# American Institute of Mathematical Sciences

January  2016, 1: 3 doi: 10.1186/s41546-016-0003-2

## Pathwise no-arbitrage in a class of Delta hedging strategies

 Department of Mathematics, University of Mannheim, 68131 Mannheim, Germany

Received  January 07, 2016 Revised  June 10, 2016 Published  August 2016

We consider a strictly pathwise setting for Delta hedging exotic options, based on Föllmer's pathwise Itô calculus. Price trajectories are d-dimensional continuous functions whose pathwise quadratic variations and covariations are determined by a given local volatility matrix. The existence of Delta hedging strategies in this pathwise setting is established via existence results for recursive schemes of parabolic Cauchy problems and via the existence of functional Cauchy problems on path space. Our main results establish the nonexistence of pathwise arbitrage opportunities in classes of strategies containing these Delta hedging strategies and under relatively mild conditions on the local volatility matrix.
Citation: Alexander Schied, Iryna Voloshchenko. Pathwise no-arbitrage in a class of Delta hedging strategies. Probability, Uncertainty and Quantitative Risk, 2016, 1 (0) : 3-. doi: 10.1186/s41546-016-0003-2
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