This note poses the problem of developing a non-stochastic version of Fernholz's stochastic portfolio theory and discusses a possible approach to it. In particular, it gives a non-stochastic interpretation of the tension between market efficiency and market diversity that is a key finding of stochastic portfolio theory  .
This paper studies a non-stochastic version of Fernholz's stochastic portfolio theory for a simple model of stock markets with continuous price paths. It establishes non-stochastic versions of the most basic results of stochastic portfolio theory and discusses connections with Stroock-Varadhan martingales .
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note poses the problem of developing
paper studies
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and discusses a possible approach to it. In particular, it gives a
for a simple model of stock markets with continuous price paths. It establishes
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interpretation of the tension between market efficiency and market diversity that is a key finding
versions of the most basic results
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and discusses connections with Stroock-Varadhan martingales