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SUMMARY:Hedging under arbitrage - Johannes Ruf (Columbia)
DTSTART:20110125T140000Z
DTEND:20110125T150000Z
UID:TALK29287@talks.cam.ac.uk
CONTACT:Berestycki
DESCRIPTION:Explicit formulas for optimal trading strategies in terms of m
 inimal required initial capital are derived to replicate a given terminal 
 wealth in a continuous-time Markovian context. To achieve this goal this t
 alk does not assume the existence of an equivalent local martingale measur
 e. Instead a new measure is constructed under which the dynamics of the st
 ock price processes simplify. It is shown that delta hedging does not depe
 nd on the ``no free lunch with vanishing risk'' assumption. However\, in t
 he case of arbitrage the problem of finding an optimal strategy is directl
 y linked to the non-uniqueness of the partial differential equation corres
 ponding to the Black-Scholes equation. The recently often discussed phenom
 enon of ``bubbles'' is a special case of the setting in this talk. 
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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