Stochastic maximum principle for optimal control of SPDEs

In this note, we give the stochastic maximum principle for optimal control of stochastic PDEs in the general case (when the control domain need not be convex and the diffusion coefficient can contain a control variable)

Stochastic Maximum Principle for Optimal Control ofPartial Differential Equations Driven by White Noise

We prove a stochastic maximum principle ofPontryagin's type for the optimal control of a stochastic partial differential equationdriven by white noise in the case when the set of control actions is convex. Particular attention is paid to well-posedness of the adjoint backward stochastic differential equation and the regularity properties of its solution with values in infinite-dimensional spaces

A linear approach for sparse coding by a two-layer neural network

Many approaches to transform classification problems from non-linear to linear by feature transformation have been recently presented in the literature. These notably include sparse coding methods and deep neural networks. However, many of these approaches require the repeated application of a learning process upon the presentation of unseen data input vectors, or else involve the use of large numbers of parameters and hyper-parameters, which must be chosen through cross-validation, thus increasing running time dramatically. In this paper, we propose and experimentally investigate a new approach for the purpose of overcoming limitations of both kinds. The proposed approach makes use of a linear auto-associative network (called SCNN) with just one hidden layer. The combination of this architecture with a specific error function to be minimized enables one to learn a linear encoder computing a sparse code which turns out to be as similar as possible to the sparse coding that one obtains by re-training the neural network. Importantly, the linearity of SCNN and the choice of the error function allow one to achieve reduced running time in the learning phase. The proposed architecture is evaluated on the basis of two standard machine learning tasks. Its performances are compared with those of recently proposed non-linear auto-associative neural networks. The overall results suggest that linear encoders can be profitably used to obtain sparse data representations in the context of machine learning problems, provided that an appropriate error function is used during the learning phase

Economic Growth and the Environment with Clean and Dirty Consumption

This paper aims to verify the existence of the Environmental Kuznets Curve (EKC) or inverted U-shaped relationship between economic growth and environmental degradation in the context of endogenous growth. An important feature of this study is that the EKC is examined in the presence of pollution as a by product of consumption activities; also, pollution is a stock variable rather than a flow and tends to accumulate over time. In order to highlight the role of consumption on the environment, consumers do not consider directly pollution in the maximization problem and are assumed to choose between two different consumption types, characterized by a different impact on the environment (i.e. dirty and clean consumption). We find that substitution of dirty consumption with clean consumption alone is not sufficient to reduce environmental pollution. The result depends on the product differentiation and the cost to achieve it. From a social welfare perspective, more environmental awareness is unambiguously desirable when it generates less pollution. However, it could be that more environmental awareness leads to a lower level of social welfare depending on the costs of product differentiation and social marginal damage of pollution.Environmental Kuznets Curve, Economic Growth, Pollution, Consumption, Consumption behaviour

Eco-innovation and economic performance in industrial clusters: evidence from Italy

The article aims to investigate the presence of a correlation between eco-innovation and economic performance of an industrial district. The case analyzed in this article takes its cue from a study on a sample of 54 Italian industrial districts entitled "Eco-Districts" that, based on a series of criteria, has compiled a list of the most eco-efficient industrial districts. After selecting two districts in the field, but analyzed in this study for their different levels of eco-innovation, the article assesses the economic performance of the last three years through the analysis of trends in four indicators. However, the results show that only in some cases there is a connection between eco innovation and economic performance.industrial clusters, industrial districts, eco-innovation, economic performance

Consumer driven market mechanisms to fight inequality: the case of CSR/product differentiation models with asymmetric information

The bottom up pressure of "concerned" consumers and the rise of "socially responsible" products represents a new market mechanism to fight inequality and promote social inclusion. To analyze the new phenomenon of competition in corporate social responsibility (CSR) amid doubts on consumer tastes and of the effective corporate SR stance we adopt a horizontal differentiation approach in which the Hotelling segment is reinterpreted as the space of product SR characteristics and consumer tastes are uncertain. We find equilibria of the pure location and of the price-location games and show what changes when we move from a duopoly of profit maximizing producers to a mixed duopoly. Our findings illustrate that a nonzero degree of CSR is the optimal choice of profit maximizing corporations under reasonable parametric intervals of consumers’ "costs of ethical distance", corporate cost of CSR and uncertainty about consumer tastes.

Vico trecentocinquant’anni dopo

Traducción del italiano por José M. Sevilla Fernández.El autor centra su contribución a los estudios viquianos dentro del “nuevo curso” de estudios que generó su maestro Pietro Piovani, y en torno al Centro di Studi Vichiani y al correspondiente Bollettino desde sus mismas fundaciones. Y muestra el proceso constructivo de su filosofía viquiana como una filosofía histórica y no como una historia filosófica; destancando en este proceso investigador-constructivo una definida orientación “filológica”.The author places his contribution to Viquian studies within the “new course” of studies that his teacher Pietro Piovani produced, and around the Centro di Studi Vichiani and the corresponding Bollettino since their respective foundations. And he shows the constructive process of Viquian philosophy as a historical philosophy, and not just as a philosophical history; he thus highlights in this investigative-constructive process a clear-cut “philological” orientation.L’autore incentra il suo contributo sugli studi vichiani nell’ambito del “nuovo corso” di indagini inaugurato dal suo maestro Pietro Piovani, sul Centro di Studi Vichiani e sul corrispettivo Bollettino a partire dalla loro fondazione. Mostra altresì il processo costruttivo della propria filosofia vichiana intesa come una filosofia storica e non come una storia filosofica, evidenziando, in questo processo investigativo-costruttivo, un preciso orientamento “filologico”

Well Posedness of Operator Valued Backward Stochastic Riccati Equations in Infinite Dimensional Spaces

We prove existence and uniqueness of the mild solution of an infinite dimensional, operator valued, backward stochastic Riccati equation. We exploit the regularizing properties of the semigroup generated by the unbounded operator involved in the equation. Then the results will be applied to characterize the value function and optimal feedback law for a infinite dimensional, linear quadratic control problem with stochastic coefficients