Search

The aim of this paper is threefold. Firstly, we define the necessary quantities associated to the lumpability of a Markov chain and study their fundamental properties. Secondly, we examine the case of approximate lumpability of a non-lumpable Markov and an efficient method of minimizing the error in the approximation. Finally, we introduce a family of general minimization problems that can be approached using this method and examine applications in credit risk modelling, particularly under recent regulatory changes related to loan classification and provision calculations under IFRS 9.

In this review, the fundamental basis of machine learning (ML) and data mining (DM) are summarized together with the techniques for distilling knowledge from state-of-the-art omics experiments. This includes an introduction to the basic mathematical principles of unsupervised/supervised learning methods, dimensionality reduction techniques, deep neural networks architectures and the applications of these in bioinformatics. Several case studies under evaluation mainly involve next generation sequencing (NGS) experiments, like deciphering gene expression from total and single cell (scRNA-seq) analysis; for the latter, a description of all recent artificial intelligence (AI) methods for the investigation of cell sub-types, biomarkers and imputation techniques are described. Other areas of interest where various ML schemes have been investigated are for providing information regarding transcription factors (TF) binding sites, chromatin organization patterns and RNA binding proteins (RBPs), while analyses on RNA sequence and structure as well as 3D dimensional protein structure predictions with the use of ML are described. Furthermore, we summarize the recent methods of using ML in clinical oncology, when taking into consideration the current omics data with pharmacogenomics to determine personalized treatments. With this review we wish to provide the scientific community with a thorough investigation of main novel ML applications which take into consideration the latest achievements in genomics, thus, unraveling the fundamental mechanisms of biology towards the understanding and cure of diseases.

The present paper is devoted to the study of robust control problems of parabolic stochastic partial differential equations under model uncertainty. To be more precise, the robust control problem under investigation is expressed as a stochastic differential game in a real separable infinite dimensional Hilbert space. By resorting to the theory of mild solutions, we prove that the elliptic partial differential equation associated with the problem at hand, also known as the Hamilton-Jacobi-Bellman-Isaacs equation, admits a unique solution, which is the value function of the game. Furthermore, we investigate the problem of existence of an optimal control pair that satisfies a saddle point property. Finally, as a demonstration of the proposed approach, we apply our results to the study of a certain robust control problem arising in the spatiotemporal management of natural resources.

The main objective of this chapter is to propose a hybrid evolutionary feature selection approach for solving credit scoring problems subject to constraints. A hybrid scheme combining filter and wrapper-based approaches is proposed to develop an accurate credit scoring model with a high predictive performance. Initially, the minimum redundancy maximum relevance algorithm is applied to find an optimal set of features that is mutually and maximally dissimilar and can represent the response variable effectively, allowing for an ordering of features by their importance. Subsequently, an iterative procedure, where supervised machine learning algorithms such as the logistic regression and the linear-discriminant analysis are combined with an evolutionary optimization algorithm like the genetic algorithm, is applied to choose the feature subset that maximizes an appropriate classification measure according to the predefined features and subject to the predefined constraints. The performance of the proposed method is illustrated using standard credit scoring datasets.

Spatiotemporal dynamics are introduced in a standard Ramsey model of optimal growth in which capital moves toward locations where the marginal productivity of capital is relatively higher. We extend Pontryagin s maximum principle to account for transition dynamics governed by a nonlinear partial di⁄erential equation emerging from spatial capital ows. The potential spatial heterogeneity of optimal growth, as seen from the point of view of an optimizing social planner, is examined. Our results suggest that for a high utility discount rate, the spatial capital ows induce the emergence of optimal spatial patterns, while for a low utility discount, a at earth steady state is socially optimal. Furthermore, when spatial heterogeneities exist due to total factor productivity di⁄erences across locations, we identify conditions under which the spatial capital ows could intensify or weaken spatial inequalities.

This paper contributes to the literature on decision making under multiple probability models by studying a class of variational preferences. These preferences are defined in terms of Fréchet mean utility functionals, which are based on the Wasserstein metric in the space of probability models. In order to produce a measure that is the “closest” to all probability models in the given set, we find the barycenter of the set. We derive explicit expressions for the Fréchet–Wasserstein mean utility functionals and show that they can be expressed in terms of an expansion that provides a tractable link between risk aversion and ambiguity aversion. The proposed utility functionals are illustrated in terms of two applications. The first application allows us to define the social discount rate under model uncertainty. In the second application, the functionals are used in risk securitization. The barycenter in this case can be interpreted as the model that maximizes the probability that different decision makers will agree on, which could be useful for designing and pricing a catastrophe bond. This paper was accepted by Manel Baucells, decision analysis.

The present paper aims to study a robust-entropic optimal control problem arising in the management of financial institutions. More precisely, we consider an economic agent who manages the portfolio of a financial firm. The manager has the possibility to invest part of the firm's wealth in a classical Black-Scholes type financial market, and also, as the firm is exposed to a stochastic cash flow of liabilities, to proportionally transfer part of its liabilities to a third party as a means of reducing risk. However, model uncertainty aspects are introduced as the manager does not fully trust the model she faces, hence she decides to make her decision robust. By employing robust control and dynamic programming techniques, we provide closed form solutions for the cases of the (i) logarithmic; (ii) exponential and (iii) power utility functions. Moreover, we provide a detailed study of the limiting behavior, of the associated stochastic differential game at hand, which, in a special case, leads to break down of the solution of the resulting Hamilton-Jacobi-Bellman-Isaacs equation. Finally, we present a detailed numerical study that elucidates the effect of robustness on the optimal decisions of both players.

Most credit scoring algorithms are designed with the assumption to be executed in an environment characterized by an automatic processing of credit applications, without considering the input of expert opinions. Since in credit scoring applications expert opinions have been proved very helpful, in this work, we propose a combination strategy of integrating soft computing methods with expert knowledge. The ability of interpretation of the predictive power of each feature in the credit dataset is strengthened by the engagement of experts in the credit scoring process, and the proposed wrapper-based feature selection approach which explores how the features contributing most towards the classification of borrowers. In particular, an unsupervised machine learning algorithm allows experts to create one or more clustering scenarios regarding the features by defining a desired number of clusters per scenario. For each clustering scenario, the Analytic Hierarchy Process is applied for helping experts to make preferences for features of each cluster, set pair-wise constraints for features of equal importance, and evaluate their subjective judgments in terms of consistency. Then, expert opinions are taken into consideration for solving a credit scoring problem in the form of an optimization problem subject to constraints via soft computing methods based on supervised machine learning and evolutionary optimization algorithms. Testing instances on standard credit dataset are established to verify the effectiveness of the proposed methodology.

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.

This paper deals with the exterior Calderón operator for not necessarily spherical domains. We present a new approach of finding the norm of the exterior Calderón operator for a wide class of surfaces. The basic tool in the treatment is the set of eigenfunctions and eigenvalues to the Laplace–Beltrami operator for the surface. The norm is obtained in view of an eigenvalue problem of a quadratic form containing the exterior Calderón operator. The connection of the exterior Calderón operator to the transition matrix for a perfectly conducting surface is analyzed.