Week 7 Detailed Learning Outcomes
Actuarial Practice #
n/a #
Actuarial Techniques #
Characteristics, causes and trends of mortality experience #
- Explain why and how mortality can change from one table to another, from one group to another.
- Explain what we mean by “rectangularisation” of the survival function.
- Describe typical characteristics of mortality rates (shape, trends)
Mathematical models of mortality #
- Gompertz Law of mortality:
Paremeters and in Gompertz Law can be found if two values for are given. - Makeham’s Law of mortality:
Parameters , , and in Makeham’s Law can be found if three values for are given.
The relationship between and
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: integer part of , as
Mesures of fertility #
Crude Birth Rate ( )
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General Fertility Rate ( )
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Age Specific Fertility Rate ( )
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Total Fertility Rate ( )
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Comparison of with
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We have
over an age group (e.g. 15-19 following the previous table)
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Gross Reproduction Rate ( )
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- We have
which then leads to - The sex ratio at birth is typically 1.05. Hence, we can use
as an approximation. - To sustain population we typically require (replacement level fertility rate)
Net Reproduction Rate ( )
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- We have
- One can use the approximation
- We typically need
to sustain population.
Fertility vs Reproduction Rates #
- Explain the difference between fertility and reproduction rates.
- Contrast both in developing vs developed countries.
Population projections #
- Polynomial Model: for given
where , , are the required parameters. - Linear Model (special case of polynomial model): for given
is the simple annual growth rate. Note, - Geometric Growth Model: for given
where is the compound rate of growth per unit time. Note, - Logistic Model: for given
where , , and are required parameters. Note, we have