Hedging under arbitrage

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• Johannes Ruf (Columbia)
• Tuesday 25 January 2011, 14:00-15:00
• MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB.

If you have a question about this talk, please contact Berestycki.

Explicit formulas for optimal trading strategies in terms of minimal required initial capital are derived to replicate a given terminal wealth in a continuous-time Markovian context. To achieve this goal this talk does not assume the existence of an equivalent local martingale measure. Instead a new measure is constructed under which the dynamics of the stock price processes simplify. It is shown that delta hedging does not depend on the ``no free 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 corresponding to the Black-Scholes equation. The recently often discussed phenomenon of ``bubbles’’ is a special case of the setting in this talk.

This talk is part of the Probability series.

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