Outperforming the market portfolio with a given probability
Our goal is to resolve a problem proposed by Fernholz and Karatzas [On optimal arbitrage (2008) Columbia Univ.]: to characterize the minimum amount of initial capital with which an investor can beat the market portfolio with a certain probability, as a function of the market configuration and time to maturity. We show that this value function is the smallest nonnegative viscosity supersolution of a nonlinear PDE. As in Fernholz and Karatzas [On optimal arbitrage (2008) Columbia Univ.], we do not assume the existence of an equivalent local martingale measure, but merely the existence of a local martingale deflator.
Year of publication: |
2010-06
|
---|---|
Authors: | Bayraktar, Erhan ; Huang, Yu-Jui ; Song, Qingshuo |
Institutions: | arXiv.org |
Saved in:
freely available
Saved in favorites
Similar items by person
-
On the Stochastic Solution to a Cauchy Problem Associated with Nonnegative Price Processes
Chen, Xiaoshan, (2013)
-
Robust maximization of asymptotic growth under covariance uncertainty
Bayraktar, Erhan, (2011)
-
On the Multi-Dimensional Controller and Stopper Games
Bayraktar, Erhan, (2010)
- More ...