April 2011
Intermediate to advanced
328 pages
9h 5m
English
Content preview from Risk Analysis in Finance and Insurance, 2nd Edition
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214 Risk Analysis in Finance and Insurance
The net-premium in this case is
m|
A
x
= E(Z)=
∞
m
ν
t
p
x
(t) μ
x+t
dt .
Next, we consider contracts with variable amounts of benefit paid upon
the death of life insured.
Increasing whole life insurance :
b
t
=[[t +1]],t≥ 0 ,
ν
t
= ν
t
,t≥ 0 ,
Z =[[T (x)+1]]ν
T (x)
,T(x) ≥ 0 .
Net-premium is
I
A
x
= E(Z)=
∞
0
[[ t +1]]ν
t
p
x
(t) μ
x+t
dt .
Decreasing term-life insurance :
b
t
=
n −[[ t]] ,t≤ n
0 ,t>n
,
ν
t
= ν
t
,t≥ 0 ,
Z =
ν
T (x)
(n −[[ T (x)]]) ,T(x) ≤ n
0 ,T(x) >n
.
Net-premium is
D
A
1
x:
n|
=
n
0
ν
t
(n − [[ t]] ) p
x
(t) μ
x+t
dt .
One can consider variations of these contracts in the case when benefits are
paid at the end of the year in which death occurred, ...
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