parametric Reforms:
– Changes to retirement age, replacement ratio (avg.pension/avg.wage), contribution
rate, indexing
• Systemic Reforms:
– Changes to system structure or financing of the system
• Moving to Funding
• Making benefit more actuarial (DC)
• “Multi-Pillar” Model (World Bank):
– 1st: Minimum State Pension (flat)
– 2nd: Mandatory Occupational Pension (funded)
– 3rd: Voluntary Private Pension Savings

25. Rate of Return and Internal Rate of Return
• Rate of return (ROR) comprises the proportional difference of what participant pay
as contribution and the amount he gets as pension. In this research we get the
following formula:
RORG+,1 = λt + ρt + λt ⋅ ρt = λt + ρt
t
A

Neglible
where ρ t : The growth rate of working generation. λt : Wage growth rate.
• Internal rate of return (IRR) is one of the most important money measures for
pension schemes promises and contracts. IRR is the rate that makes the present value
of future promised benefits equal to the present value of all injected contributions in
the system. Mathematically speaking, IRR is the discount rate (r) that solves the
following equation: LE
Bt RA
Crm ⋅ Ym
∑+1 (1 + r )t = m∑ (1 + r )m
t = RA = EA
t m
where Bt is the value of benefits at age t, RA represents the age at which the person retires,
LE life expectancy at the age of retirement, Crm: the contribution rate at age m, r: the discount
rate, Y is the level of income on which the contribution is based on and EA is the age at which
m
the pensioner starts his career.

26. The framework
Basic Inputs by year Base Line assumptions
Types of pension schemes
Impact of
• Population growth
• Interest rate
Pension Reform Illustrated Different scenarios
•Decline in fertility rate
Simulation Model (PRISM) #1, #2, #3, …..
•Increase in longevity
•Change in employment rates
•Increase in retirement age
Repeat it “lot of times”
With & Without the rule Aggregate sums, counts,
Contributions
Pension benefits (Average Gain & IRR)
Balance Ratio (assets & liabilities)
Analyse
& make your choice
Ready!

27. An Overview of the PRISM Model
• This model is a tool for illustrating the basic principles of pension-
system finance. The model is "stylized" -- it is not a model of a real
pension system, but rather a model of a very simple fictitious pension
system.
• The model can simulate defined benefit systems, defined contribution
systems, pay-as-you-go systems, capitalized systems, partially
capitalized systems, and mixed systems (defined benefit and defined
contribution).
• In this system, all individuals enter the labor market at age 20, work
continuously through age 59, retire at age 60, and die on their 80th
birthday.
• The system is launched in the year 1920. Thus, in 1920, only persons
who are 20 years old make contributions to the system. In 1960, the
first pensioners appear, retiring on their 60th birthday. In 1980, the first
cohort of pensioners reaches age 80, and they die. Thus, the system
requires 60 years to reach maturity.

28. Scenario 1.The impact of population growth on PAYG(DB) system
• Assume:
– promised benefit (RR) = 40% wage
– Contribution rate (CR) =10% wage .
– Population growth rate is 0%.
//The key mathematic idea is "internal-rate-of-return". The IRR is the interest rate
that equalizes the present value of a person's contributions with the present
value of their pensions. The sustainable IRR of a PAYG plan is equal to wage
growth (w) plus population growth (e).
• In this case, the IRR is 2.3% greater than wage growth. To sustain this
promised IRR, either population growth must be above a particular threshold.
Why?
• The IRR promised to participants is equal to wage growth plus 2.3%, and the
IRR that the system can afford to pay is equal to wage growth plus population
growth. Thus, population growth must be at least 2.3%.

29. Scenario 2.How is PAYG(DB) system affected by a decline in fertility rate
• Assume:
– promised benefit (RR) = 40% wage
– Contribution rate (CR) =10% wage .
– Population growth rate is 2.3%, but in 1990we assume that we assume that
birth rates decline such that the number of babies born each year remains
constant, rather than increasing at a rate of 2.3%.This change in birth rates
causes the entire population to stabilize such that it is neither growing.
• In this case, the IRR is 2.3% greater than wage growth. To sustain this
promised IRR, either population growth must be above a particular threshold.
Why?
• Begin by examining the ratio of the population above the age of 60 to the
population of ages 20 to 59 .Initially, this ratio is 25%, but beginning in the
year 2010 (20 years after the decrease of fertility rates), this ratio begins to
increase. By the year 2065, the ratio has increased to 50%. This dramatic
demographic change has a profound impact on the operation of the pension
system.
• Due to the demographic changes, a large deficit emerges in the long run:
contributions are merely 10% of wage bill, while expenditures are 20% of wage

30. Scenario 3.How is Funded system affected by a decline in fertility rate
• Assume:
– promised benefit (RR) = 40% wage
– Contribution rate (CR) =10% wage .
– Population growth rate is 2.3%, but in 1990we assume that we assume that
birth rates decline such that the number of babies born each year remains
constant, rather than increasing at a rate of 2.3%.This change in birth rates
causes the entire population to stabilize such that it is neither growing.
• Despite this dramatic demographic change, the pension system remains stable
throughout the simulation. This is clearly evident if we examine the ratio of the
system's assets to liabilities.
• This ratio remains constant at 100% throughout the simulation, implying that
the system is always fully funded, despite the demographic changes. How is
this possible?
• It is possible because we have assumed that the interest rate earned on the
system's assets is 2.3% -- precisely equal to the IRR that the system promises to its
participants. Therefore, growth of the system's assets will keep pace with growth
of the system's liabilities, regardless of changes in fertility rates.

31. Scenario 4.How is PAYG DB and Funded affected by an increase in longevity
• Assume:
– promised benefit (RR) = 40% wage
– Contribution rate (CR) =10% wage .
– Population growth rate is 2.3%, but in 1990 and 2030 we gradually increase
the post-retirement lifetime from 20 years to 24 years.
•The results are not surprising: deficits emerge as the post-retirement lifetime
increases, because pensions must be paid over a longer period.
• But in Funded system, when we increase longevity, participants receive
pension benefits for a longer period, which means the IRR promised to each
individual participant must increase. It is no longer 2.3%. Rather, the promised
IRR has increased to 2.7%.
• But the interest rate earned on the system's assets remains 2.3%. Therefore, the
system's assets are slowly depleted over time, because asset growth does not
keep pace with liability growth. In 2227, all assets will be depleted.

32. Scenario 4.How is PAYG DB affected by a retirement age increase
• Assume:
– promised benefit (RR) = 44% wage
– Contribution rate (CR) =10% wage .
– Population growth rate is 0%
• When considering the long-range effects of a retirement age will the retirement age change lead
to an increase or a decrease of the promised IRR?
• On the one hand, the retirement age increase will shorten the period over which individuals
receive their pensions, which will have a downward effect on the promised IRR.
•On the other hand, the retirement age change may lead to an increase in replacement rates, which
will have an upward effect on the promised IRR. The net effect of these two opposing forces will
depend, to a large extent, on the design of the benefit formula.
• Given these parameters, the promised IRR is equal to wage growth plus 0.3%. This means that
the system requires population growth of 0.3% per year to ensure long run balance between
contributions and expenditures. However, we have assumed population growth of 0%, and, as a
consequence, the system runs small deficits: contributions are equal to 20% of wage bill,
expenditures are equal to 22%, and the deficit is equal to 2% of wage bill.
• To eliminate these deficits, the Government raises the retirement age from 60 to 63. This
increases the replacement rate (because people work longer), but decreases the average period over
which people receive pensions. The net effect is to reduce the promised IRR from wage growth
plus 0.3% to wage growth minus 0.2%. Because population growth is greater than -0.2%, the
system runs small surpluses

33. Turkish Life Table based actuarial
calculations
Calculation of the value of the accrued liabilities
Assumptions male/female by age
1. Investment income (Inv) – 12%
2. Inflation rate (Inf.) - 0%
3- Technical rate of interest = (1+Inv)/ (1+inf.) -1
4- Survivor’s benefit: This liability is assumed to be a percentage of the liability for old age pension – 30%
Male Female
Age l(x) q(x) D(x) N(x) Age q(y) l(y) D(y) N(y)
20 99690 0,00170 99 690 299 540 20 0,00080 99 181 99 181 598 221
30 97843 0,00190 97 843 1 286 520 30 0,00120 98 207 98 207 2 571 677
40 95121 0,00330 95 121 2 251 294 40 0,00210 96 507 96 507 4 519 082
50 89443 0,00860 89 443 3 175 285 50 0,00480 92 950 92 950 6 414 988
55 83782 0,01390 83 782 3 606 541 55 0,00710 89 731 89 731 7 326 084
60 75150 0,02140 75 150 4 001 105 60 0,01150 84 948 84 948 8 196 467
65 63040 0,03280 63 040 4 341 912 65 0,01950 76 969 76 969 9 001 054
70 47310 0,05250 47 310 4 610 079 70 0,03490 65 768 65 768 9 707 327
80 16628 0,13010 16 628 4 906 129 80 0,10250 30 327 30 327 10 647 942
90 2003,4 0,27420 2 003 4 976 374 90 0,25040 4 941 4 941 10 936 890
100 0,0576 1,00000 0 4 980 095 100 1,00000 0 0 10 956 655

34. Some actuarial calculations with regards to the Turkish pension system
(Calculation of the value of the accrued liabilities)
Assumptions male/female by age
1. Investment income (Inv) – 12%
2. Inflation rate (Inf.) - 0%
3- Technical rate of interest = (1+Inv)/ (1+inf.) -1
4- Survivor’s benefit: This liability is assumed to be a percentage of the liability for old age pension – 30%
Mortality table used for males and females (All rates are per 1000 lives)
Male Female
Age l(x) q(x) D(x) N(x) Age q(y) l(y) D(y) N(y)
20 99690 0,00170 99 690 299 540 20 0,00080 99 181 99 181 598 221
30 97843 0,00190 97 843 1 286 520 30 0,00120 98 207 98 207 2 571 677
40 95121 0,00330 95 121 2 251 294 40 0,00210 96 507 96 507 4 519 082
50 89443 0,00860 89 443 3 175 285 50 0,00480 92 950 92 950 6 414 988
55 83782 0,01390 83 782 3 606 541 55 0,00710 89 731 89 731 7 326 084
60 75150 0,02140 75 150 4 001 105 60 0,01150 84 948 84 948 8 196 467
65 63040 0,03280 63 040 4 341 912 65 0,01950 76 969 76 969 9 001 054
70 47310 0,05250 47 310 4 610 079 70 0,03490 65 768 65 768 9 707 327
80 16628 0,13010 16 628 4 906 129 80 0,10250 30 327 30 327 10 647 942
90 2003,4 0,27420 2 003 4 976 374 90 0,25040 4 941 4 941 10 936 890
100 0,0576 1,00000 0 4 980 095 100 1,00000 0 0 10 956 655

35. Present value factors and Total actuarial liability
• Present value factors are calculated on the basis of the assumptions per unit of annual benefit.
Active Pensioner
Age Male Female Age Male Female
PV factor
Ret.Age (Nx/Dx) Ret. Age PV factor PV factor PV factor
20 57 0,84 55 1,20 20 15,25 15,56
30 52 2,59 49 3,74 30 14,61 15,04
40 47 7,70 48 7,73 40 13,48 14,16
50 53 8,97 57 7,00 50 11,76 12,75
60 70 2,66 68 4,43 60 9,56 10,63
65 74 2,15 74 2,82 65 8,29 9,30
70 80 1,05 81 1,20 70 6,97 7,85
80 80 4,71 92 0,10 80 4,71 5,26
90 90 2,62 92 1,04 90 2,62 2,74
100 100 100
• Liabilities are calculated on the basis of the present value factors and the total pension (old age, mortality,
survivors) amount by sex and age. If the interest rate increases, then total liability will be decrease.
TOTAL LIABILITY PER 31-12-2001 IN TL 1.000.000
Technıcal ınterest rate 0% % 6% % 12% %
Actıve insureds 346 030 144 765 69% 65 450 816 224 89% 28 686 362 148 84%
Pensioners 152 573 772 622 31% 7 732 068 204 11% 5 278 595 965 16%
TOTAL 498 603 917 387 100% 73 182 884 429 100% 33 964 958 112 100%

36. Aging in Azerbaijan
 Currently, Azerbaijan’s population is nearly 8, 5 million. . As UN projection
model finds, total population would increase up to approximately 10, 5 million
in 2050.
 The total fertility rate dropped from 2.6 in 1990 to a low point of
1.8 in 2006. But it will be increase up to approximately 1, 94 in 2050.
 Azerbaijan is young: + 60 “only” 10.5%. But…Proportion of +60
projected to be 32.1 % in 2050
 Dependency ratio (+60/15-59) will increase  from 17.3% to 42.9%
end of 2050.
 The dependency ratio will be effect after 2015 year

37. Dependency Ratio
Source: UN’s World population projection model

38. Expected life expectancy
90
81,27 81,77
80 77,07 77,87 78,37 79,17 79,97 80,77
75,47 76,27 74,91 75,71 76,21
74,47 73,31 74,11
71,51 72,31
70 67,21 68,71 69,71 70,71
60
50
40
30 26,3 26,7 27 27,2
24,2 24,5 24,9 25,2 25,5 25,9
23,8 22,2
22,3 22,6 23
22,8 23,1
23,2
21,3 21,5 21,9
20 20,1
19,7
16,7
20,4
20,2
17,1
20,7
20,5
17,3
21
20,9
17,6
21,2
17,9 18,1 18,5 18,8 19 19,4 19,6
10
0
2000 2005 2010 2015 2020 2025 2030 2035 2040 2045 2050
Male at birth Female at birth Male at age 60
Female at age 60 Male at age 65 Female at age 65
2000 2005 2010 2015 2020 2025 2030 2035 2040 2045 2050
At birth 67,21 68,71 69,71 70,71 71,51 72,31 73,31 74,11 74,91 75,71 76,21
Male at age 60 19,7 20,2 20,5 20,9 21,2 21,5 21,9 22,3 22,6 23,0 23,2
at age 65 16,7 17,1 17,3 17,6 17,9 18,1 18,5 18,8 19,0 19,4 19,6
At birth 74,47 75,47 76,27 77,07 77,87 78,37 79,17 79,97 80,77 81,27 81,77
Female at age 60 23,8 24,2 24,5 24,9 25,2 25,5 25,9 26,3 26,7 27,0 27,2
at age 65 20,1 20,4 20,7 21,0 21,3 21,5 21,9 22,2 22,6 22,8 23,1

39. Conclusion
The study is devoted to the mechanisms of the actuarial analysis being applied in various
countries.
• EU model (PRISM) and ILO pension model were used for the simulations. However almost all of the
demographic and economic assumptions were updated based on UN’s statistical data.
• A number of different actuarial calculations have been done on the effects of population ageing .
Management of the economic and social consequences of population ageing will require three mutually supportive
elements.
1. The volumes needed for financing pensions mean the system will always have to be based on a public pay-
as-you-go scheme.
2. In top of this there will also be a need for a solid funded element to balance out disturbances, spread
the burden between generations and thus help the economy adapt to the demographic changes.
3. As a third pillar , we will also need to provide a clear framework for private pension savings that will
provide scope for personal planning and fill any gaps that remain in the public system.
• Finally, consideration should be given as to whether there should be greater integration of demographic and
economic assumptions; in other words, should greater consideration be given to their interdependencies since, in
the long term at least, the demographic situation of a country is closely linked to its economic situation.

40. Thank you
for your attention !