Approximation bias in estimating risk aversion

The asymmetric approximation originally employed by Pratt (1964) to construct reduced-form measures of risk aversion s a downward bias when used for empirical estimation. Calculations based on recent survey data indicate that estimates from a symmetric approximation are generally three times larger than their asymmetric counterparts, a finding that may help to explain the equity premium puzzle.

Measuring Aversion to Health Risks

Researchers have commonly used financial gambles to assess risk preferences, though attitudes regarding monetary gambles may differ from those concerning health risks. Moreover, the conventional measure of risk preference—the Pratt-Arrow coefficient of relative risk aversion—is a point-elasticity suitable only for trivial risks, whereas the risks pertaining to medical treatment—often involving life-ordeath decisions—are quite substantial. Our objective is to examine attitudes toward health risks and the variables that influence those attitudes. In addition to the conventional metric, we employ an alternative measure of risk aversion designed for large-scale risks; the latter is calculated as an arc-elasticity of marginal utility. Both measures are applied to responses from a health preference survey, which incorporates a standard gamble over longevity. Measured risk aversion is then related to health and demographic variables using multiple linear regressions. Our research suggests that tolerance of health risks may be influenced by an endowment effect reflecting the asymmetry of medical information between patients and providers. We also find that the arc-elasticity measure captures more of the significant differences and has a stronger correlation to demographic and socio-economic variables than does the more traditional point-elasticity measure, indicating that the conventional measures of risk aversion are indeed ill suited to large-scale risks such as those involving health. In addition, our results suggest that health-related risk preferences may differ from financial risk attitudes. Although our sample is relatively small and largely homogeneous, these results collectively provide a basis for replication and a justification for additional study on the measurement of risk aversion with regard to health

Algebraic Optimization: Marginal Analysis Without Calculus

Teaching students to conduct marginal analysis before they have studied calculus is a major challenge in introductory economics courses.  This paper offers a simple algebraic approach to optimization that allows students to extract explicit marginal revenue and marginal cost functions from quadratic total revenue and total cost functions.  For first- or second-degree polynomials, the algebraic results are identical to those derived from differential calculus.  The technique offers students a deeper understanding of the profit maximization process than can be obtained from spreadsheets and other conventional teaching methods. The resulting functions can be used to develop related insights regarding issues such as deadweight loss and competitive market adjustments.  Numerical examples of monopoly and perfect competition are used to illustrate the algebraic optimization technique

PRICE ELASTICITY, TAX INCIDENCE, AND SALES VOLUME: A SIMPLE MODEL

Most intermediate microeconomics textbooks introduce taxes into the basic market model by using a supply-and-demand diagram, and explaining that the economic incidence of the tax falls most heavily on the group (buyers or sellers) whose behavior is least price-elastic. We extend that presentation by using algebra to relate the tax incidence more explicitly to the measurement of price elasticity. The result is a convenient equation showing that the ratio of tax burdens is exactly the inverse of the ratio of (absolute) price elasticities, along with well-known expressions for each group’s share of the tax burden. Additionally, the model generates the impact factor by which an excise tax reduces the quantity of a good sold. Both hypothetical and empirical examples of price elasticity are provided to illustrate the effects of excise and sales taxes

Performance of astrometric detection of a hotspot orbiting on the innermost stable circular orbit of the galactic centre black hole

The galactic central black hole Sgr A* exhibits outbursts of radiation in the near infrared (so-called IR flares). One model of these events consists in a hotspot orbiting on the innermost stable circular orbit (ISCO) of the hole. These outbursts can be used as a probe of the central gravitational potential. One main scientific goal of the second generation VLTI instrument GRAVITY is to observe these flares astrometrically. Here, the astrometric precision of GRAVITY is investigated in imaging mode, which consists in analysing the image computed from the interferometric data. The capability of the instrument to put in light the motion of a hotspot orbiting on the ISCO of our central black hole is then discussed. We find that GRAVITY's astrometric precision for a single star in imaging mode is smaller than the Schwarzschild radius of Sgr A*. The instrument can also demonstrate that a body orbiting on the last stable orbit of the black hole is indeed moving. It yields a typical size of the orbit, if the source is as bright as m_K=14. These results show that GRAVITY allows one to study the close environment of Sgr A*. Having access to the ISCO of the central massive black hole probably allows constraining general relativity in its strong regime. Moreover, if the hotspot model is appropriate, the black hole spin can be constrained.Comment: 13 pages, 11 figures ; accepted by MNRA

Kalman-filter control schemes for fringe tracking. Development and application to VLTI/GRAVITY

The implementation of fringe tracking for optical interferometers is inevitable when optimal exploitation of the instrumental capacities is desired. Fringe tracking allows continuous fringe observation, considerably increasing the sensitivity of the interferometric system. In addition to the correction of atmospheric path-length differences, a decent control algorithm should correct for disturbances introduced by instrumental vibrations, and deal with other errors propagating in the optical trains. We attempt to construct control schemes based on Kalman filters. Kalman filtering is an optimal data processing algorithm for tracking and correcting a system on which observations are performed. As a direct application, control schemes are designed for GRAVITY, a future four-telescope near-infrared beam combiner for the Very Large Telescope Interferometer (VLTI). We base our study on recent work in adaptive-optics control. The technique is to describe perturbations of fringe phases in terms of an a priori model. The model allows us to optimize the tracking of fringes, in that it is adapted to the prevailing perturbations. Since the model is of a parametric nature, a parameter identification needs to be included. Different possibilities exist to generalize to the four-telescope fringe tracking that is useful for GRAVITY. On the basis of a two-telescope Kalman-filtering control algorithm, a set of two properly working control algorithms for four-telescope fringe tracking is constructed. The control schemes are designed to take into account flux problems and low-signal baselines. First simulations of the fringe-tracking process indicate that the defined schemes meet the requirements for GRAVITY and allow us to distinguish in performance. In a future paper, we will compare the performances of classical fringe tracking to our Kalman-filter control.Comment: 17 pages, 8 figures, accepted for publication in A&

GCIRS16SW: a massive eclipsing binary in the Galactic Center

We report on the spectroscopic monitoring of GCIRS16SW, an Ofpe/WN9 star and LBV candidate in the central parsec of the Galaxy. SINFONI observations show strong daily spectroscopic changes in the K band. Radial velocities are derived from the HeI 2.112 um line complex and vary regularly with a period of 19.45 days, indicating that the star is most likely an eclipsing binary. Under various assumptions, we are able to derive a mass of ~ 50 Msun for each component.Comment: 4 pages, 4 figures, ApJ Letters accepte

Distinguishing an ejected blob from alternative flare models at the Galactic centre with GRAVITY

The black hole at the Galactic centre exhibits regularly flares of radiation, the origin of which is still not understood. In this article, we study the ability of the near-future GRAVITY infrared instrument to constrain the nature of these events. We develop realistic simulations of GRAVITY astrometric data sets for various flare models. We show that the instrument will be able to distinguish an ejected blob from alternative flare models, provided the blob inclination is >= 45deg, the flare brightest magnitude is 14 <= mK <= 15 and the flare duration is >= 1h30.Comment: 11 pages, 9 figures, accepted by MNRA

GRAVITY: The AO-Assisted, Two-Object Beam-Combiner Instrument

We present the proposal for the infrared adaptive optics (AO) assisted, two-object, high-throughput, multiple-beam-combiner GRAVITY for the VLTI. This instrument will be optimized for phase-referenced interferometric imaging and narrow-angle astrometry of faint, red objects. Following the scientific drivers, we analyze the VLTI infrastructure, and subsequently derive the requirements and concept for the optimum instrument. The analysis can be summarized with the need for highest sensitivity, phase referenced imaging and astrometry of two objects in the VLTI beam, and infrared wavefront-sensing. Consequently our proposed instrument allows the observations of faint, red objects with its internal infrared wavefront sensor, pushes the optical throughput by restricting observations to K-band at low and medium spectral resolution, and is fully enclosed in a cryostat for optimum background suppression and stability. Our instrument will thus increase the sensitivity of the VLTI significantly beyond the present capabilities. With its two fibers per telescope beam, GRAVITY will not only allow the simultaneous observations of two objects, but will also push the astrometric accuracy for UTs to 10 micro-arcsec, and provide simultaneous astrometry for up to six baselines.Comment: 12 pages, to be published in the Proceedings of the ESO Workshop on "The Power of Optical/IR Interferometry: Recent Scientific Results and 2nd Generation VLTI Instrumentation", eds. F. Paresce, A. Richichi, A. Chelli and F. Delplancke, held in Garching, Germany, 4-8 April 200