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Title: mortality improvement models additional
Description: This note allows master's students to learn additional mortality improvement models representing multiple models. It is as straightforward as possible.
Description: This note allows master's students to learn additional mortality improvement models representing multiple models. It is as straightforward as possible.
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Mortality Improvement Models
Stochastic Models
1
...
Central death rate
ππ₯ =
-
1
ππ₯
=
1
β«0 π ππ₯
ππ
With constant force of mortality, ππ₯ = ππ₯ and
Under UDD:
1
β«
π ππ₯ ππ₯+π ππ
1
β«0 π ππ₯ ππ
ππ₯ = 1 β π βππ₯
β«0
1
π ππ₯
ππ = β« (1 β π ππ₯ ) ππ = 1 β 0
...
5ππ₯
ππ₯
ππ₯ =
1 + 0
...
Lee-Carter model
ln π(π₯, π‘) = πΌπ₯ + π½π₯ πΎπ‘ + ππ₯,π‘
-
Ignore ππ₯,π‘
πΌπ₯ and π½π₯ only depend on age
πΎπ‘ is a time series
...
Lognormal distribution
For π~ππππππ(π, π 2 ),
2
πΈ[π π ] = π π+0
...
d
...
Cairns-Blake-Dowd Models
a
...
Original CBD model
(1)
(2)
ππ(π₯, π‘) = πΎπ‘ + πΎπ‘ (π₯ β π₯)
- π₯ = average age in the data set
(1)
(2)
- πΎπ‘ and πΎπ‘ are time series
...
(1) (2)
- πΈ[ππ‘ ππ‘ ] = π, β1 β€ π β€ 1
(π) (π)
- πΈ [ππ‘ ππ’ ] = 0, πππ π‘ β π’, π = 1,2; π = 1,2
- Advantages: fewer parameters and less parameter uncertainty
- Disadvantage: fit to population is sometimes worse
c
...
π π₯2 is the variance of age
-
Let π = π₯πππ₯ β π₯πππ, then
-
range in the data set
...
(ARIMA time series)
Advantages: includes a cohort effect and a quadratic age difference term
Title: mortality improvement models additional
Description: This note allows master's students to learn additional mortality improvement models representing multiple models. It is as straightforward as possible.
Description: This note allows master's students to learn additional mortality improvement models representing multiple models. It is as straightforward as possible.