Classical approaches to optimal portfolio selection problems are based on probabilistic models for the asset returns or prices. However, by now it is well observed that the performance of optimal portfolios are highly sensitive to model misspecifications. To account for various type of model risk, robust and model-free approaches have gained more and more importance in portfolio theory.
Based on a rough path foundation, we develop a model-free approach to stochastic portfolio theory and Cover’s universal portfolio. The use of rough path theory allows treating significantly more general portfolios in a model-free setting, compared to previous model-free approaches. Without the assumption of any underlying probabilistic model, we present pathwise Master formulae analogously to the classical ones in stochastic portfolio theory, describing the growth of wealth processes generated by pathwise portfolios relative to the wealth process of the market portfolio, and we show that the appropriately scaled asymptotic growth rate of Cover’s universal portfolio is equal to the one of the best retrospectively chosen portfolio.
The talk is based on a joint work with Andrew Allan, Christa Cuchiero and Chong Liu.