A unified framework for robust modelling of financial markets in discrete time

We unify and establish equivalence between the pathwise and the quasi-sure approaches to robust modelling of financial markets in finite discrete time. In particular, we prove a fundamental theorem of asset pricing and a superhedging theorem which encompass the formulations of Bouchard and Nutz [12] and Burzoni et al. [13]. In bringing the two streams of literature together, we examine and compare their many different notions of arbitrage. We also clarify the relation between robust and classical ℙ-specific results. Furthermore, we prove when a superhedging property with respect to the set of martingale measures supported on a set $\Omega $ Ω of paths may be extended to a pathwise superhedging on $\Omega $ Ω without changing the superhedging price.

Single-Trial EEG Classification via Common Spatial Patterns with Mixed Lp- and Lq-Norms

As a multichannel spatial filtering technique, common spatial patterns (CSP) have been successfully applied in brain-computer interfaces (BCI) community based on electroencephalogram (EEG). However, it is sensitive to outliers because of the employment of the L2-norm in its formulation. It is beneficial to perform robust modelling for CSP. In this paper, we propose a robust framework, called CSP-Lp/q, by formulating the variances of two EEG classes with Lp- and Lq-norms ( 0 < p and q < 2 ) separately. The method CSP-Lp/q with mixed Lp- and Lq-norms takes the class-wise difference into account in formulating the sample dispersion. We develop an iterative algorithm to optimize the objective function of CSP-Lp/q and show its monotonity theoretically. The superiority of the proposed CSP-Lp/q technique is experimentally demonstrated on three real EEG datasets of BCI competitions.

Rapid development of fast and flexible environmental models: the Mobius framework v1.0

The Mobius model building system is a new open-source framework for building fast and flexible environmental models. Mobius makes it possible for researchers with limited programming experience to build performant models with potentially complicated structures. Mobius models can be easily interacted with through the MobiView graphical user interface and through the Python programming language. Mobius was initially developed to support catchment-scale hydrology and water-quality modelling but can be used to represent any system of hierarchically structured ordinary differential equations, such as population dynamics or toxicological models. Here, we demonstrate how Mobius can be used to quickly prototype several different model structures for a dissolved organic carbon catchment model and use built-in auto-calibration and statistical uncertainty analysis tools to help decide on the best model structures. Overall, we hope the modular model building platform offered by Mobius will provide a step forward for environmental modelling, providing an alternative to the “one size fits all” modelling paradigm. By making it easier to explore a broader range of model structures and parameterisations, users are encouraged to build more appropriate models, and in turn this improves process understanding and allows for more robust modelling in support of decision making.

Robust modelling to address UPH19 to predict future hydrological responses for water resources adaptation under climate change

&lt;p&gt;This paper addresses the implications of UPH19 in extrapolating hydrological models to predict the future and assessing water resources adaptation to climate change. Many studies have now shown that traditional application of hydrological models calibrated against past observations will underestimate the range in the projected future hydrological impact, that is, it will underestimate the decline in runoff where a runoff decrease is projected, and underestimate the increase in runoff where a runoff increase is projected. This study opportunistically uses data from south-eastern Australia which recently experienced a long and severe drought lasting more than ten years and subsequent partial hydrological recovery from the drought. The paper shows that a more robust calibration of rainfall-runoff models to produce good calibration metrics in both the dry periods and wet periods, at the expense of the best calibration over the entire data period, can produce a more accurate estimate of the uncertainty in the projected future runoff, but cannot entirely eliminate the modelling limitation of underestimating the projected range in future runoff. This is because of the need to consider trade-offs between the calibration objectives, particularly in simulating the dry periods, versus enhanced bias that results from the consideration. Hydrological models must therefore also need to be adapted to reflect the non-stationary nature of catchment and vegetation responses in a changing climate under warmer conditions, higher CO&lt;sub&gt;2&lt;/sub&gt; and changed precipitation patterns. This is an active area of research in UPH19, and some ideas relevant to this region will be presented.&lt;/p&gt;