Question
Suppose an investor has initial wealth W 0 and has the opportunity for an investment such that the end-of-period wealth is W = W 0
Suppose an investor has initial wealth
W
0
and has the opportunity for an investment such
that the end-of-period wealth is
W
=
W
0
+
H
. If the investor uses exponential utiliy, show that
W
C
W
0
does not depend on
W
0
.
ii) Suppose an investor has initial wealth
W
0
and has the opportunity for an investment such that the
end-of-period wealth is
W
=
HW
0
. If the investor uses power utility show that
W
C
W
0
does not depend on
W
0
.
Question 2:
Let
W
, a random variable, represent the amount of future wealth held by an investor, and
let
u
1
and
u
2
be two different utility functions. The certainty equivalent of
W
under
u
1
is denoted
W
(1)
C
,
and the certainty equivalent of
W
under
u
2
is denoted
W
(2)
C
. Using the definition of certainty equivalent
and the definition of equivalent utility functions, show that if
u
1
u
2
then
W
(1)
C
=
W
(2)
C
. You may assume
u
1
and
u
2
are strictly increasing.
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