Back to basics: historical option pricing revisited

We reconsider the problem of option pricing using historical probability distributions. We first discuss how the risk-minimisation scheme proposed recently is an adequate starting point under the realistic assumption that price increments are uncorrelated (but not necessarily independent) and of arbitrary probability density. We discuss in particular how, in the Gaussian limit, the Black-Scholes results are recovered, including the fact that the average return of the underlying stock disappears from the price (and the hedging strategy). We compare this theory to real option prices and find these reflect in a surprisingly accurate way the subtle statistical features of the underlying asset fluctuations.Comment: 14 pages, 2 .ps figures. Proceedings, to appear in Proc. Roy. So

Quantum Sign Permutation Polytopes

Convex polytopes are convex hulls of point sets in the $n$-dimensional space \E^n that generalize 2-dimensional convex polygons and 3-dimensional convex polyhedra. We concentrate on the class of $n$-dimensional polytopes in \E^n called sign permutation polytopes. We characterize sign permutation polytopes before relating their construction to constructions over the space of quantum density matrices. Finally, we consider the problem of state identification and show how sign permutation polytopes may be useful in addressing issues of robustness

2D pattern evolution constrained by complex network dynamics

Complex networks have established themselves along the last years as being particularly suitable and flexible for representing and modeling several complex natural and human-made systems. At the same time in which the structural intricacies of such networks are being revealed and understood, efforts have also been directed at investigating how such connectivity properties define and constrain the dynamics of systems unfolding on such structures. However, lesser attention has been focused on hybrid systems, \textit{i.e.} involving more than one type of network and/or dynamics. Because several real systems present such an organization (\textit{e.g.} the dynamics of a disease coexisting with the dynamics of the immune system), it becomes important to address such hybrid systems. The current paper investigates a specific system involving a diffusive (linear and non-linear) dynamics taking place in a regular network while interacting with a complex network of defensive agents following Erd\"os-R\'enyi and Barab\'asi-Albert graph models, whose nodes can be displaced spatially. More specifically, the complex network is expected to control, and if possible to extinguish, the diffusion of some given unwanted process (\textit{e.g.} fire, oil spilling, pest dissemination, and virus or bacteria reproduction during an infection). Two types of pattern evolution are considered: Fick and Gray-Scott. The nodes of the defensive network then interact with the diffusing patterns and communicate between themselves in order to control the spreading. The main findings include the identification of higher efficiency for the Barab\'asi-Albert control networks.Comment: 18 pages, 32 figures. A working manuscript, comments are welcome

The escape problem under stochastic volatility: the Heston model

We solve the escape problem for the Heston random diffusion model. We obtain exact expressions for the survival probability (which ammounts to solving the complete escape problem) as well as for the mean exit time. We also average the volatility in order to work out the problem for the return alone regardless volatility. We look over these results in terms of the dimensionless normal level of volatility --a ratio of the three parameters that appear in the Heston model-- and analyze their form in several assymptotic limits. Thus, for instance, we show that the mean exit time grows quadratically with large spans while for small spans the growth is systematically slower depending on the value of the normal level. We compare our results with those of the Wiener process and show that the assumption of stochastic volatility, in an apparent paradoxical way, increases survival and prolongs the escape time.Comment: 29 pages, 12 figure

The impact of periodontal disease on hospital admission and mortality during COVID-19 pandemic

Introduction: COVID-19 has had a huge impact on society and healthcare and it has been suggested that people with periodontal disease are at risk of having worse outcomes from the disease. The aim of this study was to quantify the impact of periodontal disease on hospital admission and mortality during the COVID-19 pandemic. Materials and Methods: The study extracted UK Biobank participants who had taken a COVID-19 test between March and June 2020 (n = 13,253), of which 1,616 were COVID-19 positive (12%) and 11,637 were COVID-19 negative (88%). Self-reported oral health indicators of painful or bleeding gums and loose teeth were used as surrogates for periodontal disease, participants who did not report any of the aforementioned indicators were used as controls. Multivariable logistic regressions were used to obtain crude and adjusted odds ratios of COVID-19 infection, subsequent hospital admission and mortality adjusted for demographics, BMI, biomarkers, lifestyle and co-morbidities. Results: Painful gums, bleeding gums and loose teeth were reported in 2.7, 11.2 and 3.3% of participants with COVID-19 infection, respectively. Risk of COVID-19 infection in participants with painful or bleeding gums and loose teeth compared to controls was not increased (odds ratio [OR]: 1.10, 95% CI: 0.72–1.69; OR: 1.15, 95% CI: 0.84–1.59). COVID-19 positive participants with painful or bleeding gums had a higher risk of mortality (OR: 1.71, 95% CI: 1.05–2.72) but not hospital admission (OR: 0.90, 95% CI: 0.59–1.37). Participants with loose teeth did not show higher risk of hospital admission or mortality compared to the control group (OR = 1.55, 95% CI: 0.87–2.77; OR: 1.85; 95% CI: 0.92–2.72). Conclusion: There was insufficient evidence to link periodontal disease with an increased risk of COVID-19 infection. However, amongst the COVID-19 positive, there was significantly higher mortality for participants with periodontal disease. Utilization of linked dental and hospital patient records would improve the understanding of the impact of periodontal disease on COVID-19 related outcomes

Numerical performance of penalty method for American option pricing

This paper is devoted to studying the numerical performance of a power penalty method for a linear parabolic complementarity problem arising from American option valuation. The penalized problem is a nonlinear parabolic partial differential equation (PDE). A fitted finite volume method and an implicit time-stepping scheme are used for, respectively, the spatial and time discretizations of the PDE. The rate of convergence of the penalty methods with respect to the penalty parameters is investigated both theoretically and numerically. The numerical robustness and computational effectiveness of the penalty method with respect to the market parameters are also studied and compared with those from an existing popular method, project successive over relaxation.Department of Applied Mathematic

Rendering an Account: An Open-State Archive in Postgraduate Supervision

The paper begins with a brief account of the transformation of research degree studies under the pressures of global capitalism and neo-liberal governmentality. A parallel transformation is occurring in the conduct of research through the use of information and communication technologies. Yet the potential of ICTs to shape practices of surveillance or to produce new student-supervisor relations and enhance the processes of developing the dissertation has received almost no critical attention. As doctoral supervisor and student, we then describe the features and uses of a web-based open state archive of the student's work-in-progress, developed by the student and accessible to his supervisor. Our intention was to encourage more open conversations between data and theorising, student and supervisor, and ultimately between the student and professional community. However, we recognise that relations of accountability, as these have developed within a contemporary "audit revolution" (Power, 1994, 1997) in universities, create particular "lines of visibility" (Munro, 1996). Thus while the open-state archive may help to redefine in less managerial terms notions of quality, transparency, flexibility and accountability, it might also make possible greater supervisory surveillance. How should we think about the panoptical potential of this archive? We argue that the diverse kinds of interactional patterns and pedagogical intervention it encourages help to create shifting subjectivities. Moreover, the archive itself is multiple, in bringing together an array of diverse materials that can be read in various ways, by following multiple paths. It therefore constitutes a collage, which we identify as a mode of cognition and of accounting distinct from but related to argument and narrative. As a more "open" text (Iser, 1978) it has an indeterminacy which may render it less open to abuse for the technologies of managerial accountability

Preface

Preface - The second International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE) took place at Prague, Czech Republic, from Sunday 1 September to Thursday 5 September 2013

The prognostic value of tumor mitotic rate in children and adolescents with cutaneous melanoma:A retrospective cohort study

Background: Mitotic rate is a strong predictor of outcome in adult patients with primary cutaneous melanoma, but for children and adolescent patients this is unknown. Objective: We sought to assess the prognostic value of primary tumor mitotic rate in children and adolescents with primary melanoma. Methods: This was a cohort study of 156 patients who were <20 years of age and who had clinically localized cutaneous melanoma. Patients <12 years of age were classified as children and those 12 to 19 years of age as adolescents. Clinicopathologic and outcome data were collected. Recurrence-free and melanoma-specific survival were calculated. Univariable and multivariable analyses were performed using Cox proportional hazard models. Results: Thirteen of 156 patients (8%) were children. The mitotic rate was ≥1/mm2 in 104 patients (67%) and correlated with increasing Breslow thickness. A positive sentinel node was found in 23 of 61 patients (38%) in whom a sentinel lymph node biopsy specimen was obtained. The median follow-up was 61 months. Five-year melanoma-specific and recurrence-free survival rates were 91% and 84%, respectively. Mitotic rate was a stronger predictor of outcome than tumor thickness and was the only factor independently associated with recurrence-free survival. Limitations: This research was conducted at a single institution and the sample size was small. Conclusion: Mitotic rate is an independent predictor of recurrence-free survival in children and adolescents with clinically localized melanoma