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research
A note on lower bounds of martingale measure densities
Authors
Dmitry Rokhlin
Walter Schachermayer
Publication date
1 January 2005
Publisher
View
on
arXiv
Abstract
For a given element
f
∈
L
1
f\in L^1
f
∈
L
1
and a convex cone
C
⊂
L
∞
C\subset L^\infty
C
⊂
L
∞
,
C
∩
L
+
∞
=
{
0
}
C\cap L^\infty_+=\{0\}
C
∩
L
+
∞
​
=
{
0
}
we give necessary and sufficient conditions for the existence of an element
g
≥
f
g\ge f
g
≥
f
lying in the polar of
C
C
C
. This polar is taken in
(
L
∞
)
∗
(L^\infty)^*
(
L
∞
)
∗
and in
L
1
L^1
L
1
. In the context of mathematical finance the main result concerns the existence of martingale measures, whose densities are bounded from below by prescribed random variable.Comment: 9 page
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Last time updated on 09/07/2019