No arbitrage and closure results for trading cones with transaction costs

In this paper, we consider trading with proportional transaction costs as in Schachermayer’s paper (Schachermayer in Math. Finance 14:19–48, 2004). We give a necessary and sufficient condition for ${\mathcal{A}}$ , the cone of claims attainable from zero endowment, to be closed. Then we show how to define a revised set of trading prices in such a way that, firstly, the corresponding cone of claims attainable for zero endowment, ${\tilde{ {\mathcal{A}}}}$ , does obey the fundamental theorem of asset pricing and, secondly, if ${\tilde{ {\mathcal{A}}}}$ is arbitrage-free then it is the closure of ${\mathcal{A}}$ . We then conclude by showing how to represent claims

Design and analysis of cross vaults along history

The history of cross vaults began almost 2,000 years ago with a widespread use during the Middle Ages and Renaissance, becoming nowadays one of the most diffused and fascinating structural typologies of the European building cultural heritage. However, conversely to the undeniable excellence achieved by the ancient masons, the structural behavior of these elements is still at the center of the scientific debate. In this regard, with the aim of reviewing the knowledge on this subject as a concise and valuable support for researchers involved in conservation of historical buildings, with a focus on design rules and structural analysis, the present study firstly introduces the cross vaults from a historical perspective, by describing the evolution of the main geometrical shapes together with basic practical rules used to size them. Then, the article deals with the subsequent advancements in structural analysis methods of vaults, until the development of modern limit analysis.This work was partially carried out under the program "Dipartimento di Protezione Civile - Consorzio RELUIS", signed on 2013-12-27.info:eu-repo/semantics/publishedVersio