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Math Colloquium
Johannes Ruf
Columbia University
Title: Hedging under arbitrage

Abstract: 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.

Refreshments at 4:00, WeH 6220

Date: Thursday, January 20, 2011
Time: 4:30 pm
Location: Wean Hall 8220
Submitted by:  Shreve