Research

This paper proposes a novel perspective on the relationship between Value at Risk (VaR) and Expected Shortfall (ES) by employing the mixing framework of Flexible Expected Shortfall (FES) to construct coherent representations of VaR. The methodology enables a reinterpretation of VaR within a coherent risk measure framework, thereby addressing well-known limitations of VaR, including non-subadditivity and insensitivity to tail risk. A central feature of the framework is the flexibility parameter inherent in FES, which captures salient distributional properties of the underlying risk profile. This parameter is formalized as the theta-index, a normalized measure designed to reflect tail heaviness. Theoretical properties of the theta-index are examined, and its relevance to risk assessment is established. Furthermore, risk capital allocation is analyzed using the Euler principle, facilitating consistent and meaningful marginal attribution. The practical implications of the approach are illustrated through appropriate simulation studies and an empirical analysis based on an insurance loss dataset with pronounced heavy-tailed characteristics.

Freight rate derivatives constitute a very popular financial tool in shipping industry, that allows to the market participants and the individuals operating in the field, to reassure their financial positions against the risk occurred by the volatility of the freight rates. The special structure of the shipping market attracted the interest of both academics and practitioners, since pricing of the related traded options which are written on non-storable assets (i.e. the freight service) is not a trivial task. Management of freight risk is of major importance to preserve the viability of shipping operations, especially in periods where shocks appear in the world economy, which introduces uncertainty in the freight rate prices. In practice, the reduction of freight risk is almost exclusively performed by constructing hedging portfolios relying on freight rate options. These portfolios needs to be robust to the market uncertainties, i.e. to choose the portfolio which returns will be as less as it gets affected by the market changes. Especially, for time periods where the future states of the market (even in short term) are extremely ambiguous, i.e. there are a number of different scenarios that can occur, it is of great importance for the firms to decide robustly to these uncertainties. In this work, a framework for the robust treatment of model uncertainty in (a) modeling the freight rates dynamics employing the notion of Wasserstein barycenter and (b) in choosing the optimal hedging strategy for freight risk management, is proposed. A carefully designed simulation study in the discussed hedging problem, employing standard modelling approaches in freight rates literature, illustrates the capabilities of the proposed method with very satisfactory results in approximating the optimal strategy even in high noise cases.

This study presents a novel approach to assessing food security risks at the national level, employing a probabilistic scenario-based framework that integrates both Shared Socio-economic Pathways and Representative Concentration Pathways. This innovative method allows each scenario, encompassing socio-economic, and climate factors, to be treated as a model capable of generating diverse trajectories. This approach offers a more dynamic understanding of food security risks under varying future conditions. The paper details the methodologies employed, showcasing their applicability through a focused analysis of food security challenges in Egypt and Ethiopia, and underscores the importance of considering a spectrum of socio-economic and climatic factors in national food security assessments.

We introduce a spatial economic growth model where space is described as a network of interconnected geographic locations and we study a corresponding finite-dimensional optimal control problem on a graph with state constraints. Economic growth models on networks are motivated by the nature of spatial economic data, which naturally possess a graph-like structure: this fact makes these models well-suited for numerical implementation and calibration. The network setting is different from the one adopted in the related literature, where space is modeled as a subset of a Euclidean space, which gives rise to infinite dimensional optimal control problems. After introducing the model and the related control problem, we prove existence and uniqueness of an optimal control and a regularity result for the value function, which sets up the basis for a deeper study of the optimal strategies. Then, we focus on specific cases where it is possible to find, under suitable assumptions, an explicit solution of the control problem. Finally, we discuss the cases of networks of two and three geographic locations.

In this paper we propose a consensus group decision making scheme under model uncertainty consisting of an iterative two-stage procedure based on the concept of Fréchet barycenter. Each stage consists of two steps: the agents first update their position in the opinion metric space adopting a local barycenter characterized by the agents’ immediate interactions and then a moderator makes a proposal in terms of a global barycenter, checking for consensus at each stage. In cases of large heterogeneous groups, the procedure can be complemented by an auxiliary initial homogenization stage, consisting of a clustering procedure in opinion space, leading to large homogeneous groups for which the aforementioned procedure will be applied. The scheme is illustrated in examples motivated from environmental economics.

The problem of asset liability management (ALM) is a classic problem of the financial mathematics and of great interest for the banking institutions and insurance companies. Several formulations of this problem under various model settings have been studied under the Mean-Variance (MV) principle perspective. In this paper, the ALM problem is revisited under the context of model uncertainty in the one-stage framework. In practice, uncertainty issues appear to several aspects of the problem, e.g. liability process characteristics, market conditions, inflation rates, inside information effects, etc. A framework relying on the notion of the Wasserstein barycenter is presented which is able to treat robustly this type of ambiguities by appropriate handling the various information sources (models) and appropriately reformulating the relevant decision making problem. The proposed framework can be applied to a number of different model settings leading to the selection of investment portfolios that remain robust to the various uncertainties appearing in the market. The paper is concluded with a numerical experiment for a static version of the ALM problem, employing standard modelling approaches, illustrating the capabilities of the proposed method with very satisfactory results in retrieving the true optimal strategy even in high noise cases.

Optimal sustainable management of natural resources has been one of the major lines of research in environmental economics at least for the last two decades. Several attempts have been made in order to describe in a quantitative fashion the notion of sustainability and distinguish management policies between sustainable and non-sustainable ones. Important aspects of this task are (a) appropriate modeling of the spatio-temporal dynamics of the state of the system, including the sources of uncertainty affecting either directly or indirectly the problem at hand (e.g. climate conditions, population growth, biological evolution), and (b) the development of appropriate criteria for evaluating the welfare of the system under study that guarantees sustainability and viability. In this chapter, we present and discuss popular and established optimization approaches for investigating policy selection problems within the sustainability framework, from the perspective of viability and optimal control theory.

In this work the problem of optimal harvesting policy selection for natural resources management under model uncertainty is investigated. Under the framework of the neoclassical growth model dynamics, the associated optimal control problem is investigated by introducing the concept of model uncertainty on the initial conditions of the operational procedure. At this stage, the notion of convex risk measures, and in particular the class of Fréchet risk measures, is employed in order to quantify the total operational and marginal risk, whereas simultaneously obtaining robust to model uncertainty harvesting strategies.

We propose a novel class of convex risk measures, based on the concept of the Fréchet mean, designed in order to handle uncertainty which arises from multiple information sources regarding the risk factors of interest. The proposed risk measures robustly characterize the exposure of the firm, by filtering out appropriately the partial information available in individual sources into an aggregate model for the risk factors of interest. Importantly, the proposed risks can be expressed in closed analytic forms allowing for interesting qualitative interpretations as well as comparative statics and thus facilitate their use in the everyday risk management process of the insurance firms. The potential use of the proposed risk measures in insurance is illustrated by two concrete applications, capital risk allocation and premia calculation under uncertainty.

In this work we consider the problem of numerical computation of convex risk measures, using a regularization scheme to account for undesirable fluctuations in the available historical data, combined with techniques from the Calculus of Variations.

This work investigates the problem of model averaging in the context of measure-valued data. Specifically, we study aggregation schemes in the space of probability distributions metrized in terms of the Wasserstein distance. The resulting aggregate models, defined via Wasserstein barycenters, are optimally calibrated to empirical data. To enhance model performance, we employ regularization schemes motivated by the standard elastic net penalization, which is shown to consistently yield models enjoying sparsity properties. The consistency properties of the proposed averaging schemes with respect to sample size are rigorously established using the variational framework of $\Gamma$-convergence. The performance of the methods is evaluated through carefully designed synthetic experiments that assess behavior across a range of distributional characteristics and stress conditions. Finally, the proposed approach is applied to a real-world insurance loss dataset—characterized by heavy-tailed behavior—to estimate the claim size distribution and the associated tail risk.

Increasing the generation of electric power from renewable energy sources (RESs) creates important challenges to transmission system operators (TSOs) for balancing the power system. To address these challenges, adequate system flexibility is required. In this context, TSOs carry out flexibility assessment studies to evaluate the flexibility level of the power system and ensure that a stable operation of the transmission system under high RESs integration can be achieved. These studies take into consideration numerous scenarios incorporating different assumptions for temperature, RESs penetration, load growth, and hydraulic conditions. Until now, flexibility studies usually solve the standard unit commitment problem and evaluate if the flexibility level is adequate. Although this approach provides quite accurate results, the computational requirements are significant, resulting in limiting the scenarios chosen for examination. In this paper, deep learning approaches are examined, and more precisely, an integrated system of two recurrent neural networks with long short-term memory cells is designed to carry out the flexibility assessment task, aiming at the reduction in the computational time required by the optimization process. The output of this neural network system is then used to calculate the probability of flexibility shortages. The proposed method is evaluated based on data from the Hellenic transmission system, providing quite promising results in (a) accurately calculating the probability of insufficient flexibility and (b) achieving a significant decrease in computational time. This novel approach could notably facilitate TSOs since more scenarios can be included, exploiting the computational efficiency of the method. In this way, a more complete evaluation of the flexibility level of the power system can be achieved and thus help to ensure the stable and reliable operation of the transmission system.

A modelling framework suitable for detecting shape shifts in functional profiles combining the notion of the Fréchet mean and the concept of deformation models is developed and proposed. The generalized mean sense offered by the Fréchet mean notion is employed to capture the typical pattern of the profiles under study, while the concept of deformation models, and in particular of the shape-invariant model, allows for interpretable parameterizations of the profile’s deviations from the typical shape. The EWMA-type control charts compatible with the functional nature of data and the employed deformation model are built and proposed, exploiting certain shape characteristics of the profiles under study with respect to the generalized mean sense, allowing for the identification of potential shifts concerning the shape and/or the deformation process. Potential shifts in the shape deformation process are further distinguished into significant shifts with respect to amplitude and/or the phase of the profile under study. The proposed modeling and shift detection framework is implemented to a real-world case study, where daily concentration profiles concerning air pollutants from an area in the city of Athens are modeled, while profiles indicating hazardous concentration levels are successfully identified in most cases.

The constant evolution of biomedicine, biophysics and biochemistry has enabled scientists to investigate and study each cell identity via analyzing the transciptome and its kinetics, the chromatin accessibility patterns but also via investigating the structure of proteins and RNA. Taking all this under consideration, scientists have developed algorithms and machine learning (ML) schemes that take advantage of the current state-of-the-art approaches to predict the cell states, discover the exact 3D structure of proteins and RNA and most importantly evaluate personalized medicine approaches via predicting drugs and specific immunotherapy treatments. Moreover, the recent advances in ML and chemo-informatics have also paved the way for drug repurposing models, thus evaluating and establishing in silico novel treatments. The aim of this chapter is to provide and analyze the mathematics behind such ML techniques and review the current applications being developed that walk side by the side with the continuous progress of biosciences.

Clustering schemes for uncertain and structured data are considered relying on the notion of Wasserstein barycenters, accompanied by appropriate clustering indices based on the intrinsic geometry of the Wasserstein space. Such type of clustering approaches are highly appreciated in many fields where the observational/experimental error is significant or the data nature is more complex and the traditional learning algorithms are not applicable or effective to treat. Under this perspective, each observation is identified by an appropriate probability measure and the proposed clustering schemes rely on discrimination criteria that utilize the geometric structure of the space of probability measures through core techniques from the optimal transport theory. The advantages and capabilities of the proposed approach and the geodesic criterion performance are illustrated through a simulation study and the implementation in two different applications: (a) clustering eurozone countries’ bond yield curves and (b) classifying satellite images to certain land uses categories.

The operation of buildings is linked to approximately 36% of the global energy consumption, 40% of greenhouse gas emissions, and climate change. Assessing the energy consumption and efficiency of buildings is a complex task addressed by a variety of methods. Building energy modeling is among the dominant methodologies in evaluating the energy efficiency of buildings commonly applied for evaluating design and renovation energy efficiency measures. Although building energy modeling is a valuable tool, it is rarely the case that simulation results are assessed against the building’s actual energy performance. In this context, the simulation results of the HVAC energy consumption in the case of a smart industrial near-zero energy building are used to explore areas of uncertainty and deviation of the building energy model against measured data. Initial model results are improved based on a trial and error approach to minimize deviation based on key identified parameters. In addition, a novel approach based on functional shape modeling and Kalman filtering is developed and applied to further minimize systematic discrepancies. Results indicate a significant initial performance gap between the initial model and the actual energy consumption. The efficiency and the effectiveness of the developed integrated model is highlighted.

In several environmental affected socio-economic activities, including renewable energy site assessment, search and rescue operations, and local microclimate modeling, the need of very local wind speed prediction is critical and not completely covered by the use of numerical weather prediction models. In meteorology and, particularly, in wind speed prediction, the spatial location of the prediction does not coincide with the spatial locations where numerical models provide estimates of the relevant quantity (which are typically grid points used for the numerical resolution of the wind transport equations). Hence, the important problem of constructing a predictive model for the wind speed at the required location using a combination of actual measurements and model predictions arises. This problem is far from trivial on account of the fact that measurements and predictions do not refer to the same quantity for the reason that typical grid points for the numerical scheme that provide model predictions and the location of the meteorological stations that provide measurements do not coincide. In this work, a new approach is proposed based on optimal transportation theory for the aggregation of model predictions and measurements for the construction of an optimal predictor for wind speed at the location of interest. Our model provides a linear predictive model in the space of probability distributions of the predictors (Wasserstein space), which is then mapped into observation space using a generalized quantile regression technique. Importantly, the proposed scheme allows also for the construction of zone monitoring the extremes, which when applied to real data, provides superior results with respect to other existing methods.

In this paper, we provide a critical overview of the current migration policies of the EU as framed by the recent amendments of the EU migration policies since 2015. We highlight that the construction of the migration policy is a constitutive element of the spatial process of reorganization of territorial policies through the combination and diffusion of state, regional and global. We show that the perception of permanent and static migration pressure, and countries’ specialization in migration are the basis for diffusion of asylum and migration policies to a number of different countries imposing similar migration systems and establishing a global governance of migration regime. The paper highlights a geographic and political change in migration and border management, through the patterns of EU Member States cooperation, and in particular their reluctance to establish a common asylum system based on solidarity and the focus on substituting the lack of a common asylum system by bilateral externalization agreements the main objective of which is the management of migration and border control rather than guaranteeing asylum and refugee policies.

In this work, a functional supervised learning scheme is proposed for the classification of subjects into normotensive and hypertensive groups, using solely the 24-hour blood pressure data, relying on the concepts of Fréchet mean and Fréchet variance for appropriate deformable functional models for the blood pressure data. The schemes are trained on real clinical data, and their performance was assessed and found to be very satisfactory.

The problem of model aggregation from various information sources of unknown validity is addressed in terms of a variational problem in the space of probability measures. A weight allocation scheme to the various sources is proposed, which is designed to lead to the best aggregate model compatible with the available data and the set of prior measures provided by the information sources.