Modelling Complex Flows in Porous Media by Means of Upscaling Procedures

We review a series of problems arising in the field of flows through porous media and that are highly nontrivial either because of the presence of mass exchange between the fluid and the porous matrix (or other concurrent phenomena of physical or chemical nature), or because of a particularly complex structure of the medium. In all these cases there is a small parameter $\varepsilon$, representing the ratio between the microscopic and the macroscopic space scale. Our attention is focussed on a modelling technique (upscaling) which start from the governing equations written at the pore scale, introduces an expansion in power series of $\varepsilon$of all the relevant quantities and eventually leads to the formulation of the macroscopic governing equations at the various orders in $\varepsilon$ by a matching procedure, followed by suitable averaging. Two problems will be analyzed with some detail: soil erosion and the dynamics of water ultrafiltration devices. Moreover other problems will be occasionally discussed and open questions will be proposed

Mean-variance investing with factor tilting

Factor analysis proposes an alternative approach to standard portfolio theory: the latter is optimisation based, while the former is estimation based. Also, in standard portfolio theory, returns are only explained by the portfolio volatility factor, while factor analysis proposes a multiplicity of factors, which the managers can choose from to tilt their portfolios. In attempting to reconcile these alternative worlds, we propose a penalised utility function, incorporating both the Markowitzian risk-return trade-off and the manager's preferences towards factors, and discriminating among losses and gains relative to a reference asset. The penalisation affects the optimisation process, favouring the selection of portfolios with less variance and more tilted towards the chosen risk factors. Penalty levels set by the manager generalise the traditional notion of risk aversion. We test our model by building an investment portfolio based on a combination of asset classes and selected investing factors, focussed on the eurozone. To identify the optimal portfolio, we adopt a set of three metaheuristic optimisation algorithms: the fitness function stochastic maximization using genetic algorithms, differential evolution algorithm for global optimisation, and the particle swarm optimisation, and dynamically choose the best solution. In this way, we can improve the Markowitzian optimisation by tilting the asset allocation with managers' expectations and desired exposures towards designated factors

CAPM with Sentiment

We analyse the relationship between large cap returns and sentiment indexes, using a Capital Asset Pricing Model (CAPM ) framework. We try to provide a better explanation of asset prices and their deviations from standard theories by means of sentiment indicators, assuming the latter being measures of the very inclination to speculate. Therefore, when sentiment is high, investor demand for speculative investment is high; conversely when it is low, investor demand for speculative investments is low. Unlike other studies, based on proxies, we use the European Sentiment Indicator and its constituents, based on direct surveys, to assess business and consumer confidence

Designing irrigation pipes

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