Universal Arbitrage Aggregator in Discrete Time Markets under Uncertainty

In a model independent discrete time financial market, we discuss the richness of the family of martingale measures in relation to different notions of Arbitrage, generated by a class $\mathcal{S}$ of significant sets, which we call Arbitrage de la classe $\mathcal{S}$. The choice of $\mathcal{S}$ reflects into the intrinsic properties of the class of polar sets of martingale measures. In particular: for S=${\Omega}$ absence of Model Independent Arbitrage is equivalent to the existence of a martingale measure; for $\mathcal{S}$ being the open sets, absence of Open Arbitrage is equivalent to the existence of full support martingale measures. These results are obtained by adopting a technical filtration enlargement and by constructing a universal aggregator of all arbitrage opportunities. We further introduce the notion of market feasibility and provide its characterization via arbitrage conditions. We conclude providing a dual representation of Open Arbitrage in terms of weakly open sets of probability measures, which highlights the robust nature of this concept

Frequency transfer via a two-way optical phase comparison on a multiplexed fiber network

We performed a two-way remote optical phase comparison on optical fiber. Two optical frequency signals were launched in opposite directions in an optical fiber and their phases were simultaneously measured at the other end. In this technique, the fiber noise was passively cancelled, and we compared two optical frequencies at the ultimate 1E-21 stability level. The experiment was performed on a 47 km fiber that is part of the metropolitan network for Internet traffic. The technique relies on the synchronous measurement of the optical phases at the two ends of the link, that is made possible by the use of digital electronics. This scheme offers several advantages with respect to active noise cancellation, and can be upgraded to perform more complex tasks

A VLBI experiment using a remote atomic clock via a coherent fibre link

We describe a VLBI experiment in which, for the first time, the clock reference is delivered from a National Metrology Institute to a radio telescope using a coherent fibre link 550 km long. The experiment consisted of a 24-hours long geodetic campaign, performed by a network of European telescopes; in one of those (Medicina, Italy) the local clock was alternated with a signal generated from an optical comb slaved to a fibre-disseminated optical signal. The quality of the results obtained with this facility and with the local clock is similar: interferometric fringes were detected throughout the whole 24-hours period and it was possible to obtain a solution whose residuals are comparable to those obtained with the local clock. These results encourage further investigation of the ultimate VLBI performances achievable using fibre dissemination at the highest precision of state-of-the-art atomic clocks

Measuring absolute frequencies beyond the GPS limit via long-haul optical frequency dissemination

Global Positioning System (GPS) dissemination of frequency standards is ubiquitous at present, providing the most widespread time and frequency reference for the majority of industrial and research applications worldwide. On the other hand, the ultimate limits of the GPS presently curb further advances in high-precision, scientific and industrial applications relying on this dissemination scheme. Here, we demonstrate that these limits can be reliably overcome even in laboratories without a local atomic clock by replacing the GPS with a 642-km-long optical fiber link to a remote primary caesium frequency standard. Through this configuration we stably address the 1S0—3P0 clock transition in an ultracold gas of 173Yb, with a precision that exceeds the possibilities of a GPS-based measurement, dismissing the need for a local clock infrastructure to perform beyond-GPS high-precision tasks. We also report an improvement of two orders of magnitude in the accuracy on the transition frequency reported in literature

The First Geodetic VLBI Field Test of LIFT: a 550-km-long Optical Fiber Link for Remote Antenna Synchronization

We present the first field test of the implementation of a coherent optical fiber link for remote antenna synchronization realized in Italy between the Italian Metrological Institute (INRIM) and the Medicina radio observatory of the National Institute for Astrophysics (INAF). The Medicina VLBI antenna participated in the EUR137 experiment carried out in September 2015 using, as reference systems, both the local H-maser and a remote H-maser hosted at the INRIM labs in Turin, separated by about 550 km. In order to assess the quality of the remote clock, the observed radio sources were split into two sets, using either the local or the remote H-maser. A system to switch automatically between the two references was integrated into the antenna field system. The observations were correlated in Bonn and preliminary results are encouraging since fringes were detected with both time references along the full 24 hours of the session. The experimental set-up, the results, and the perspectives for future radio astronomical and geodetic experiments are presented

Model-free superhedging duality

In a model-free discrete time financial market, we prove the superhedging duality theorem, where trading is allowed with dynamic and semistatic strategies. We also show that the initial cost of the cheapest portfolio that dominates a contingent claim on every possible path ω ∈ might be strictly greater than the upper bound of the no-arbitrage prices. We therefore characterize the subset of trajectories on which this duality gap disappears and prove that it is an analytic set

Pointwise Arbitrage Pricing Theory in Discrete Time

We develop a robust framework for pricing and hedging of derivative securities in discrete-time financial markets. We consider markets with both dynamically and statically traded assets and make minimal measurability assumptions. We obtain abstract (pointwise) fundamental theorem of asset pricing and pricing–hedging duality. Our results are general and, in particular, cover both the so-called model independent case as well as the classical probabilistic case of Dalang–Morton–Willinger. Our analysis is scenario-based: a model specification is equivalent to a choice of scenarios to be considered. The choice can vary between all scenarios and the set of scenarios charged by a given probability measure. In this way, our framework interpolates between a model with universally acceptable broad assumptions and a model based on a specific probabilistic view of future asset dynamics.ISSN:0364-765XISSN:1526-547

A Coherent Fiber Link for Very Long Baseline Interferometry

We realize a coherent fiber link for application in very long baseline interferometry (VLBI) for radio astronomy and geodesy. A 550-km optical fiber connects the Italian National Metrological Institute (INRIM) to a radio telescope in Italy and is used for the primary Cs fountain clock stability and accuracy dissemination. We use an ultrastable laser frequency- referenced to the primary standard as a transfer oscillator; at the radio telescope, an RF signal is generated from the laser by using an optical frequency comb. This scheme now provides the traceability of the local maser to the SI second, realized by the Cs fountain at the 1.7 × 10(-16) accuracy. The fiber link never limits the experiment and is robust enough to sustain radio astronomical campaigns. This experiment opens the possibility of replacing the local hydrogen masers at the VLBI sites with optically-synthesized RF signals. This could improve VLBI resolution by providing more accurate and stable frequency references and, in perspective, by enabling common- clock VLBI based on a network of telescopes connected by fiber links.We realize a coherent fiber link for application in very long baseline interferometry (VLBI) for radio astronomy and geodesy. A 550-km optical fiber connects the Italian National Metrological Institute (INRIM) to a radio telescope in Italy and is used for the primary Cs fountain clock stability and accuracy dissemination. We use an ultrastable laser frequency-referenced to the primary standard as a transfer oscillator; at the radio telescope, an RF signal is generated from the laser by using an optical frequency comb. This scheme now provides the traceability of the local maser to the SI second, realized by the Cs fountain at the 1.7 x 10(-16) accuracy. The fiber link never limits the experiment and is robust enough to sustain radio astronomical campaigns. This experiment opens the possibility of replacing the local hydrogen masers at the VLBI sites with optically-synthesized RF signals. This could improve VLBI resolution by providing more accurate and stable frequency references and, in perspective, by enabling common-clock VLBI based on a network of telescopes connected by fiber links