Department of         Mathematical Sciences Events People Colloquia and Seminars Conferences Centers Positions Areas of Research About the Department Alumni 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 6220Date: Thursday, January 20, 2011Time: 4:30 pmLocation: Wean Hall 8220Submitted by:  Shreve