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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Financial Risk Management and Related Mathematical Tools 11
Solution Since
E(ρ
1
)=E(ρ
2
)=0.2 · 0.4 − 0.1 · 0.6=0.02 ,
then
E
S
1
+ S
2
2
S
0
= 200
= E
S
0
(1 + ρ
1
)+S
0
(1 + ρ
1
)(1 + ρ
2
)
2
S
0
= 200
=
S
0
2
E(1 + ρ
1
)+E(1 + ρ
1
)E(1 + ρ
2
)
= 100
1.02 + 1.02 ·1.02
= 206.4 .
We finish this section noting that there are various indications that the
use of discrete probability spaces can significantly limit the class of stochastic
experiments available for stochastic modeling. Below, we discuss one of most
illustrative considerations of this nature.
Let function f(x),x∈ R, be non-negative with
∞
−∞
f(x) dx =1.Then
function
F (x)=
x
−∞
f(y) dy
satisfies properties (D1)–(D2) of a
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