Events Archive

15:15 pm David Prömel (University of Mannheim):

Model-free portfolio theory: a rough path approach

Abstract: 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. Using rough path theory, we provide a pathwise foundation for stochastic Ito integration, which covers most commonly applied trading strategies and mathematical models of financial markets possibly under model uncertainty. Based on this pathwise foundation, we develop a model-free approach to stochastic portfolio theory and Cover's universal portfolio. The use of rough path theory allows for treating significantly more general portfolios in a model-free setting, compared to previous model-free approaches. The talk is based on joint works with Andrew Allan, Christa Cuchiero and Chong Liu.

16:15 pm Coffee break

16:45 pm Christoph Czichowsky (London School of Economics):

Hedging and portfolio optimisation in rough volatility models

Abstract: Rough volatility models have become quite popular recently, as they capture both the fractional scaling of the time series of the historic volatility (Gatheral et al. 2018) and the behaviour of the implied volatility surface (Fukasawa 2011, Bayer et al. 2016) remarkably well. In contrast to classical stochastic volatility models, the volatility process is neither a Markov process nor a semimartingale. Therefore, these models fall outside the scope of standard stochastic analysis and provide new mathematical challenges. In this talk, we present an overview of of this new paradigm in volatility modelling and consider the impact of rough volatility on hedging and portfolio optimisation. The talk is based on joint works with David Martins, Johannes Muhle-Karbe and Denis Schelling.