Ioannis Karatzas
Optimal Arbitrage
In a Markovian model for a financial market, we
characterize the best arbitrage with respect to the market portfolio
that can be achieved using non-anticipative 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 also used to
generate the investment strategy that realizes the best possible
arbitrage. Some extensions to non-Markovian situations are also
presented. (Joint work with Daniel Fernholz)