In a Markovian model for a financial market, we characterize the best arbitrage with respect to the market portfolio that can be achieved using nonanticipative investment strategies, in terms of the smallest positive solution to a parabolic partial differential inequality; this is determined entirely on the basis of the covariance structure of the model. The solution is intimately related to properties of strict local martingales and is used to generate the investment strategy which realizes the best possible arbitrage. Some extensions to non-Markovian situations are also presented.
Publié le : 2010-08-15
Classification:
Portfolios,
arbitrage,
parabolic operators,
maximum principle,
strict local martingales,
exit measures for supermartingales,
diffusions,
Fichera drift,
60H10,
91B28,
60G44,
35B50
@article{1279638783,
author = {Fernholz, Daniel and Karatzas, Ioannis},
title = {On optimal arbitrage},
journal = {Ann. Appl. Probab.},
volume = {20},
number = {1},
year = {2010},
pages = { 1179-1204},
language = {en},
url = {http://dml.mathdoc.fr/item/1279638783}
}
Fernholz, Daniel; Karatzas, Ioannis. On optimal arbitrage. Ann. Appl. Probab., Tome 20 (2010) no. 1, pp. 1179-1204. http://gdmltest.u-ga.fr/item/1279638783/