WEIGHTED EXPECTED UTILITY HEDGE RATIOS

We derive a new hedge ratio based on weighted expected utility. Weighted expected utility is a generalization of expected utility that permits non-linear probability weights. Generally speaking weighted expected utility hedge ratios are less than minimum variance hedge ratios and larger than expected utility hedge ratios.Hedging, hedge ratio, weighted expected utility, Allais Paradox, Marketing,

NON-EXPECTED UTILITY THEORIES: WEIGHTED EXPECTED, RANK DEPENDENT, AND CUMULATIVE PROSPECT THEORY UTILITY

This paper discusses some of the failings of expected utility including the Allais paradox and expected utility's inadequate one dimensional characterization of risk. Three alternatives to expected utility are discussed at length; weighted expected utility, rank dependent utility, and cumulative prospect theory. Each alternative is capable of explaining Allais paradox type problems and permits more sophisticated multi dimensional risk preferences.Risk and Uncertainty,

High Angular Resolution Mid-infrared Imaging of Young Stars in Orion BN/KL

We present Keck LWS images of the Orion BN/KL star forming region obtained in the first multi-wavelength study to have 0.3-0.5" resolution from 4.7 to 22 microns. The young stellar objects designated infrared source-n and radio source-I are believed to dominate the BN/KL region. We have detected extended emission from a probable accretion disk around source-n but infer a stellar luminosity on the order of only 2000 Lsun. Although source-I is believed to be more luminous, we do not detect an infrared counterpart even at the longest wavelengths. However, we resolve the closeby infrared source, IRc2, into an arc of knots ~1000 AU long at all wavelengths. Although the physical relation of source-I to IRc2 remains ambiguous, we suggest these sources mark a high density core (10^7-10^8 pc^-3 over 1000 AU) within the larger BN/KL star forming cluster. The high density may be a consequence of the core being young and heavily embedded. We suggest the energetics of the BN/KL region may be dominated by this cluster core rather than one or two individual sources.Comment: 13 pages including 3 color figures. Accepted to The Astrophysical Journal Letters pending slight reduction in length. High resolution figures (jpeg) may be found at http://cfa-www.harvard.edu/~lincoln/keck.bnkl.midir.ppr

Photonic ring resonator filters for astronomical OH suppression

Ring resonators provide a means of filtering specific wavelengths from a waveguide, and optionally dropping the filtered wavelengths into a second waveguide. Both of these features are potentially useful for astronomical instruments. In this paper we focus on their use as notch filters to remove the signal from atmospheric OH emission lines from astronomical spectra, however we also briefly discuss their use as frequency combs for wavelength calibration and as drop filters for Doppler planet searches. We derive the design requirements for ring resonators for OH suppression from theory and finite difference time domain simulations. We find that rings with small radii (<10 microns) are required to provide an adequate free spectral range, leading to high index contrast materials such as Si and Si$_{3}$N$_{4}$. Critically coupled rings with high self-coupling coefficients should provide the necessary Q factors, suppression depth, and throughput for efficient OH suppression. We report on our progress in fabricating both Si and Si$_{3}$N$_{4}$ rings for OH suppression, and give results from preliminary laboratory tests. Our early devices show good control over the free spectral range and wavelength separation of multi-ring devices. The self-coupling coefficients are high (>0.9), but further optimisation is required to achieve higher Q and deeper notches, with current devices having $Q \approx 4000$ and $\approx 10$ dB suppression. The overall prospects for the use of ring resonators in astronomical instruments is promising, provided efficient fibre-chip coupling can be achieved.Comment: Submitted to Optics Express feature issue on Recent Advances in Astrophotonics (27 pages, 20 figs

Limits of ultra-high-precision optical astrometry: Stellar surface structures

We investigate the astrometric effects of stellar surface structures as a practical limitation to ultra-high-precision astrometry, e.g. in the context of exoplanet searches, and to quantify the expected effects in different regions of the HR-diagram. Stellar surface structures are likely to produce fluctuations in the integrated flux and radial velocity of the star, as well as a variation of the observed photocentre, i.e. astrometric jitter, and closure phase. We use theoretical considerations supported by Monte Carlo simulations to derive statistical relations between the corresponding astrometric, photometric, and radial-velocity effects. For most stellar types the astrometric jitter due to stellar surface structures is expected to be of order 10 micro-AU or greater. This is more than the astrometric displacement typically caused by an Earth-size exoplanet in the habitable zone, which is about 1-4 micro-AU for long-lived main-sequence stars. Only for stars with extremely low photometric variability (<0.5 mmag) and low magnetic activity, comparable to that of the Sun, will the astrometric jitter be of order 1 micro-AU, suffcient to allow the astrometric detection of an Earth-sized planet in the habitable zone. While stellar surface structure may thus seriously impair the astrometric detection of small exoplanets, it has in general negligible impact on the detection of large (Jupiter-size) planets and on the determination of stellar parallax and proper motion. From the starspot model we also conclude that the commonly used spot filling factor is not the most relevant parameter for quantifying the spottiness in terms of the resulting astrometric, photometric and radial-velocity variations.Comment: 12 pages, 4 figures, submitted to A&

Probing the close environment of young stellar objects with interferometry

The study of Young Stellar Objects (YSOs) is one of the most exciting topics that can be undertaken by long baseline optical interferometry. The magnitudes of these objects are at the edge of capabilities of current optical interferometers, limiting the studies to a few dozen, but are well within the capability of coming large aperture interferometers like the VLT Interferometer, the Keck Interferometer, the Large Binocular Telescope or 'OHANA. The milli-arcsecond spatial resolution reached by interferometry probes the very close environment of young stars, down to a tenth of an astronomical unit. In this paper, I review the different aspects of star formation that can be tackled by interferometry: circumstellar disks, multiplicity, jets. I present recent observations performed with operational infrared interferometers, IOTA, PTI and ISI, and I show why in the next future one will extend these studies with large aperture interferometers.Comment: Review to be published in JENAM'2002 proceedings "The Very Large Telescope Interferometer Challenges for the future

Long-Baseline Interferometric Multiplicity Survey of the Sco-Cen OB Association

We present the first multiplicity-dedicated long baseline optical interferometric survey of the Scorpius-Centaurus-Lupus-Crux association. We used the Sydney University Stellar Interferometer to undertake a survey for new companions to 58 Sco-Cen B- type stars and have detected 24 companions at separations ranging from 7-130mas, 14 of which are new detections. Furthermore, we use a Bayesian analysis and all available information in the literature to determine the multiplicity distribution of the 58 stars in our sample, showing that the companion frequency is F = 1.35 and the mass ratio distribution is best described as a power law with exponent equal to -0.46, agreeing with previous Sco-Cen high mass work and differing significantly from lower-mass stars in Tau-Aur. Based on our analysis, we estimate that among young B-type stars in moving groups, up to 23% are apparently single stars. This has strong implications for the understanding of high-mass star formation, which requires angular momentum dispersal through some mechanism such as formation of multiple systems.Comment: 7 figures, 5 tables, accepted for publication in MNRA