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CATEGORIES:Probability
SUMMARY:Hedging under arbitrage - Johannes Ruf (Columbia)
DTSTART;TZID=Europe/London:20110125T140000
DTEND;TZID=Europe/London:20110125T150000
UID:TALK29287AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/29287
DESCRIPTION:Explicit formulas for optimal trading strategies i
n terms of minimal required initial capital are de
rived to replicate a given terminal wealth in a co
ntinuous-time Markovian context. To achieve this g
oal this talk does not assume the existence of an
equivalent local martingale measure. Instead a new
measure is constructed under which the dynamics o
f the stock price processes simplify. It is shown
that delta hedging does not depend on the ``no fre
e lunch with vanishing risk'' assumption. However\
, in the case of arbitrage the problem of finding
an optimal strategy is directly linked to the non-
uniqueness of the partial differential equation co
rresponding to the Black-Scholes equation. The rec
ently often discussed phenomenon of ``bubbles'' is
a special case of the setting in this talk.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:Berestycki
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