This paper presents models of equity valuation where future dividends are assumed to follow a generalized Bernoulli process consistent with the actual dividend payout behavior of many firms. This uncertain dividend stream induces a probability distribution of present value. We show how to calculate the first moment of this distribution using functional equations. As well, we demonstrate how to calculate a confidence interval using Monte Carlosimulation. This first moment and interval allows an analyst to determine whether a stock is overor under-valued.

Abstract:
We use N-body simulations to explore the influence of orbital eccentricity on the dynamical evolution of star clusters. Specifically we compare the mass loss rate, velocity dispersion, relaxation time, and the mass function of star clusters on circular and eccentric orbits. For a given perigalactic distance, increasing orbital eccentricity slows the dynamical evolution of a cluster due to a weaker mean tidal field. However, we find that perigalactic passes and tidal heating due to an eccentric orbit can partially compensate for the decreased mean tidal field by energizing stars to higher velocities and stripping additional stars from the cluster, accelerating the relaxation process. We find that the corresponding circular orbit which best describes the evolution of a cluster on an eccentric orbit is much less than its semi-major axis or time averaged galactocentric distance. Since clusters spend the majority of their lifetimes near apogalacticon, the properties of clusters which appear very dynamically evolved for a given galactocentric distance can be explained by an eccentric orbit. Additionally we find that the evolution of the slope of the mass function within the core radius is roughly orbit-independent, so it could place additional constraints on the initial mass and initial size of globular clusters with solved orbits. We use our results to demonstrate how the orbit of Milky Way globular clusters can be constrained given standard observable parameters like galactocentric distance and the slope of the mass function. We then place constraints on the unsolved orbits of NGC 1261,NGC 6352, NGC 6496, and NGC 6304 based on their positions and mass functions.

Abstract:
We have performed N-body simulations of tidally filling star clusters with a range of orbits in a Milky Way-like potential to study the effects of orbital inclination and eccentricity on their structure and evolution. At small galactocentric distances Rgc, a non-zero inclination results in increased mass loss rates. Tidal heating and disk shocking, the latter sometimes consisting of two shocking events as the cluster moves towards and away from the disk, help remove stars from the cluster. Clusters with inclined orbits at large Rgc have decreased mass loss rates than the non-inclined case, since the strength the disk potential decreases with Rgc. Clusters with inclined and eccentric orbits experience increased tidal heating due to a constantly changing potential, weaker disk shocks since passages occur at higher Rgc, and an additional tidal shock at perigalacticon. The effects of orbital inclination decrease with orbital eccentricity, as a highly eccentric cluster spends the majority of its lifetime at a large Rgc. The limiting radii of clusters with inclined orbits are best represented by the rt of the cluster when at its maximum height above the disk, where the cluster spends the majority of its lifetime and the rate of change in rt is a minimum. Conversely, the effective radius is independent of inclination in all cases.

Abstract:
We have performed N-body simulations of star clusters orbiting in a spherically symmetric smooth galactic potential. The model clusters cover a range of initial half-mass radii and orbital eccentricities in order to test the historical assumption that the tidal radius of a cluster is imposed at perigalacticon. The traditional assumption for globular clusters is that since the internal relaxation time is larger than its orbital period, the cluster is tidally stripped at perigalacticon. Instead, our simulations show that a cluster with an eccentric orbit does not need to fully relax in order to expand. After a perigalactic pass, a cluster re-captures previously unbound stars, and the tidal shock at perigalacticon has the effect of energizing inner region stars to larger orbits. Therefore, instead of the limiting radius being imposed at perigalacticon, it more nearly traces the instantaneous tidal radius of the cluster at any point in the orbit. We present a numerical correction factor to theoretical tidal radii calculated at perigalacticon which takes into consideration both the orbital eccentricity and current orbital phase of the cluster.

Abstract:
Monte Carlo simulations of long SGR event sequences based on lognormal distributions with a range of time intervals and intensity distribution parameters have been investigated. The main conclusions are that the majority of SGRs with properties similar to SGR 1806-20 have been detected but SGRs with mean waiting times much longer than SGR 1806-20 remain to be discovered. A large decrease in the probability for detection of an SGR source results from a relatively small increase in the distribution parameters obtained for SGR 1806-20. A new breed of experiments with very long observation times are required to search for this type of source.

Abstract:
We propose an evolutionary model to describe the dynamical evolution of star cluster systems in tidal fields, in which we calibrated the parametric equations defining the model by running direct N-body simulations of star clusters with a wide range of initial masses and set of orbital parameters, living within the external tidal field generated by a disc-like galaxy. We derived a new method to solve numerically the evolutionary equations, allowing us to infer constraints on the mass of a star cluster from its age, present-day mass, orbital parameters and external gravitational potential. The result has been applied to the metal-rich subsample of Galactic globular clusters, being a good representation of a disc-bulge population. We reconstructed the initial mass function of these objects from the present-day mass function, finding that a lognormal distribution is well preserved during the evolution of the globular cluster system. The evolution of a power-law initial mass function has been evaluated, confirming that it transforms into a lognormal distribution of the cluster masses within an Hubble time. Our results are consistent with a formation scenario in which metal-rich Galactic globular clusters formed from giant molecular clouds in high-pressure regions during the early phases of the evolution of the Galactic disc and bulge.

Abstract:
(shortened) Direct N-body calculations are presented of the formation of Galactic clusters using GasEx, which is a variant of the code Nbody6. The calculations focus on the possible evolution of the Orion Nebula Cluster (ONC) by assuming that the embedded OB stars explosively drove out 2/3 of its mass in the form of gas about 0.4 Myr ago. A bound cluster forms readily and survives for 150 Myr despite additional mass loss from the large number of massive stars, and the Galactic tidal field. This is the very first time that cluster formation is obtained under such realistic conditions. The cluster contains about 1/3 of the initial 10^4 stars, and resembles the Pleiades Cluster to a remarkable degree, implying that an ONC-like cluster may have been a precursor of the Pleiades. This scenario predicts the present expansion velocity of the ONC, which will be measurable by upcoming astrometric space missions (DIVA and GAIA). These missions should also detect the original Pleiades members as an associated expanding young Galactic-field sub-population. The results arrived at here suggest that Galactic clusters form as the nuclei of expanding OB associations.

Abstract:
The 2008 financial crisis has produced volatility levels not seen since the 1987 stock market crash more than 20 years ago. During that time, the culprit was thought to be index futures and program trading. This time, leveraged ETFs and their rebalancing trades have been singled out by some to explain both the spike in volatility and the appearance of large price swings at the end of the trading day. This study examines the merit of these accusations and whether the increase in volatility and end of the day price momentum is indeed linked to leveraged ETFs and their rebalancing trades. For the S&P 500, the relationship appears to be a spurious coincidence.

Abstract:
This paper presents the results of a behavioral
economics study to test if the tax rates submitted to financethe public provision of a
private good are influenced by changing the nameof the private good. A revealed-preference
laboratory decision-making experiment is used to test if participants choose
significantly different tax rates to supportprovision of a private good named as a health care
investment compared to an identical good named as a neutral monetary
investment.Although
some previous studies focusing on both framing and context effects find
differences associated with health versus non-health environments, these
studies have not involved voting over public provision of a private good. In
our experimental environment, participants with different income endowments provide
their preferred proportional tax rates for financing public provision of a
private good in either a neutral or a health context. The implemented tax rate is the median preferred tax
rate, and once the budget is determined, each participant receives the same
quantity of the publicly provided private good. In each context, the payoff functions are
the same. The only difference between the contexts is the name attached to the
publicly provided private good, regardless
of the name attached to the publicly provided private good,consuming it imposes no
externalities. This controls for the positive externality characteristics of
many health care goods, but not for preferences evoked by the merit good
character of health care which factor into decisions about the public provision
of health care. We find that the theoretical predictions of the median voter
model are generally supported by the data. However, the conjecture that

Abstract:
in this paper, we study systems of two conservation laws with homogeneous quadratic flux functions. we use the viscous profile criterion for shock admissibility. this criterion leads to the occurrence of non-classical transitional shock waves, which are sensitively dependent on the form of the viscosity matrix. the goal of this paper is to lay a foundation for investigating how the structure of solutions of the riemann problem is affected by the choice of viscosity matrix. working in the framework of the fundamental wave manifold, we derive a necessary and sufficient condition on the model parameters for the presence of transitional shock waves. using this condition, we are able to identify the regions in the wave manifold that correspond to transitional shock waves. also, we determine the boundaries in the space of model parameters that separate models with differing numbers of transitional regions.