Monte Carlo methods for the valuation of multiple exercise options

We discuss Monte Carlo methods for valuing options with multiple exercise features in discrete time. By extending the recently developed duality ideas for American option pricing we show how to obtain estimates on the prices of such options using Monte Carlo techniques. We prove convergence of our approach and estimate the error. The methods are applied to options in the energy and interest rate derivative markets

Astrometric and photometric initial mass functions from the UKIDSS Galactic Clusters Survey - II. The Alpha Persei open cluster

This article has been accepted for publication in Monthly Notices of the Royal Astronomical Society © 2012 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved.We present the results of a deep (J = 19.1mag) infrared (ZYJHK) survey over the full α Per open cluster extracted from the Data Release 9 of the United Kingdom Infrared Telescope Infrared Deep Sky Survey Galactic Clusters Survey (UKIDSS). We have selected ∼700 cluster member candidates in ∼56 square degrees in α Per by combining photometry in five near-infrared passbands and proper motions derived from the multiple epochs provided by the UKIDSS Galactic Clusters Survey (GCS) Data Release 9 (DR9). We also provide revised membership for all previously published α Per low-mass stars and brown dwarfs recovered in GCS based on the new photometry and astrometry provided by DR9. We find no evidence of K-band variability in members of α Per with dispersion less than 0.06-0.09mag. We employed two independent but complementary methods to derive the cluster luminosity and mass functions: a probabilistic analysis and a more standard approach consisting of stricter astrometric and photometric cuts. We find that the resulting luminosity and mass functions obtained from both methods are consistent. We find that the shape of the α Per mass function is similar to that of the Pleiades although the characteristic mass may be higher after including higher mass data from earlier studies (the dispersion is comparable). We conclude that the mass functions of α Per, the Pleiades and Praesepe are best reproduced by a log-normal representation similar to the system field mass function although with some variation in the characteristic mass and dispersion values.Peer reviewe

Southern Infrared Proper Motion Survey I: Discovery of New High Proper Motion Stars From First Full Hemisphere Scan

We present the first results from the Southern Infrared Proper Motion Survey. Using 2 Micron All Sky Survey data along with that of the SuperCOSMOS sky survey we have been able to produce the first widefield infrared proper motion survey. Having targeted the survey to identify nearby M, L and T dwarfs we have discovered 72 such new objects with proper motions greater than 0.5''/yr with 10 of these having proper motions in excess of 1''/yr. The most interesting of these objects is SIPS1259-4336 a late M dwarf. We have calculated a trigonometric parallax for this object of $\pi = 276 \pm 41$ milliarcseconds yielding a distance of $3.62\pm0.54$pc. We have also discovered a common proper motion triple system and an object with a common proper motion with LHS 128. The survey completeness is limited by the small epoch differences between many 2MASS and UKI observations. Hence we only recover 22% of Luyten objects with favourable photometry. However the Luyten study is itself unquantifiably incomplete. We discuss the prospect of enhancing the survey volume by reducing the lower proper motion limit.Comment: 20 pages, 11 figures, accepted for publication in Astronomy and Astrophysic

A New Ultracool White Dwarf Discovered in the SuperCOSMOS Sky Survey

We present photographic B, R and I photometry, and optical and near-infrared spectroscopy, of a new ultracool white dwarf (UCWD) discovered in the SuperCOSMOS Sky Survey. The spectrum of SSSJ1556-0806 shows strong flux suppression due to the presence of collisionally induced absorption by molecular hydrogen (H2CIA), a feature characteristic of the cool, high density environments found in the atmospheres of ultracool white dwarfs. SSSJ1556-0806 therefore joins a list of <10 ultracool white dwarfs displaying extreme flux suppression. Synthetic model fitting suggests an effective temperature <3000K, which if true would make this one of the coolest white dwarfs currently known. We also exploit the similarity between the SEDs of SSSJ1556-0806 and the well-studied UCWD LHS 3250 to aid in the determination of the atmospheric parameters in a regime where models consistently fail to reproduce observations. SSSJ1556-0806 is relatively bright (R ~ 17.8), making it particularly amenable to follow up observations to obtain trigonometric parallax and IR photometry.Comment: Accepted for publication in MNRA

Cleaning sky survey databases using Hough Transform and Renewal String approaches

Large astronomical databases obtained from sky surveys such as the SuperCOSMOS Sky Survey (SSS) invariably suffer from spurious records coming from artefactual effects of the telescope, satellites and junk objects in orbit around earth and physical defects on the photographic plate or CCD. Though relatively small in number these spurious records present a significant problem in many situations where they can become a large proportion of the records potentially of interest to a given astronomer. Accurate and robust techniques are needed for locating and flagging such spurious objects, and we are undertaking a programme investigating the use of machine learning techniques in this context. In this paper we focus on the four most common causes of unwanted records in the SSS: satellite or aeroplane tracks, scratches, fibres and other linear phenomena introduced to the plate, circular halos around bright stars due to internal reflections within the telescope and diffraction spikes near to bright stars. Appropriate techniques are developed for the detection of each of these. The methods are applied to the SSS data to develop a dataset of spurious object detections, along with confidence measures, which can allow these unwanted data to be removed from consideration. These methods are general and can be adapted to other astronomical survey data.Comment: Accepted for MNRAS. 17 pages, latex2e, uses mn2e.bst, mn2e.cls, md706.bbl, shortbold.sty (all included). All figures included here as low resolution jpegs. A version of this paper including the figures can be downloaded from http://www.anc.ed.ac.uk/~amos/publications.html and more details on this project can be found at http://www.anc.ed.ac.uk/~amos/sattrackres.htm

Optical spectroscopy of candidate Alpha Persei white dwarfs

As part of an investigation into the high mass end of the initial mass-final mass relation we performed a search for new white dwarf members of the nearby (172.4 pc), young (80-90 Myr) $\alpha$ Persei open star cluster. The photometric and astrometric search using the UKIRT Infrared Deep Sky Survey and SuperCOSMOS sky surveys discovered 14 new white dwarf candidates. We have obtained medium resolution optical spectra of the brightest 11 candidates using the William Herschel Telescope and confirmed that while 7 are DA white dwarfs, 3 are DB white dwarfs and one is an sdOB star, only three have cooling ages within the cluster age, and from their position on the initial mass-final mass relation, it is likely none are cluster members. This result is disappointing, as recent work on the cluster mass function suggests that there should be at least one white dwarf member, even at this young age. It may be that any white dwarf members of $\alpha$ Per are hidden within binary systems, as is the case in the Hyades cluster, however the lack of high mass stars within the cluster also makes this seem unlikely. One alternative is that a significant level of detection incompleteness in the legacy optical image survey data at this Galactic latitude has caused some white dwarf members to be overlooked. If this is the case, Gaia will find them.Comment: 8 pages, 7 Figures, 3 Tables. Accepted for publication in MNRA

Proper motion surveys of the young open clusters Alpha Persei and the Pleiades

In this paper we present surveys of two open clusters using photometry and accurate astrometry from the SuperCOSMOS microdensitometer. These use plates taken by the Palomar Oschin Schmidt Telescope giving a wide field ($5^{\circ}$ from the cluster centre in both cases), accurate positions and a long time baseline for the proper motions. Distribution functions are fitted to proper motion vector point diagrams yeilding formal membership probabilities. Luminosity and mass functions are then produced along with a catalogue of high probability members. Background star contamination limited the depth of the study of Alpha Per to R=18. Due to this the mass function found for this cluster could only be fitted with a power law ($\xi(m) = m^{-\alpha}$) with $\alpha=0.86^{+0.14}_{-0.19}$. However with the better seperation of the Pleiades' cluster proper motion from the field population results were obtained down to R=21. As the mass function produced for this cluster extends to lower masses it is possible to see the gradient becoming increasingly shallow. This mass function is well fitted by a log normal distribution.Comment: 13 pages, 20 Figures, Accepted for publication in Astronomy and Astrophysic