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

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

Stability of central finite difference schemes for the Heston PDE

This paper deals with stability in the numerical solution of the prominent Heston partial differential equation from mathematical finance. We study the well-known central second-order finite difference discretization, which leads to large semi-discrete systems with non-normal matrices A. By employing the logarithmic spectral norm we prove practical, rigorous stability bounds. Our theoretical stability results are illustrated by ample numerical experiments

Gender differences in health-related quality of life of adolescents with cystic fibrosis

BACKGROUND: Female patients with cystic fibrosis (CF) have consistently poorer survival rates than males across all ages. To determine if gender differences exist in health-related quality of life (HRQOL) of adolescent patients with CF, we performed a cross-section analysis of CF patients recruited from 2 medical centers in 2 cities during 1997–2001. METHODS: We used the 87-item child self-report form of the Child Health Questionnaire to measure 12 health domains. Data was also collected on age and forced expiratory volume in 1 second (FEV(1)). We analyzed data from 98 subjects and performed univariate analyses and linear regression or ordinal logistic regression for multivariable analyses. RESULTS: The mean (SD) age was 14.6 (2.5) years; 50 (51.0%) were female; and mean FEV(1 )was 71.6% (25.6%) of predicted. There were no statistically significant gender differences in age or FEV(1). In univariate analyses, females reported significantly poorer HRQOL in 5 of the 12 domains. In multivariable analyses controlling for FEV(1 )and age, we found that female gender was associated with significantly lower global health (p < 0.05), mental health (p < 0.01), and general health perceptions (p < 0.05) scores. CONCLUSION: Further research will need to focus on the causes of these differences in HRQOL and on potential interventions to improve HRQOL of adolescent patients with CF

LNK suppresses interferon signaling in melanoma.

LNK (SH2B3) is a key negative regulator of JAK-STAT signaling which has been extensively studied in malignant hematopoietic diseases. We found that LNK is significantly elevated in cutaneous melanoma; this elevation is correlated with hyperactive signaling of the RAS-RAF-MEK pathway. Elevated LNK enhances cell growth and survival in adverse conditions. Forced expression of LNK inhibits signaling by interferon-STAT1 and suppresses interferon (IFN) induced cell cycle arrest and cell apoptosis. In contrast, silencing LNK expression by either shRNA or CRISPR-Cas9 potentiates the killing effect of IFN. The IFN-LNK signaling is tightly regulated by a negative feedback mechanism; melanoma cells exposed to IFN upregulate expression of LNK to prevent overactivation of this signaling pathway. Our study reveals an unappreciated function of LNK in melanoma and highlights the critical role of the IFN-STAT1-LNK signaling axis in this potentially devastating disease. LNK may be further explored as a potential therapeutic target for melanoma immunotherapy

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

The influence of lateral advection on the residual estuarine circulation : a numerical modeling study of the Hudson River Estuary

Author Posting. © American Meteorological Society, 2009. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 39 (2009): 107-124, doi:10.1175/2008JPO3952.1.In most estuarine systems it is assumed that the dominant along-channel momentum balance is between the integrated pressure gradient and bed stress. Scaling the amplitude of the estuarine circulation based on this balance has been shown to have predictive skill. However, a number of authors recently highlighted important nonlinear processes that contribute to the subtidal dynamics at leading order. In this study, a previously validated numerical model of the Hudson River estuary is used to examine the forces driving the residual estuarine circulation and to test the predictive skill of two linear scaling relationships. Results demonstrate that the nonlinear advective acceleration terms contribute to the subtidal along-channel momentum balance at leading order. The contribution of these nonlinear terms is driven largely by secondary lateral flows. Under a range of forcing conditions in the model runs, the advective acceleration terms nearly always act in concert with the baroclinic pressure gradient, reinforcing the residual circulation. Despite the strong contribution of the nonlinear advective terms to the subtidal dynamical balance, a linear scaling accurately predicts the strength of the observed residual circulation in the model. However, this result is largely fortuitous, as this scaling does not account for two processes that are fundamental to the estuarine circulation. The skill of this scaling results because of the compensatory relationship between the contribution of the advective acceleration terms and the suppression of turbulence due to density stratification. Both of these processes, neither of which is accounted for in the linear scaling, increase the residual estuarine circulation but have an opposite dependence on tidal amplitude and, consequently, strength of stratification.This research was supported by the Beacon Institute for Rivers and Estuaries—Woods Hole Oceanographic Institution postdoctoral fellowship program, as well as NSF Grants OCE-0452054 and OCE-0451740

Subtidal salinity and velocity in the Hudson River estuary : observations and modeling

Author Posting. © American Meteorological Society, 2008. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 38 (2008): 753-770, doi:10.1175/2007JPO3808.1.A tidally and cross-sectionally averaged model based on the temporal evolution of the quasi-steady Hansen and Rattray equations is applied to simulate the salinity distribution and vertical exchange flow along the Hudson River estuary. The model achieves high skill at hindcasting salinity and residual velocity variation during a 110-day period in 2004 covering a wide range of river discharges and tidal forcing. The approach is based on an existing model framework that has been modified to improve model skill relative to observations. The external forcing has been modified to capture meteorological time-scale variability in salinity, stratification, and residual velocity due to sea level fluctuations at the open boundary and along-estuary wind stress. To reflect changes in vertical mixing due to stratification, the vertical mixing coefficients have been modified to use the bottom boundary layer height rather than the water depth as an effective mixing length scale. The boundary layer parameterization depends on the tidal amplitude and the local baroclinic pressure gradient through the longitudinal Richardson number, and improves the model response to spring–neap variability in tidal amplitude during periods of high river discharge. Finally, steady-state model solutions are evaluated for both the Hudson River and northern San Francisco Bay over a range of forcing conditions. Agreement between the model and scaling of equilibrium salinity intrusions lends confidence that the approach is transferable to other estuaries, despite significant differences in bathymetry. Discrepancies between the model results and observations at high river discharge are indicative of limits at which the formulation begins to fail, and where an alternative approach that captures two-layer dynamics would be more appropriate.This research was supported by the Hudson River Foundation Grant 005/03A, NSF Grant OCE-0452054, and by the Postdoctoral Scholar Program at the Woods Hole Oceanographic Institution, with funding provided by the J. Seward Johnson Fund

A finite difference method for pricing European and American options under a geometric Lévy process

In this paper we develop a numerical approach to a fractional-order differential Linear Complementarity Problem (LCP) arising in pricing European and American options under a geometric Lévy process. The LCP is first approximated by a nonlinear penalty fractional Black-Scholes (fBS) equation. We then propose a finite difference scheme for the penalty fBS equation. We show that both the continuous and the discretized fBS equations are uniquely solvable and establish the convergence of the numerical solution to the viscosity solution of the penalty fBS equation by proving the consistency, stability and monotonicity of the numerical scheme. We also show that the discretization has the 2nd-order truncation error in both the spatial and time mesh sizes. Numerical results are presented to demonstrate the accuracy and usefulness of the numerical method for pricing both European and American options under the geometric Lévy process