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Unformatted text preview: comes m = 0, 1, 2, 3,
our problem m is to
P3
P3
Maximize m=0 pm ln ym subject to (1 + r) 2 m=0 p⇤ ym = W0 .
m
Consider the unconstrained optimization problem of maximizing
L= 3
X pm U (ym ) m=0 Di↵erentiating we have (1 + r)2 @L
pm
=
@ ym
ym 3
X p⇤ y m
m W0 (1 + r) m=0 2 ! p⇤
m
(1 + r)2 Setting these equal to 0 we have
ym =
The ﬁnal detail is to pick pm (1 + r)2
p⇤
m to satisfy the constraint, i.e.,
3
(1 + r)2 X pm = W 0 m=0 or since the pm sum to 1, = 1/W0 and
ym = W0 (1 + r)2 pm
p⇤
m Since 1 + r = 5/4, p3 = 4/9, p2 = p1 = 2/9, p0 = 1/9, and all the p⇤ = 1/4
m
this agrees with (6.19). However from the new solution we can easily see the
nature of the solution in general. 6.5 American Options European option contracts specify an expiration date, and if the option is to be
exercised at all, this must occur at the expiration date. An option whose owner
can choose to exercise it at any time is called an American option. We will
mostly be concerned with call and put options where the value at exercise is a
function of the stock price,...
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This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).
 Spring '10
 DURRETT
 The Land

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