Notesale: Turn your study into money

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Profit Measurements
Profit test – usually use spreadsheet to do it
1
...
Some formulas
(𝑤)
′(𝑤)
′(𝑑)
a
...

b
...

c
...
Interest is 𝑖( 𝑘−1𝑉 + 𝑃 − 𝐸), where P is premium, and E is expenses
...
The net profit is the sum of beginning-of-year reserve, premium, and interest minus the sum of
expenses, expected death and surrender benefits, and expected end-of-year reserves
...
If we are given associated single decrement (or independent) rates for death and withdrawal,
set 𝑞(𝑑) = 𝑞′(𝑑) in the above equation
...
𝑞(𝑤) = (1 − 𝑞′(𝑑) )𝑞′(𝑤)
3
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Reserve at time (k-1), where it is added to profit
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Interest includes 𝑖 𝑘−1𝑉
(𝜏)
c
...

- If those three items are put together, this combination is called the change in reserve:
(𝜏)
∆ 𝑘𝑉 = (1 + 𝑖) 𝑘−1𝑉 − 𝑝𝑥+𝑘−1 𝑘𝑉
4
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Π𝑘 : the net profit at the end of year t per policy issued
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Profit measures
1
...

𝑛
Π𝑘
∑
=0
(1 + 𝑗)𝑘
𝑘=0

2
...
This rate
is also called the hurdle interest rate (hurdle rate) for short
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Profit margin: is the ratio of the NPV to the (expected) present value of future gross premiums
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DPP: discounted payback period, (break-even period), is the lowest m such that
𝑣𝑟 =

𝑚

∑ Π𝑘 𝑣 𝑟 = 0
𝑘=0

-

To calculate the DPP, we must discount each profit starting with year 0 and cumulatively sum
the up in the order of the years until we get a non-negative result
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Zeroization: of reserves means setting the reserves so that the profit is 0 in each year except the
first
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Calculate net cash flows per policy in force at beginning of each year for each non-terminal state
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(𝑖)
2
...
The
profits per policies are the net cash flows minus the increase in reserves
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(𝑖)
3
...
For t>0: Π𝑡 = ∑𝑖 𝑡−1𝑝𝑥0𝑖 𝑃𝑟𝑡

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