There once was a dream that data-driven models would replace their theory-guided counterparts. We have awoken from this dream. We now know that data cannot replace theory. Data-driven models still have their advantages, mainly in computational efficiency but also providing us with some special sauce that is unreachable by our current theories. This dissertation aims to provide a way in which both the accuracy of theory-guided models, and the computational efficiency of data-driven models can be combined. This combination of theory-guided and data-driven allows us to combine ideas from a much broader set of disciplines, and can help pave the way for robust and fast methods. / Doctor of Philosophy / As an illustrative example take the problem of predicting the weather. Typically a supercomputer will run a model several times to generate predictions few days into the future. Sensors such as those on satellites will then pick up observations about a few points on the globe, that are not representative of the whole atmosphere. These observations are combined, ``assimilated'' with the computer model predictions to create a better representation of our current understanding of the state of the earth. This predict-assimilate cycle is repeated every day, and is called (sequential) data assimilation. The prediction step traditional was performed by a computer model that was based on rigorous mathematics. With the advent of big-data, many have wondered if models based purely on data would take over. This has not happened. This thesis is concerned with taking traditional mathematical models and running them alongside data-driven models in the prediction step, then building a theory in which both can be used in data assimilation at the same time in order to not have a drop in accuracy and have a decrease in computational cost.

The mean variance framework (MV) developed by Markowitz in his groundbreaking paper offers a quantitative and rational approach to portfolio selection. It is well known to market practitioners however that the MV optimal portfolios tend to perform subpar. One of the issues of the MV portfolios is that they require the inverse of a large covariance matrix, which is often ill-conditioned. In this thesis, we develop a new approach to circumvent these issues. We propose an optimisation approach akin to least squares linear regression and compare the performance with an establish method, covariance shrinkage. When tested on a set of 30 futures contracts, we find that the models yield promising results albeit somewhat lower than that of the benchmark. / Mean variance ramverket (MV) framtaget av Markowitz i sin banbrytande artikel möjliggör en kvantitativ och rationell metod för portföljallokering. Det är däremot ett väletablerat faktum bland marknadsaktörer att Markowitz-optimala portföljer tenderar att prestera relativt dåligt. Ett av tillkortakommandena av ramverket är den ofta problemtyngda inverteringen av, den ofta stora, kovariansmatrisen som är illa konditionerad. I denna uppsats föreslår vi en ny metod för att kringgå detta problem. Vi föreslår en optimeringsmetodologi mycket lik minsta kvadratmetoden i linjär regression. Denna metod utvärderas sedan mot en vedertagen metod, kovarianskrympning. När vi utvärderar vår modell på 30 stycken terminskontrakt ser vi lovande resultat men finner en Sharpekvot något lägre än referensportföljens.