Notesale: Turn your study into money

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Pension
Gain By Source
(𝑑)

-

(𝑑)

(𝑤)

(𝑤)

(𝜏)

𝑃𝑟𝑘 = ( 𝑘−1𝑉 + 𝐺𝑘−1 − 𝑒𝑘−1 )(1 + 𝑖) − 𝑞𝑥+𝑘−1 (𝑏𝑘 + 𝐸𝑘 ) − 𝑞𝑥+𝑘−1 (𝐶𝑉𝑘 + 𝐸𝑘 ) − 𝑝𝑥+𝑘−1 𝑘 𝑉
𝑃𝑟𝑘 : profit in year k per policy in force at the beginning of year k
...
Expected profit: the profit computed using the interest, mortality, surrender, and expense rates
assumed in pricing the product; in other words, the assumptions used in computing the premium
...
Actual profit: is computed using actual experience for interest, mortality, surrender, and expense
...
Gross premium reserve recursion formula if surrenders are considered is:
(𝑑)
(𝑑)
(𝑤)
(𝑤)
( 𝑘−1𝑉 + 𝐺𝑘−1 − 𝑒𝑘−1 )(1 + 𝑖) − 𝑞𝑥+𝑘−1 (𝑏𝑘 + 𝐸𝑘 ) − 𝑞𝑥+𝑘−1 (𝐶𝑉𝑘 + 𝐸𝑘 )
𝑘𝑉 =
(𝜏)
𝑝𝑥+𝑘−1
4
...
Gain can be broken down into interest, mortality, surrender, and expense components
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Gain By Source analysis:
a
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To the extent they
are different, this represents a gain from a previous year, which was accounted for in that
year
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Calculate the difference in interest rates times the starting assets plus beginning-of-year cash
flows
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Mortality and expense are as
assumed)
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Calculate the expense difference, the excess of assumed over actual expenses, both for
beginning-of-year and settlement expenses
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d
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The net amount at risk is the face amount minus
the end-of-year reserve
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e
...

- Components of gain: in each component, primed are actual, starred are assumed

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