A Penalty Method for the Numerical Solution of Hamilton-Jacobi-Bellman (HJB) Equations in Finance

We present a simple and easy to implement method for the numerical solution of a rather general class of Hamilton-Jacobi-Bellman (HJB) equations. In many cases, the considered problems have only a viscosity solution, to which, fortunately, many intuitive (e.g. finite difference based) discretisations can be shown to converge. However, especially when using fully implicit time stepping schemes with their desirable stability properties, one is still faced with the considerable task of solving the resulting nonlinear discrete system. In this paper, we introduce a penalty method which approximates the nonlinear discrete system to first order in the penalty parameter, and we show that an iterative scheme can be used to solve the penalised discrete problem in finitely many steps. We include a number of examples from mathematical finance for which the described approach yields a rigorous numerical scheme and present numerical results.Comment: 18 Pages, 4 Figures. This updated version has a slightly more detailed introduction. In the current form, the paper will appear in SIAM Journal on Numerical Analysi

Relation of modifiable neighborhood attributes to walking

Abstract Background There is a paucity of research examining associations between walking and environmental attributes that are more modifiable in the short term, such as car parking availability, access to transit, neighborhood traffic, walkways and trails, and sidewalks. Methods Adults were recruited between April 2004 and September 2006 in the Minneapolis-St Paul metropolitan area and in Montgomery County, Maryland using similar research designs in the two locations. Self-reported and objective environmental measures were calculated for participants\u27 neighborhoods. Self-reported physical activity was collected through the long form of the International Physical Activity Questionnaire (IPAQ-LF). Generalized estimating equations were used to examine adjusted associations between environmental measures and transport and overall walking. Results Participants (n = 887) averaged 47 years of age (SD = 13.65) and reported 67 min/week (SD = 121.21) of transport walking and 159 min/week (SD = 187.85) of non-occupational walking. Perceived car parking difficulty was positively related to higher levels of transport walking (OR 1.41, 95%CI: 1.18, 1.69) and overall walking (OR 1.18, 95%CI: 1.02, 1.37). Self-reported ease of walking to a transit stop was negatively associated with transport walking (OR 0.86, 95%CI: 0.76, 0.97), but this relationship was moderated by perceived access to destinations. Walking to transit also was related to non-occupational walking (OR 0.85, 95%CI: 0.73, 0.99). Conclusions Parking difficulty and perceived ease of access to transit are modifiable neighborhood characteristics associated with self-reported walking

On the magnetospheric ULF wave counterpart of substorm onset

One near‐ubiquitous signature of substorms observed on the ground is the azimuthal structuring of the onset auroral arc in the minutes prior to onset. Termed auroral beads, these optical signatures correspond to concurrent exponential increases in ground ultralow frequency (ULF) wave power and are likely the result of a plasma instability in the magnetosphere. Here, we present a case study showing the development of auroral beads from a Time History of Events and Macroscale Interactions during Substorms (THEMIS) all‐sky camera with near simultaneous exponential increases in auroral brightness, ionospheric and conjugate magnetotail ULF wave power, evidencing their intrinsic link. We further present a survey of magnetic field fluctuations in the magnetotail around substorm onset. We find remarkably similar superposed epoch analyses of ULF power around substorm onset from space and conjugate ionospheric observations. Examining periods of exponential wave growth, we find the ground‐ and space‐based observations to be consistent, with average growth rates of ∼0.01 s−1, lasting for ∼4 min. Cross‐correlation suggests that the space‐based observations lead those on the ground by approximately 1–1.5 min. Meanwhile, spacecraft located premidnight and ∼10 RE downtail are more likely to observe enhanced wave power. These combined observations lead us to conclude that there is a magnetospheric counterpart of auroral beads and exponentially increasing ground ULF wave power. This is likely the result of the linear phase of a magnetospheric instability, active in the magnetotail for several minutes prior to auroral breakup

Large Chiral Diffeomorphisms on Riemann Surfaces and W-algebras

The diffeomorphism action lifted on truncated (chiral) Taylor expansion of a complex scalar field over a Riemann surface is presented in the paper under the name of large diffeomorphisms. After an heuristic approach, we show how a linear truncation in the Taylor expansion can generate an algebra of symmetry characterized by some structure functions. Such a linear truncation is explicitly realized by introducing the notion of Forsyth frame over the Riemann surface with the help of a conformally covariant algebraic differential equation. The large chiral diffeomorphism action is then implemented through a B.R.S. formulation (for a given order of truncation) leading to a more algebraic set up. In this context the ghost fields behave as holomorphically covariant jets. Subsequently, the link with the so called W-algebras is made explicit once the ghost parameters are turned from jets into tensorial ghost ones. We give a general solution with the help of the structure functions pertaining to all the possible truncations lower or equal to the given order. This provides another contribution to the relationship between KdV flows and W-diffeomorphimsComment: LaTeX file, 31 pages, no figure. Version to appear in J. Math. Phys. Work partly supported by Region PACA and INF

N-methyl-N-alkylpyrrolidinium nonafluoro-1-butanesulfonate salts : Ionic liquid properties and plastic crystal behaviour

A series of N-methyl-N-alkylpyrrolidinium nonafluoro-1-butanesulfonate salts were synthesised and characterised. The thermophysical characteristics of this family of salts have been investigated with respect to potential use as ionic liquids and solid electrolytes. N-Methyl-N-butylpyrrolidinium nonafluoro-1-butanesulfonate (p1,4NfO) has the lowest melting point of the family, at 94 &deg;C. Electrochemical analysis of p1,4 NfO in the liquid state shows an electrochemical window of ~6 V. All compounds exhibit one or more solid&ndash;solid transitions at sub-ambient temperatures, indicating the existence of plastic crystal phases.<br /

The origin of centennial- to millennial-scale chronological gaps in storm emplaced beach ridge plains

Recent studies of tropical cyclone surge and wave emplaced beach ridge plains have shown that these sequences often contain centennial to millennial scale gaps in their chronologies. Two explanations for the gaps exist — they are due to erosion, or alternatively a cessation or substantial slowing of depositional processes suggestive of a quieter phase in intense storm activity. Differentiating between the two is important for uncovering reliable long-term storm histories from these sequences. We use landform morphology, sediment texture and luminescence chronology to determine the origin of substantial chronological gaps in a plain containing more than 100 shore-parallel ridges composed of fine-grained sand located in northeast Australia. We identify and describe the characteristics associated with both erosional and non-erosional gaps. The erosional gaps are associated with changes in orientation between ridge sets and often a high ridge with hummocky topography that appears to have been disturbed by aeolian activity. River floods likely caused the partial erosion of ridge sets. Non-erosional gaps do not display these morphological characteristics and are likely associated with quiescence in severe tropical cyclone activity. These geomorphic and chronological signatures can be used to identify different sorts of gaps in other ridge plains and are an important tool in the reconstruction of long-term storm histories from these coastal landforms. The data also suggests that fine-grained ridges can, like their coarse-grained counterparts, be predominantly deposited by storm waves and surge and their texture need not necessarily be indicative of the processes responsible for ridge development

Invariants of differential equations defined by vector fields

We determine the most general group of equivalence transformations for a family of differential equations defined by an arbitrary vector field on a manifold. We also find all invariants and differential invariants for this group up to the second order. A result on the characterization of classes of these equations by the invariant functions is also given.Comment: 13 page

Measured Sensitivity of the First Mark II Phased Array Feed on an ASKAP Antenna

This paper presents the measured sensitivity of CSIRO's first Mk. II phased array feed (PAF) on an ASKAP antenna. The Mk. II achieves a minimum system-temperature-over-efficiency $T_\mathrm{sys}/\eta$ of 78 K at 1.23 GHz and is 95 K or better from 835 MHz to 1.8 GHz. This PAF was designed for the Australian SKA Pathfinder telescope to demonstrate fast astronomical surveys with a wide field of view for the Square Kilometre Array (SKA).Comment: 5 pages, 2 figures, accepted for publication in Electromagnetics in Advanced applications (ICEAA), 2015 International Conference o