On optimal arbitrage

Details On optimal arbitrage On optimal arbitrage

2010-10-21

arxiv.org/abs/1010.4987v1

Annals of Applied Probability 2010, Vol. 20, No. 4, 1179-1204

Economy

Quantitative Finance

Computational Finance

Published in at http://dx.doi.org/10.1214/09-AAP642 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/09-AAP642

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.

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