Non-stochastic portfolio theory
Vladimir Vovk
TL;DR
This paper develops a non-stochastic framework for portfolio theory, extending Fernholz's stochastic approach to models with continuous stock prices, and explores connections with martingale processes.
Contribution
It introduces a non-stochastic version of Fernholz's stochastic portfolio theory and establishes foundational results in this new framework.
Findings
Non-stochastic portfolio theory analogous to stochastic results
Connections with Stroock-Varadhan martingales established
Foundational results for non-stochastic models derived
Abstract
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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Taxonomy
TopicsStochastic processes and financial applications · Risk and Portfolio Optimization · Financial Markets and Investment Strategies