Treffer: A model‐free approach to continuous‐time finance.

We present a pathwise approach to continuous‐time finance based on causal functional calculus. Our framework does not rely on any probabilistic concept. We introduce a definition of continuous‐time self‐financing portfolios, which does not rely on any integration concept and show that the value of a self‐financing portfolio belongs to a class of nonanticipative functionals, which are pathwise analogs of martingales. We show that if the set of market scenarios is generic in the sense of being stable under certain operations, such self‐financing strategies do not give rise to arbitrage. We then consider the problem of hedging a path‐dependent payoff across a generic set of scenarios. Applying the transition principle of Rufus Isaacs in differential games, we obtain a pathwise dynamic programming principle for the superhedging cost. We show that the superhedging cost is characterized as the solution of a path‐dependent equation. For the Asian option, we obtain an explicit solution. [ABSTRACT FROM AUTHOR]

Copyright of Mathematical Finance is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Volltext ist im Gastzugang nicht verfügbar. Login für vollen Zugriff.