An optimal Skorokhod embedding for diffusions

AbstractGiven a Brownian motion (Bt)t⩾0 and a general target law μ (not necessarily centered or even in L1) we show how to construct an embedding of μ in B. This embedding is an extension of an embedding due to Perkins, and is optimal in the sense that it simultaneously minimises the distribution of the maximum and maximises the distribution of the minimum among all embeddings of μ. The embedding is then applied to regular diffusions, and used to characterise the target laws for which a Hp-embedding may be found

The joint law of the extrema, final value and signature of a stopped random walk

A complete characterization of the possible joint distributions of the maximum and terminal value of uniformly integrable martingale has been known for some time, and the aim of this paper is to establish a similar characterization for continuous martingales of the joint law of the minimum, final value, and maximum, along with the direction of the final excursion. We solve this problem completely for the discrete analogue, that of a simple symmetric random walk stopped at some almost-surely finite stopping time. This characterization leads to robust hedging strategies for derivatives whose value depends on the maximum, minimum and final values of the underlying asset

Robust pricing and hedging of double no-touch options

Double no-touch options, contracts which pay out a fixed amount provided an underlying asset remains within a given interval, are commonly traded, particularly in FX markets. In this work, we establish model-free bounds on the price of these options based on the prices of more liquidly traded options (call and digital call options). Key steps are the construction of super- and sub-hedging strategies to establish the bounds, and the use of Skorokhod embedding techniques to show the bounds are the best possible. In addition to establishing rigorous bounds, we consider carefully what is meant by arbitrage in settings where there is no {\it a priori} known probability measure. We discuss two natural extensions of the notion of arbitrage, weak arbitrage and weak free lunch with vanishing risk, which are needed to establish equivalence between the lack of arbitrage and the existence of a market model.Comment: 32 pages, 5 figure

Haplotype of prostaglandin synthase 2/cyclooxygenase 2 is involved in the susceptibility to inflammatory bowel disease

AIM: Prostaglandin G/H synthase 2 (PTGS2 or COX2) is one of the key factors in the cellular response to inflammation. PTGS2 is expressed in the affected intestinal segments of patients with inflammatory bowel diseases (IBD). In IBD patients, non-steroidal anti-inflammatory drugs, which have been shown to reduce both the production and activity of PTGS2, may activate IBD and aggravate the symptoms. We aimed at examining genetic variants of PTGS2 that may be risk factors for IBD. METHODS: We genotyped 291 individuals diagnosed with IBD and 367 controls from the Dutch population for the five most frequent polymorphisms of the PTGS2 gene. Clinical data were collected on all patients. DNA was extracted via normal laboratory methods. Genotyping was carried out using multiplex PCR followed by the Invader Assay and the 5 exonuclease assay (TaqMan). New polymorphism screening was performed by pre-screening with denaturing high-performance liquid chromatography, followed by fluorescent sequencing. RESULTS: Allele 5209G was weakly associated with Crohn's disease (odds ratio [OR] 1.63, 95% confidence interval [CI] 1.03-2.57), and allele 8473T with ulcerative colitis (OR 1.50, 95%CI 1.00-2.27). The haplotype including both alleles showed a strong association with IBD (OR 13.15, 95%CI 3.17-116.15). This haplotype, while rare (-0.3%) in the general population, is found more frequently in patients (3.5%). CONCLUSION: Our data suggest that this haplotype of PTGS2 contributes to the susceptibility of IBD

Liver fat in adults with GH deficiency: comparison to matched controls and the effect of GH replacement

CONTEXT: Existing data regarding the association between growth hormone deficiency (GHD) and liver fat content are conflicting. OBJECTIVE: We aimed i) to assess intrahepatocellular lipid (IHCL) content in hypopituitary adults with GHD compared to matched controls and ii) to evaluate the effect of growth hormone (GH) replacement on IHCL content. DESIGN: Cross-sectional comparison and controlled intervention study. PATIENTS, PARTICIPANTS: Cross-sectional comparison: 22 hypopituitary adults with GHD and 44 healthy controls matched for age, BMI, gender and ethnicity. Intervention study: 9 GHD patients starting GH replacement (GH Rx group), 9 GHD patients not starting replacement therapy (non-GH Rx group). INTERVENTION: Intervention study:GH replacement for 6 months in the GH Rx group, dosage was titrated to achieve normal IGF-1 levels. MAIN OUTCOME MEASURES: IHCL content determined by proton magnetic resonance spectroscopy (1 H MRS). RESULTS: Cross-sectional comparison: There was no difference in IHCL content between GHD patients and healthy controls (1.89% (0.30, 4.03) vs. 1.14% (0.22, 2.32); p=0.2), the prevalence of patients with hepatic steatosis (IHCL of ≥ 5.56%) was similar in the two groups (22.7% vs. 15.9%; chi square probability = 0.4). Intervention study: The change in IHCL content over 6 months did not differ between the GH Rx group and the non-GH Rx group (-0.63 ± 4.53% vs. +0.11 ± 1.46%; p=0.6). CONCLUSIONS: In our study liver fat content and the prevalence of hepatic steatosis did not differ between hypopituitary adults with GHD and matched controls. In GHD patients GH replacement had no effect on liver fat content

Photometric Analysis of Recently Discovered Eclipsing Binary GSC 00008-00901

Photometric analysis of $BVR_C$ light curves of newly discovered eclipsing binary GSC 0008-00901 is presented. The orbital period is improved to 0.28948(11) days. Photometric parameters are determined, as well. The analysis yielded to conclusion that system is an over-contact binary of W UMa type with components not in thermal contact. The light curves from 2005 show the presence of a spot on the surface of one of the components, while light curves from 2006 are not affected by maculation.Comment: Accepted for publication in Astrophysics & Space Scienc

Excess electron transport in cryoobjects

Experimental results on excess electron transport in solid and liquid phases of Ne, Ar, and solid N₂-Ar mixture are presented and compared with those for He. Muon spin relaxation technique in frequently switching electric fields was used to study the phenomenon of delayed muonium formation: excess electrons liberated in the m⁺ ionization track converge upon the positive muons and form Mu (m⁺e⁻) atoms. This process is shown to be crucially dependent upon the electron`s interaction with its environment (i.e., whether it occupies the conduction band or becomes localized in a bubble of tens of angstroms in radius) and upon its mobility in these states. The characteristic lengths involved are 10⁻⁶-10⁻⁴ cm, the characteristic times range from nanoseconds to tens microseconds. Such a microscopic length scale sometimes enables the electron spend its entire free lifetime in a state which may not be detected by conventional macroscopic techniques. The electron transport processes are compared in: liquid and solid helium (where electron is localized in buble); liquid and solid neon (where electrons are delocalized in solid and the coexistence of localized and delocalized electrons states was found in liquid recently); liquid and solid argon (where electrons are delocalized in both phases); orientational glass systems (solid N₂-Ar mixtures), where our results suggest that electrons are localized in orientational glass. This scaling from light to heavy rare gases enables us to reveal new features of excess electron localization on microscopic scale. Analysis of the experimental data makes it possible to formulate the following tendency of the muon end-of-track structure in condensed rare gases. The muon-self track interaction changes from the isolated pair (muon plus the nearest track electron) in helium to multi-pair (muon in the vicinity of tens track electrons and positive ions) in argon

Anderson-Yuval approach to the multichannel Kondo problem

We analyze the structure of the perturbation expansion of the general multichannel Kondo model with channel anisotropic exchange couplings and in the presence of an external magnetic field, generalizing to this case the Anderson-Yuval technique. For two channels, we are able to map the Kondo model onto a generalized resonant level model. Limiting cases in which the equivalent resonant level model is solvable are identified. The solution correctly captures the properties of the two channel Kondo model, and also allows an analytic description of the cross-over from the non Fermi liquid to the Fermi liquid behavior caused by the channel anisotropy.Comment: 23 pages, ReVTeX, 4 figures av. on reques

Women, anger, and aggression an interpretative phenomenological analysis

This study reports a qualitative phenomenological investigation of anger and anger-related aggression in the context of the lives of individual women. Semistructured interviews with five women are analyzed using interpretative phenomenological analysis. This inductive approach aims to capture the richness and complexity of the lived experience of emotional life. In particular, it draws attention to the context-dependent and relational dimension of angry feelings and aggressive behavior. Three analytic themes are presented here: the subjective experience of anger, which includes the perceptual confusion and bodily change felt by the women when angry, crying, and the presence of multiple emotions; the forms and contexts of aggression, paying particular attention to the range of aggressive strategies used; and anger as moral judgment, in particular perceptions of injustice and unfairness. The authors conclude by examining the analytic observations in light of phenomenological thinking

A Fermi Surface study of Ba1−x_{1-x}Kx_{x}BiO3_{3}

We present all electron computations of the 3D Fermi surfaces (FS's) in Ba$_{1-x}$K$_{x}$BiO$_{3}$ for a number of different compositions based on the selfconsistent Korringa-Kohn-Rostoker coherent-potential-approximation (KKR-CPA) approach for incorporating the effects of Ba/K substitution. By assuming a simple cubic structure throughout the composition range, the evolution of the nesting and other features of the FS of the underlying pristine phase is correlated with the onset of various structural transitions with K doping. A parameterized scheme for obtaining an accurate 3D map of the FS in Ba$_{1-x}$K$_{x}$BiO$_{3}$ for an arbitrary doping level is developed. We remark on the puzzling differences between the phase diagrams of Ba$_{1-x}$K$_{x}$BiO$_{3}$ and BaPb$_{x}$Bi$_{1-x}$O$_{3}$ by comparing aspects of their electronic structures and those of the end compounds BaBiO$_{3}$, KBiO$_3$ and BaPbO$_3$. Our theoretically predicted FS's in the cubic phase are relevant for analyzing high-resolution Compton scattering and positron-annihilation experiments sensitive to the electron momentum density, and are thus amenable to substantial experimental verification.Comment: 12 pages, 7 figures, to appear in Phys. Rev.