A Semi-Parametric Approach to the Detection of Non-Gaussian Gravitational Wave Stochastic Backgrounds

Using a semi-parametric approach based on the fourth-order Edgeworth expansion for the unknown signal distribution, we derive an explicit expression for the likelihood detection statistic in the presence of non-normally distributed gravitational wave stochastic backgrounds. Numerical likelihood maximization exercises based on Monte-Carlo simulations for a set of large tail symmetric non-Gaussian distributions suggest that the fourth cumulant of the signal distribution can be estimated with reasonable precision when the ratio between the signal and the noise variances is larger than 0.01. The estimation of higher-order cumulants of the observed gravitational wave signal distribution is expected to provide additional constraints on astrophysical and cosmological models.Comment: 26 pages, 3 figures, to appear in Phys. Rev.

On the valuation and incentive effects of executive cash bonus contracts

Executive compensation packages are often valued in an inconsistent manner: while employee stock options (ESOs) are typically valued ex-ante, cash bonuses are valued ex-post. This renders the existing valuation models of employee compensation packages theoretically unsatisfactory and, potentially, empirically distortive. In this paper, we propose an option-based framework for ex-ante valuation of cash bonus contracts. After obtaining closed-form expressions for ex-ante values of several frequently used types of bonus contracts, we utilize them to explore the e¤ects that the shape of a bonus contract has on the executive’s attitude toward risk-taking. We, also, study pay-performance sensitivity of such contracts. We show that the terms of a bonus contract can dramatically impact both risk-taking behavior as well as pay-performance incentives. Several testable predictions are made, and venues of future research outlined.Executive compensation, cash bonus, incentives, risk-taking behavior

Quantum delay in the time-of-arrival of free falling atoms

We use a stochastic representation of measured trajectories to derive an exact analytical expression for the probability distribution of the time-of-arrival (TOA) for a free falling particle, as well as approximate expressions for its mean value and standard-deviation in the semiclassical regime. We predict the existence of a positive shift $\delta$ between the semiclassical TOA ($t_{\text{mean}}$) and the classical TOA ($t_{\text{cl}}$) for a particle of mass $m$ falling in a constant and uniform gravitational field $g$ with zero initial velocity, with a value given by $\delta \equiv \frac{t_{\text{mean}}-t_{\text{cl}}}{t_{\text{cl}}} = \frac{\hbar^2}{16gx m^2\sigma^2},\$ where $\sigma$ is the width of the initial Gaussian wavepacket, and $x$ is the distance between the initial position of the source and that of the detector. We discuss the implications of this result on the weak equivalence principle in the quantum regime.Comment: 5 pages + 2 pages supplementary material. 1 Figure + 1 Tabl

On the mutual exclusiveness of time and position in quantum physics and the corresponding uncertainty relation for free falling particles

The uncertainty principle is one of the characteristic properties of quantum theory, where it signals the incompatibility of two types of measurements. In this paper, we argue that measurements of time-of-arrival $T_x$ at position $x$ and position $X_t$ at time $t$ are mutually exclusive for a quantum system, each providing complementary information about the state of that system. For a quantum particle of mass $m$ falling in a uniform gravitational field $g$, we show that the corresponding uncertainty relation can be expressed as $\Delta T_x \Delta X_t \geq \frac{\hbar}{2mg}$. This uncertainty relationship can be taken as evidence of the presence of a form of epistemic incompatibility in the sense that preparing the initial state of the system so as to decrease the measured position uncertainty will lead to an increase in the measured time-of-arrival uncertainty. These findings can be empirically tested in the context of ongoing or forthcoming experiments on measurements of time-of-arrival for free-falling quantum particles.Comment: 7 pages, 2 figures, 2 pages supplementary materia

Forward-Looking Measures of Higher-Order Dependencies with an Application to Portfolio Selection

This paper provides implied measures of higher-order dependencies between assets. The measures exploit only forward-looking information from the options market and can be used to construct an implied estimator of the covariance, co-skewness, and co-kurtosis matrices of asset returns. We implement the estimator using a sample of US stocks. We show that the higher-order dependencies vary heavily over time and identify which driving them. Furthermore, we run a portfolio selection exercise and show that investors can benefit from the better out-of-sample performance of our estimator compared to various historical benchmark estimators. The benefit is up to seven percent per year

Le fond gravitationnel stochastique : méthodes de détection en régimes non-Gaussiens

The new generation of interferometers should allow us to detect stochastic gravitational wave backgrounds that are expected to arise from a large number of random, independent, unresolved events of astrophysical or cosmological origin. Most detection methods for gravitational waves are based upon the assumption of Gaussian gravitational wave stochastic background signals and noise processes. Our main objective is to improve the methods that can be used to detect gravitational backgrounds in the presence of non-Gaussian distributions. We first maintain the assumption of Gaussian noise distributions so as to better focus on the impact of deviations from normality of the signal distribution in the context of the standard cross-correlation detection statistic. Using a 4th-order Edgeworth expansion of the unknown density for the signal and noise distributions, we first derive an explicit expression for the non-Gaussian likelihood ratio statistic, which is obtained as a function of the variance, but also skewness and kurtosis of the unknown signal and noise distributions. We use numerical procedures to generate maximum likelihood estimates for the gravitational wave distribution parameters for a set of symmetric heavy-tailed distributions, and we find that the fourth cumulant can be estimated with reasonable precision when the ratio between the signal and the noise variances is larger than 1%, which should be useful for analyzing the constraints on astrophysical and cosmological models. In a second step, we analyze the efficiency of the standard cross-correlation statistic in situations that also involve non-Gaussian noise distributions.Les méthodes standard de détection du fond gravitationnel stochastique reposent sur l'hypothèse simplificatrice selon laquelle sa distribution ainsi que celle du bruit des détecteurs sont Gaussiennes. Nous proposons dans cette thèse des méthodes améliorées de détection du fond gravitationnel stochastique qui tiennent compte explicitement du caractère non-Gaussien de ces distributions. En utilisant un développement d'Edgeworth, nous obtenons dans un premier temps une expression analytique pour la statistique du rapport de vraisemblance en présence d'une distribution non Gaussienne du fonds gravitationnel stochastique. Cette expression généralise l'expression habituelle lorsque le coefficient de symétrie et le coefficient d'aplatissement de la distribution du fond stochastique sont non nuls. Sur la base de simulations stochastiques pour différentes distributions symétriques présentant des queues plus épaisses que celles de la distribution Gaussienne, nous montrons par ailleurs que le 4eme cumulant peut-être estimé avec une précision acceptable lorsque le ratio signal à bruit est supérieur à 1%, ce qui devrait permettre d'apporter des contraintes supplémentaires intéressantes sur les valeurs de paramètres issus des modèles astrophysiques et cosmologiques. Dans un deuxième temps, nous cherchons à analyser l'impact sur les méthodes de détection du fond gravitationnel stochastique de déviations par rapport à la normalité dans la distribution du bruit des détecteurs

Stochastic gravitational wave background : detection methods in non-Gaussian regimes

Les méthodes standard de détection du fond gravitationnel stochastique reposent sur l'hypothèse simplificatrice selon laquelle sa distribution ainsi que celle du bruit des détecteurs sont Gaussiennes. Nous proposons dans cette thèse des méthodes améliorées de détection du fond gravitationnel stochastique qui tiennent compte explicitement du caractère non-Gaussien de ces distributions. En utilisant un développement d'Edgeworth, nous obtenons dans un premier temps une expression analytique pour la statistique du rapport de vraisemblance en présence d'une distribution non Gaussienne du fonds gravitationnel stochastique. Cette expression généralise l'expression habituelle lorsque le coefficient de symétrie et le coefficient d'aplatissement de la distribution du fond stochastique sont non nuls. Sur la base de simulations stochastiques pour différentes distributions symétriques présentant des queues plus épaisses que celles de la distribution Gaussienne, nous montrons par ailleurs que le 4eme cumulant peut-être estimé avec une précision acceptable lorsque le ratio signal à bruit est supérieur à 1%, ce qui devrait permettre d'apporter des contraintes supplémentaires intéressantes sur les valeurs de paramètres issus des modèles astrophysiques et cosmologiques. Dans un deuxième temps, nous cherchons à analyser l'impact sur les méthodes de détection du fond gravitationnel stochastique de déviations par rapport à la normalité dans la distribution du bruit des détecteurs.The new generation of interferometers should allow us to detect stochastic gravitational wave backgrounds that are expected to arise from a large number of random, independent, unresolved events of astrophysical or cosmological origin. Most detection methods for gravitational waves are based upon the assumption of Gaussian gravitational wave stochastic background signals and noise processes. Our main objective is to improve the methods that can be used to detect gravitational backgrounds in the presence of non-Gaussian distributions. We first maintain the assumption of Gaussian noise distributions so as to better focus on the impact of deviations from normality of the signal distribution in the context of the standard cross-correlation detection statistic. Using a 4th-order Edgeworth expansion of the unknown density for the signal and noise distributions, we first derive an explicit expression for the non-Gaussian likelihood ratio statistic, which is obtained as a function of the variance, but also skewness and kurtosis of the unknown signal and noise distributions. We use numerical procedures to generate maximum likelihood estimates for the gravitational wave distribution parameters for a set of symmetric heavy-tailed distributions, and we find that the fourth cumulant can be estimated with reasonable precision when the ratio between the signal and the noise variances is larger than 1%, which should be useful for analyzing the constraints on astrophysical and cosmological models. In a second step, we analyze the efficiency of the standard cross-correlation statistic in situations that also involve non-Gaussian noise distributions

Fixed-income securities : dynamic methods for interest rate risk pricing and hedging

xv, 254 p. : ill. ; 24 cm