Geometry of vectorial martingale optimal transport and robust option pricing

This paper addresses robust finance, which is concerned with the development of models and approaches that account for market uncertainties. Specifically, we investigate the Vectorial Martingale Optimal Transport (VMOT) problem, the geometry of its solutions, and its application with robust option pricing problems in finance. To this end, we consider two-period market models and show that when the spatial dimension $d$ (the number of underlying assets) is 2, the extremal model for the cap option with a sub- or super-modular payout reduces to a single factor model in the first period, but not in general when $d > 2$. The result demonstrates a subtle relationship between spatial dimension, cost function supermodularity, and their effect on the geometry of solutions to the VMOT problem. We investigate applications of the model to financial problems and demonstrate how the dimensional reduction caused by monotonicity can be used to improve existing computational methods

Progressive collapse analysis of steel structures under fire conditions

This is the post-print version of the final paper published in Engineering Structures. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2011 Elsevier B.V.In this paper a robust static-dynamic procedure has been developed. The development extends the capability of the Vulcan software to model the dynamic and static behaviour of steel buildings during both local and global progressive collapse of the structures under fire conditions. The explicit integration method was adopted in the dynamic procedure. This model can be utilized to allow a structural analysis to continue beyond the temporary instabilities which would cause singularities in the full static analyses. The automatic switch between static and dynamic analysis makes the Vulcan a powerful tool to investigate the mechanism of the progressive collapse of the structures generated by the local failure of components. The procedure was validated against several practical cases. Some preliminary studies of the collapse mechanism of steel frame due to columns’ failure under fire conditions are also presented. It is concluded that for un-braced frame the lower loading ratio and bigger beam section can give higher failure temperature in which the global structural collapse happens. However, the localised collapse of the frame with the higher loading ratio and smaller beam section can more easily be generated. The bracing system is helpful to prevent the frame from progressive collapse. The higher lateral stiffness of the frame can generate the smaller vertical deformation of the failed column at the re-stable position. However, the global failure temperature of the frame is not sensitive to the lateral stiffness of the frame

Outcomes of ethnic minority groups with node-positive, non-metastatic breast cancer in two tertiary referral centers in Sydney, Australia

Purpose: There is a lack of information in ethnic minority groups with regard to presentation and treatment of early node-positive breast cancer. We carried out a retrospective study of patients referred to two tertiary cancer centers in South Western Sydney, both of which serve a high proportion of this ethnic minority population. Patients and methods: Women who had pathologically node-positive non-metastatic breast cancer (T1-3, N1-3, M0) diagnosed between 2003 and 2006 were studied, with variables of interest being tumor size, number of positive nodes, histological grade, hormone receptor status, age at diagnosis, country of birth and treatment. We compared the Asian and Western subgroups with regard to tumor characteristics, treatment and clinical outcomes. Results: A total of 652 eligible patients were identified, with a median follow-up of 6.1 years. Women with Asian backgrounds (n = 125, 20%) were significantly younger at presentation (48 years versus 55 years, p-value <0.0001) and more likely to undergo mastectomy (53% versus 39%, p-value 0.0009) and chemotherapy (86% versus 72%, p-value 0.0063) than their non-Asian counterparts. Tumor stage, grade and receptor status were not statistically different between these two groups. There were also no differences in disease-free survival and overall survival, with medians of 12.7 and 14.8 years respectively. Conclusion: Women of Asian background are younger at diagnosis, which may reflect population epidemiology and likely results in higher uptake of chemotherapy. Higher mastectomy rates may be influenced by cultural factors. Future research is warranted to investigate potential differences in tumor biology, psychosocial, economic and cultural factors

Empirical regularities of opening call auction in Chinese stock market

We study the statistical regularities of opening call auction using the ultra-high-frequency data of 22 liquid stocks traded on the Shenzhen Stock Exchange in 2003. The distribution of the relative price, defined as the relative difference between the order price in opening call auction and the closing price of last trading day, is asymmetric and that the distribution displays a sharp peak at zero relative price and a relatively wide peak at negative relative price. The detrended fluctuation analysis (DFA) method is adopted to investigate the long-term memory of relative order prices. We further study the statistical regularities of order sizes in opening call auction, and observe a phenomenon of number preference, known as order size clustering. The probability density function (PDF) of order sizes could be well fitted by a $q$-Gamma function, and the long-term memory also exists in order sizes. In addition, both the average volume and the average number of orders decrease exponentially with the price level away from the best bid or ask price level in the limit-order book (LOB) established immediately after the opening call auction, and a price clustering phenomenon is observed.Comment: 11 pages, 6 figures, 3 table

Association between microsatellite instability status and peri-operative release of circulating tumour cells in colorectal cancer

Microsatellite instability (MSI) in colorectal cancer (CRC) is a marker of immunogenicity and is associated with an increased abundance of tumour infiltrating lymphocytes (TILs). In this subgroup of colorectal cancer, it is unknown if these characteristics translate into a measurable difference in circulating tumour cell (CTC) release into peripheral circulation. This is the first study to compare MSI status with the prevalence of circulating CTCs in the peri-operative colorectal surgery setting. For this purpose, 20 patients who underwent CRC surgery with curative intent were enrolled in the study, and peripheral venous blood was collected at pre- (t1), intra- (t2), immediately post-operative (t3), and 14–16 h post-operative (t4) time points. Of these, one patient was excluded due to insufficient blood sample. CTCs were isolated from 19 patients using the IsofluxTM system, and the data were analysed using the STATA statistical package. CTC number was presented as the mean values, and comparisons were made using the Student t-test. There was a trend toward increased CTC presence in the MSI-high (H) CRC group, but this was not statistically significant. In addition, a Poisson regression was performed adjusting for stage (I-IV). This demonstrated no significant difference between the two MSI groups for pre-operative time point t1. However, time points t2, t3, and t4 were associated with increased CTC presence for MSI-H CRCs. In conclusion, there was a trend toward increased CTC release pre-, intra-, and post-operatively in MSI-H CRCs, but this was only statistically significant intra-operatively. When adjusting for stage, MSI-H was associated with an increase in CTC numbers intra-operatively and post-operatively, but not pre-operatively

Finite-size effect and the components of multifractality in financial volatility

Many financial variables are found to exhibit multifractal nature, which is usually attributed to the influence of temporal correlations and fat-tailedness in the probability distribution (PDF). Based on the partition function approach of multifractal analysis, we show that there is a marked finite-size effect in the detection of multifractality, and the effective multifractality is the apparent multifractality after removing the finite-size effect. We find that the effective multifractality can be further decomposed into two components, the PDF component and the nonlinearity component. Referring to the normal distribution, we can determine the PDF component by comparing the effective multifractality of the original time series and the surrogate data that have a normal distribution and keep the same linear and nonlinear correlations as the original data. We demonstrate our method by taking the daily volatility data of Dow Jones Industrial Average from 26 May 1896 to 27 April 2007 as an example. Extensive numerical experiments show that a time series exhibits effective multifractality only if it possesses nonlinearity and the PDF has impact on the effective multifractality only when the time series possesses nonlinearity. Our method can also be applied to judge the presence of multifractality and determine its components of multifractal time series in other complex systems.Comment: 9 RevTex pages including 9 eps figures. Comments and suggestions are warmly welcom

Health-related quality of life during chemoradiation in locally advanced rectal cancer : impacts and ethnic disparities

Aims: There is limited data on health-related quality of life (HRQoL) in locally advanced rectal cancer. We assessed HRQoL before, during and after neoadjuvant chemoradiation, correlated this to corresponding clinician-reported adverse events (CR-AEs) and explored disparities between patients of Asian ethnicity versus Caucasians. Correlation between HRQoL and treatment response was also assessed. Methods: A consecutive sample of patients was recruited. HRQoL was assessed with the EORTC QLQ-C30 before chemoradiation, week three of chemoradiation and one-week pre-surgery. Clinical variables including CR-AEs were recorded at these time-points. Patients self-reported socio-demographic variables. Treatment response was assessed by the tumour regression grade. HRQoL data were analysed with multilevel models. Results: Fifty-one patients were recruited. HRQoL completion rates were ≥86%. Cognitive and role functioning worsened significantly during treatment. Emotional, role and social functioning improved significantly at pre-surgery. Fatigue and nausea/vomiting worsened during treatment while fatigue, appetite loss, diarrhoea and financial difficulties improved from treatment to pre-surgery. Almost 30% of the cohort were Asian ethnicity. Differences were found in multiple HRQoL domains between Asians and Caucasians, with Asians faring worse. Significant differences were evident in physical, role and cognitive functioning, and in seven out of the 8 symptom scales. The correlation between patient-reported outcomes and clinician-reported outcomes was weak, with diarrhoea having the strongest correlation (r = 0.58). Vomiting during treatment correlated with poor response, whilst baseline constipation correlated with good response. Conclusion: Chemoradiation for locally advanced rectal cancer affects multiple HRQoL domains. Our findings highlight the importance of psychological aspects of treatment. Significant differences were identified between the Asian and Caucasian populations, with Asians consistently performing worse. Poor correlations between patient and clinician reporting strongly support the inclusion of patient-reported outcomes in clinical studies. HRQoL domains of vomiting and constipation are potential biomarkers of treatment response

Circulating tumour cell associated microRNA profiles change during chemoradiation and are predictive of response in locally advanced rectal cancer

Locally advanced rectal cancer (LARC) has traditionally been treated with trimodality therapy consisting of neoadjuvant radiation +/− chemotherapy, surgery, and adjuvant chemotherapy. There is currently a clinical need for biomarkers to predict treatment response and outcomes, especially during neoadjuvant therapy. Liquid biopsies in the form of circulating tumour cells (CTCs) and circulating nucleic acids in particular microRNAs (miRNA) are novel, the latter also being highly stable and clinically relevant regulators of disease. We studied a prospective cohort of 52 patients with LARC, and obtained samples at baseline, during treatment, and post-treatment. We enumerated CTCs during chemoradiation at these three time-points, using the IsofluxTM (Fluxion Biosciences Inc., Alameda, CA, USA) CTC Isolation and detection platform. We then subjected the isolated CTCs to miRNA expression analyses, using a panel of 106 miRNA candidates. We identified CTCs in 73% of patients at baseline; numbers fell and miRNA expression profiles also changed during treatment. Between baseline and during treatment (week 3) time-points, three microRNAs (hsa-miR-95, hsa-miR-10a, and hsa-miR-16-1*) were highly differentially expressed. Importantly, hsa-miR-19b-3p and hsa-miR-483-5p were found to correlate with good response to treatment. The latter (hsa-miR-483-5p) was also found to be differentially expressed between good responders and poor responders. These miRNAs represent potential predictive biomarkers, and thus a potential miRNA-based treatment strategy. In this study, we demonstrate that CTCs are present and can be isolated in the non-metastatic early-stage cancer setting, and their associated miRNA profiles can potentially be utilized to predict treatment response

Optical multiband surface photometry of a sample of Seyfert galaxies. I. Large-scale morphology and local environment analysis of matched Seyfert and inactive galaxy samples

Parallel analysis of the large-scale morphology and local environment of matched active and control galaxy samples plays an important role in studies of the fueling of active galactic nuclei. We carry out a detailed morphological characterization of a sample of 35 Seyfert galaxies and a matched sample of inactive galaxies in order to compare the evidence of non-axisymmetric perturbation of the potential and, in the second part of this paper, to be able to perform a multicomponent photometric decomposition of the Seyfert galaxies. We constructed contour maps, BVRcIc profiles of the surface brightness, ellipticity, and position angle, as well as colour index profiles. We further used colour index images, residual images, and structure maps, which helped clarify the morphology of the galaxies. We studied the presence of close companions using literature data. By straightening out the morphological status of some of the objects, we derived an improved morphological classification and built a solid basis for a further multicomponent decomposition of the Seyfert sample. We report hitherto undetected (to our knowledge) structural components in some Seyfert galaxies - a bar (Ark 479), an oval/lens (Mrk 595), rings (Ark 120, Mrk 376), a nuclear bar and ring (Mrk 352), and nuclear dust lanes (Mrk 590). We compared the large-scale morphology and local environment of the Seyfert sample to those of the control one and found that (1) the two samples show similar incidences of bars, rings, asymmetries, and close companions; (2) the Seyfert bars are generally weaker than the bars of the control galaxies; (3) the bulk of the two samples shows morphological evidence of non-axisymmetric perturbations of the potential or close companions; (4) the fueling of Seyfert nuclei is not directly related to the large-scale morphology and local environment of their host galaxies.Comment: Accepted for publication in A&