Towards a probability-free theory of continuous martingales
Mathematical Finance
2017-03-28 v1
Abstract
Without probability theory, we define classes of supermartingales, martingales, and semimartingales in idealized financial markets with continuous price paths. This allows us to establish probability-free versions of a number of standard results in martingale theory, including the Dubins-Schwarz theorem, the Girsanov theorem, and results concerning the It\^o integral. We also establish the existence of an equity premium and a CAPM relationship in this probability-free setting.
Keywords
Cite
@article{arxiv.1703.08715,
title = {Towards a probability-free theory of continuous martingales},
author = {Vladimir Vovk and Glenn Shafer},
journal= {arXiv preprint arXiv:1703.08715},
year = {2017}
}
Comments
26 pages