Pathwise stochastic integrals for model free finance

We present two different approaches to stochastic integration in frictionless model free financial mathematics. The first one is in the spirit of It\^o's integral and based on a certain topology which is induced by the outer measure corresponding to the minimal superhedging price. The second one is based on the controlled rough path integral. We prove that every "typical price path" has a naturally associated It\^o rough path, and justify the application of the controlled rough path integral in finance by showing that it is the limit of non-anticipating Riemann sums, a new result in itself. Compared to the first approach, rough paths have the disadvantage of severely restricting the space of integrands, but the advantage of being a Banach space theory. Both approaches are based entirely on financial arguments and do not require any probabilistic structure.Comment: Published at http://dx.doi.org/10.3150/15-BEJ735 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Continuity of Local Time: An applied perspective

Continuity of local time for Brownian motion ranks among the most notable mathematical results in the theory of stochastic processes. This article addresses its implications from the point of view of applications. In particular an extension of previous results on an explicit role of continuity of (natural) local time is obtained for applications to recent classes of problems in physics, biology and finance involving discontinuities in a dispersion coefficient. The main theorem and its corollary provide physical principles that relate macro scale continuity of deterministic quantities to micro scale continuity of the (stochastic) local time.Comment: To appear in: "The fascination of Probability, Statistics and Their Applications. In honour of Ole E. Barndorff-Nielsen on his 80th birthday

Experimental setup and procedure for the measurement of the 7Be(n,p)7Li reaction at n_TOF

Following the completion of the second neutron beam line and the related experimental area (EAR2) at the n_TOF spallation neutron source at CERN, several experiments were planned and performed. The high instantaneous neutron flux available in EAR2 allows to investigate neutron induced reactions with charged particles in the exit channel even employing targets made out of small amounts of short-lived radioactive isotopes. After the successful measurement of the 7Be(n,) cross section, the 7Be(n,p)7Li reaction was studied in order to provide still missing cross section data of relevance for Big Bang Nucleosynthesis (BBN), in an attempt to find a solution to the cosmological Lithium abundance problem. This paper describes the experimental setup employed in such a measurement and its characterization.Séptimo Programa Marco de la Comunidad Europea de la Energía Atómica (Euratom)-Proyecto CHANDA (No. 605203)Narodowe Centrum Nauki (NCN)-UMO-2012/04/M/ST2/00700-UMO-2016/22/M/ST2/00183Croatian Science Foundation-HRZZ 168

Measurement of the 70Ge(n,γ) cross section up to 300 keV at the CERN n_TOF facility

Neutron capture data on intermediate mass nuclei are of key importance to nucleosynthesis in the weak component of the slow neutron capture processes, which occurs in massive stars. The (n,γ) cross section on 70Ge, which is mainly produced in the s process, was measured at the neutron time-of-flight facility n_TOF at CERN. Resonance capture kernels were determined up to 40 keV neutron energy and average cross sections up to 300 keV. Stellar cross sections were calculated from kT =5 keV tokT =100 keV and are in very good agreement with a previous measurement by Walter and Beer (1985) and recent evaluations. Average cross sectionsareinagreementwithWalterandBeer(1985)overmostoftheneutronenergyrangecovered,whilethey aresystematicallysmallerforneutronenergiesabove150keV.Wehavecalculatedisotopicabundancesproduced in s-process environments in a 25 solar mass star for two initial metallicities (below solar and close to solar). While the low metallicity model reproduces best the solar system germanium isotopic abundances, the close to solar model shows a good global match to solar system abundances in the range of mass numbers A=60–80.Austrian Science Fund J3503Adolf Messer Foundation ST/M006085/1European Research Council ERC2015-StGCroatian Science Foundation IP-2018-01-857

Present Status and Future Programs of the n_TOF Experiment

This is an Open Access article distributed under the terms of the Creative Commons Attribution-Noncommercial License 3.0, which permits unrestricted use, distribution, and reproduction in any noncommercial medium, provided the original work is properly citedThe neutron time-of-flight facility n_TOF at CERN, Switzerland, operational since 2001, delivers neutrons using the Proton Synchrotron (PS) 20 GeV/c proton beam impinging on a lead spallation target. The facility combines a very high instantaneous neutron flux, an excellent time of flight resolution due to the distance between the experimental area and the production target (185 meters), a low intrinsic background and a wide range of neutron energies, from thermal to GeV neutrons. These characteristics provide a unique possibility to perform neutron-induced capture and fission cross-section measurements for applications in nuclear astrophysics and in nuclear reactor technology.The most relevant measurements performed up to now and foreseen for the future will be presented in this contribution. The overall efficiency of the experimental program and the range of possible measurements achievable with the construction of a second experimental area (EAR-2), vertically located 20 m on top of the n_TOF spallation target, might offer a substantial improvement in measurement sensitivities. A feasibility study of the possible realisation of the installation extension will be also presented

Measurement of the Ge 70 (n,γ) cross section up to 300 keV at the CERN n-TOF facility

©2019 American Physical Society.Neutron capture data on intermediate mass nuclei are of key importance to nucleosynthesis in the weak component of the slow neutron capture processes, which occurs in massive stars. The (n,γ) cross section on Ge70, which is mainly produced in the s process, was measured at the neutron time-of-flight facility n-TOF at CERN. Resonance capture kernels were determined up to 40 keV neutron energy and average cross sections up to 300 keV. Stellar cross sections were calculated from kT=5 keV to kT=100 keV and are in very good agreement with a previous measurement by Walter and Beer (1985) and recent evaluations. Average cross sections are in agreement with Walter and Beer (1985) over most of the neutron energy range covered, while they are systematically smaller for neutron energies above 150 keV. We have calculated isotopic abundances produced in s-process environments in a 25 solar mass star for two initial metallicities (below solar and close to solar). While the low metallicity model reproduces best the solar system germanium isotopic abundances, the close to solar model shows a good global match to solar system abundances in the range of mass numbers A=60-80.Peer reviewedFinal Published versio

New measurement of the 242Pu(n,γ) cross section at n-TOF-EAR1 for MOX fuels : Preliminary results in the RRR

The spent fuel of current nuclear reactors contains fissile plutonium isotopes that can be combined with 238U to make mixed oxide (MOX) fuel. In this way the Pu from spent fuel is used in a new reactor cycle, contributing to the long-term sustainability of nuclear energy. The use of MOX fuels in thermal and fast reactors requires accurate capture and fission cross sections. For the particular case of 242Pu, the previous neutron capture cross section measurements were made in the 70's, providing an uncertainty of about 35% in the keV region. In this context, the Nuclear Energy Agency recommends in its "High Priority Request List" and its report WPEC-26 that the capture cross section of 242Pu should be measured with an accuracy of at least 7-12% in the neutron energy range between 500 eV and 500 keV. This work presents a brief description of the measurement performed at n-TOF-EAR1, the data reduction process and the first ToF capture measurement on this isotope in the last 40 years, providing preliminary individual resonance parameters beyond the current energy limits in the evaluations, as well as a preliminary set of average resonance parameters

High accuracy 234U(n,f) cross section in the resonance energy region

New results are presented of the 234U neutron-induced fission cross section, obtained with high accuracy in the resonance region by means of two methods using the 235U(n,f) as reference. The recent evaluation of the 235U(n,f) obtained with SAMMY by L. C. Leal et al. (these Proceedings), based on previous n-TOF data [1], has been used to calculate the 234U(n,f) cross section through the 234U/235U ratio, being here compared with the results obtained by using the n-TOF neutron flux

Characterization of the n-TOF EAR-2 neutron beam

The experimental area 2 (EAR-2) at CERNs neutron time-of-flight facility (n-TOF), which is operational since 2014, is designed and built as a short-distance complement to the experimental area 1 (EAR-1). The Parallel Plate Avalanche Counter (PPAC) monitor experiment was performed to characterize the beam prole and the shape of the neutron 'ux at EAR-2. The prompt γ-flash which is used for calibrating the time-of-flight at EAR-1 is not seen by PPAC at EAR-2, shedding light on the physical origin of this γ-flash

238U(n, γ) reaction cross section measurement with C 6D6 detectors at the n-TOF CERN facility

This is an Open Access article distributed under the terms of the Creative Commons Attribution License 2.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly citedThe radiative capture cross section of 238U is very important for the developing of new reactor technologies and the safety of existing ones. Here the preliminary results of the 238U(n,γ) cross section measurement performed at n-TOF with C6D6 scintillation detectors are presented, paying particular attention to data reduction and background subtraction.Peer reviewe