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.
Speaker: Johannes Ruf, Columbia University
Slides: (TBA)
Event Details
Hedging under arbitrage
- Event Date: September 21, 2010
- Event End Date: September 21, 2010
- Event Start Time: 1:45 PM
- Event End Time: 2:45 PM
- Event Location: Hill 525
- Event Type: Mathematical Finance and Probability Seminars
- Extra Info: (First seminar Fall 2010)<br /> Speaker: Johannes Ruf, Columbia University