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

Local times for typical price paths and pathwise Tanaka formulas

Following a hedging based approach to model free financial mathematics, we prove that it should be possible to make an arbitrarily large profit by investing in those one-dimensional paths which do not possess local times. The local time is constructed from discrete approximations, and it is shown that it is $\alpha$-H\"older continuous for all $\alpha<1/2$. Additionally, we provide various generalizations of F\"ollmer's pathwise It\^o formula

Pathwise super-replication via Vovk's outer measure

Since Hobson's seminal paper [D. Hobson: Robust hedging of the lookback option. In: Finance Stoch. (1998)] the connection between model-independent pricing and the Skorokhod embedding problem has been a driving force in robust finance. We establish a general pricing-hedging duality for financial derivatives which are susceptible to the Skorokhod approach. Using Vovk's approach to mathematical finance we derive a model-independent super-replication theorem in continuous time, given information on finitely many marginals. Our result covers a broad range of exotic derivatives, including lookback options, discretely monitored Asian options, and options on realized variance.Comment: 18 page

A segmented total energy detector (sTED) for (n, γ) cross section measurements at n_TOF EAR2

This work was supported in part by the I+D+i grant PGC2018-096717-B-C21 funded by MCIN/AEI/10.13039/501100011033 and by the European Commission H2020 Framework Programme project SANDA (Grant agreement ID: 847552).The neutron time-of-flight facility n_TOF is characterised by its high instantaneous neutron intensity, high resolution and broad neutron energy spectra, specially conceived for neutron-induced reaction cross section measurements. Two Time-Of-Flight (TOR) experimental areas are available at the facility: experimental area 1 (EAR1), located at the end of the 185 m horizontal flight path from the spallation target, and experimental area 2 (EAR2), placed at 20 m from the target in the vertical direction. The neutron fluence in EAR2 is similar to 300 times more intense than in EARL in the relevant time-of-flight window. EAR2 was designed to carry out challenging cross-section measurements with low mass samples (approximately 1 mg), reactions with small cross-sections or/and highly radioactive samples. The high instantaneous fluence of EAR2 results in high counting rates that challenge the existing capture systems. Therefore, the sTED detector has been designed to mitigate these effects. In 2021, a dedicated campaign was done validating the performance of the detector up to at least 300 keV neutron energy. After this campaign, the detector has been used to perform various capture cross section measurements at n_TOF EAR2.MCIN/AEI/10.13039/501100011033 I+D+i PGC2018-096717-B-C21European Commission H2020 Framework Programme SANDA 84755

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

Molecular characterization of retinal stem cells and their niches in adult zebrafish

BACKGROUND: The persistence in adult teleost fish of retinal stem cells that exhibit all of the features of true 'adult stem cells' – self-renewal, multipotency, and the capacity to respond to injury by mitotic activation with the ability to regenerate differentiated tissues – has been known for several decades. However, the specialized cellular and molecular characteristics of these adult retinal stem cells and the microenvironmental niches that support their maintenance in the differentiated retina and regulate their activity during growth and regeneration have not yet been elucidated. RESULTS: Our data show that the zebrafish retina has two kinds of specialized niches that sustain retinal stem cells: 1) a neuroepithelial germinal zone at the interface between neural retina and ciliary epithelium, called the ciliary marginal zone (CMZ), a continuous annulus around the retinal circumference, and 2) the microenvironment around some Müller glia in the differentiated retina. In the uninjured retina, scattered Müller glia (more frequently those in peripheral retina) are associated with clusters of proliferating retinal progenitors that are restricted to the rod photoreceptor lineage, but following injury, the Müller-associated retinal progenitors can function as multipotent retinal stem cells to regenerate other types of retinal neurons. The CMZ has several features in common with the neurogenic niches in the adult mammalian brain, including access to the apical epithelial surface and a close association with blood vessels. Müller glia in the teleost retina have a complex response to local injury that includes some features of reactive gliosis (up-regulation of glial fibrillary acidic protein, GFAP, and re-entry into the cell cycle) together with dedifferentiation and re-acquisition of phenotypic and molecular characteristics of multipotent retinal progenitors in the CMZ (diffuse distribution of N-cadherin, activation of Notch-Delta signaling, and expression of rx1, vsx2/Chx10, and pax6a) along with characteristics associated with radial glia (expression of brain lipid binding protein, BLBP). We also describe a novel specific marker for Müller glia, apoE. CONCLUSION: The stem cell niches that support multi-lineage retinal progenitors in the intact, growing and regenerating teleost retina have properties characteristic of neuroepithelia and neurogenic radial glia. The regenerative capacity of the adult zebrafish retina with its ability to replace lost retinal neurons provides an opportunity to discover the molecular regulators that lead to functional repair of damaged neural tissue

Comparative study on usefulness of gentamycin-containing collagen implants in the treatment of patients with osteitis and osteomyelitis of the craniofacial skeleton

Introduction and objective A reduction in incidences of peri-surgical complications due to infections is achieved by antibiotic prophylaxis The objective of the study was to assess the usefulness of gentamycin-containing collagen implants (GCCI) in the treatment of patients with osteitis and osteomyelitis of the craniofacial skeleton. Material and Methods The retrospective study included 103 patients with osteitis and osteomyelitis. 54 patients were treated intra-operatively with GCCI (Garamycin, EusaPharma, Europe). 49 patients were treated according to standard procedures. Light microscopy and in vitro culture techniques were applied for bacteria specific identification, and to investigate the resistance of detected microbiota to antibiotics. Patients received one dose of antibiotic pre-operatively. Post-operative antibiotic treatment was administered individually, according to clinical course and microbiological tests. The patients were followed-up on days 3, 7 and 14 after discharge for local complications; radiographic follow-up was performed 3, 6 and 12 months after surgery. Results The course of post-operative antibiotic therapy was shorter in GCCI patients than in the control group (median 1 vs. 7 days); they also required shorter hospitalization (median 3 vs. 4 days). Implantation of GCCI significantly reduced the incidence of local complications (OR 0.30, 95%CI 0.11–0.83, p<0.0001), independently of the use of postoperative antibiotic therapy. On follow-up after 3–12 months, all patients presented with good soft tissue and bone healing. Conclusions The results of this comparative study advocate the use of GCCI in osteomyelitis of various origin in oral and maxillofacial surgery, as they seemed to reduce the incidence of local complications, shorten antibiotic administration time and hospital stay

Direct Catalytic Anti-Markovnikov Addition of Carboxylic Acids to Alkenes

A direct catalytic anti-Markovnikov addition of carboxylic acids to alkenes is reported. The catalyst system is comprised of the Fukuzumi acridinium photooxidant (1) and a substoichiometric quantity of a hydrogen atom donor. Oxidizable olefins such as styrenes, trisubstituted aliphatic alkenes, and enamides can be employed along with a variety of carboxylic acids to afford the anti-Markovnikov addition adducts exclusively. A deuterium-labeling experiment lends insight to the potential mechanism

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

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