A direct approach to the discounted penalty function

This paper provides a new and accessible approach to establishing certain results concerning the discounted penalty function. The direct approach consists of two steps. In the first step, closed-form expressions are obtained in the special case in which the claim amount distribution is a combination of exponential distributions. A rational function is useful in this context. For the second step, one observes that the family of combinations of exponential distributions is dense. Hence, it suffices to reformulate the results of the first step to obtain general results. The surplus process has downward and upward jumps, modeled by two independent compound Poisson processes. If the distribution of the upward jumps is exponential, a series of new results can be obtained with ease. Subsequently, certain results of Gerber and Shiu [H. U. Gerber and E. S. W. Shiu, North American Actuarial Journal 2(1): 48–78 (1998)] can be reproduced. The two-step approach is also applied when an independent Wiener process is added to the surplus process. Certain results are related to Zhang et al. [Z. Zhang, H. Yang, and S. Li, Journal of Computational and Applied Mathematics 233: 1773–1 784 (2010)], which uses different methods.

Leniency programs, antitrust enforcement and multimarket contact : three essays in industrial organization

The Layout of My Thesis This thesis contains three chapters in Industrial Organization that build on the work outlined above. The first two chapters combine leniency programs with multimarket contact and provide a thorough analysis of the potential effects of Amnesty Plus and Penalty Plus. The third chapter puts the whole discussion on leniency programs into perspective by examining other enforcement tools available to an antitrust authority. The main argument in that last chapter is that a specific instrument can only be as effective as the policy in which it is embedded. It is therefore important for an antitrust authority to know how it best accompanies the introduction or modification of a policy instrument that helps deterrence. INTRODUCTION Chapter 1 examines the efféct of Amnesty Plus and Penalty Plus on the incentives of firms to report cartel activities. The main question is whether the inclusion of these policies in a leniency program undermine the effectiveness of the latter by discouraging the firms to apply for amnesty. The model is static and focus on the ex post incentives of firms to desist from collusion. The results suggest that, because Amnesty Plus and Penalty Plus encourage the reporting of a second cartel after a first detection, a firm, anticipating this, may be reluctant to seek leniency and to report in the first place. However, the effect may also go in the opposite direction, and Amnesty Plus and Penalty Plus may encourage the simultaneous reporting of two cartels. Chapter 2 takes this idea further to the stage of cartel formation. This chapter provides a complete characterization of the potential anticompetitive and procompetitive effects of Amnesty Plus in a infinitely repeated game framework when the firms use their multimarket contact to harshen punishment. I suggest a clear-cut policy rule that prevents potential adverse effects and thereby show that, if policy makers follow this rule, a leniency program with Amnesty Plus performs better than one without. Chapter 3 characterizes the socially optimal enforcement effort of an antitrust authority and shows how this effort changes with the introduction or modification of specific policy instruments. The intuition is that the policy instrument may increase the marginal benefit of conducting investigations. If this effect is strong enough, a more rigorous detection policy becomes socially desirable.

An algebraic operator approach to the analysis of Gerber-Shiu functions

We introduce an algebraic operator framework to study discounted penalty functions in renewal risk models. For inter-arrival and claim size distributions with rational Laplace transform, the usual integral equation is transformed into a boundary value problem, which is solved by symbolic techniques. The factorization of the differential operator can be lifted to the level of boundary value problems, amounting to iteratively solving first-order problems. This leads to an explicit expression for the Gerber-Shiu function in terms of the penalty function.

Spatially selective implementation of the adiabatic T2 prep sequence for magnetic resonance angiography of the coronary arteries.

In coronary magnetic resonance angiography, a magnetization-preparation scheme for T2 -weighting (T2 Prep) is widely used to enhance contrast between the coronary blood-pool and the myocardium. This prepulse is commonly applied without spatial selection to minimize flow sensitivity, but the nonselective implementation results in a reduced magnetization of the in-flowing blood and a related penalty in signal-to-noise ratio. It is hypothesized that a spatially selective T2 Prep would leave the magnetization of blood outside the T2 Prep volume unaffected and thereby lower the signal-to-noise ratio penalty. To test this hypothesis, a spatially selective T2 Prep was implemented where the user could freely adjust angulation and position of the T2 Prep slab to avoid covering the ventricular blood-pool and saturating the in-flowing spins. A time gap of 150 ms was further added between the T2 Prep and other prepulses to allow for in-flow of a larger volume of unsaturated spins. Consistent with numerical simulation, the spatially selective T2 Prep increased in vivo human coronary artery signal-to-noise ratio (42.3 ± 2.9 vs. 31.4 ± 2.2, n = 22, P < 0.0001) and contrast-to-noise-ratio (18.6 ± 1.5 vs. 13.9 ± 1.2, P = 0.009) as compared to those of the nonselective T2 Prep. Additionally, a segmental analysis demonstrated that the spatially selective T2 Prep was most beneficial in proximal and mid segments where the in-flowing blood volume was largest compared to the distal segments. Magn Reson Med, 2013. © 2012 Wiley Periodicals, Inc.

Surface reconstruction from microscopic images in optical lithography.

This paper presents a method to reconstruct 3D surfaces of silicon wafers from 2D images of printed circuits taken with a scanning electron microscope. Our reconstruction method combines the physical model of the optical acquisition system with prior knowledge about the shapes of the patterns in the circuit; the result is a shape-from-shading technique with a shape prior. The reconstruction of the surface is formulated as an optimization problem with an objective functional that combines a data-fidelity term on the microscopic image with two prior terms on the surface. The data term models the acquisition system through the irradiance equation characteristic of the microscope; the first prior is a smoothness penalty on the reconstructed surface, and the second prior constrains the shape of the surface to agree with the expected shape of the pattern in the circuit. In order to account for the variability of the manufacturing process, this second prior includes a deformation field that allows a nonlinear elastic deformation between the expected pattern and the reconstructed surface. As a result, the minimization problem has two unknowns, and the reconstruction method provides two outputs: 1) a reconstructed surface and 2) a deformation field. The reconstructed surface is derived from the shading observed in the image and the prior knowledge about the pattern in the circuit, while the deformation field produces a mapping between the expected shape and the reconstructed surface that provides a measure of deviation between the circuit design models and the real manufacturing process.

Structural macro factors and the affine term structure of interest rates

This work consists of three essays investigating the ability of structural macroeconomic models to price zero coupon U.S. government bonds. 1. A small scale 3 factor DSGE model implying constant term premium is able to provide reasonable a fit for the term structure only at the expense of the persistence parameters of the structural shocks. The test of the structural model against one that has constant but unrestricted prices of risk parameters shows that the exogenous prices of risk-model is only weakly preferred. We provide an MLE based variance-covariance matrix of the Metropolis Proposal Density that improves convergence speeds in MCMC chains. 2. Affine in observable macro-variables, prices of risk specification is excessively flexible and provides term-structure fit without significantly altering the structural parameters. The exogenous component of the SDF is separating the macro part of the model from the term structure and the good term structure fit has as a driving force an extremely volatile SDF and an implied average short rate that is inexplicable. We conclude that the no arbitrage restrictions do not suffice to temper the SDF, thus there is need for more restrictions. We introduce a penalty-function methodology that proves useful in showing that affine prices of risk specifications are able to reconcile stable macro-dynamics with good term structure fit and a plausible SDF. 3. The level factor is reproduced most importantly by the preference shock to which it is strongly and positively related but technology and monetary shocks, with negative loadings, are also contributing to its replication. The slope factor is only related to the monetary policy shocks and it is poorly explained. We find that there are gains in in- and out-of-sample forecast of consumption and inflation if term structure information is used in a time varying hybrid prices of risk setting. In-sample yield forecast are better in models with non-stationary shocks for the period 1982-1988. After this period, time varying market price of risk models provide better in-sample forecasts. For the period 2005-2008, out of sample forecast of consumption and inflation are better if term structure information is incorporated in the DSGE model but yields are better forecasted by a pure macro DSGE model.

Ruin and related quantities in some advanced insurance risk models

Risk theory has been a very active research area over the last decades. The main objectives of the theory are to find adequate stochastic processes which can model the surplus of a (non-life) insurance company and to analyze the risk related quantities such as ruin time, ruin probability, expected discounted penalty function and expected discounted dividend/tax payments. The study of these ruin related quantities provides crucial information for actuaries and decision makers. This thesis consists of the study of four different insurance risk models which are essentially related. The ruin and related quantities are investigated by using different techniques, resulting in explicit or asymptotic expressions for the ruin time, the ruin probability, the expected discounted penalty function and the expected discounted tax payments. - La recherche en théorie du risque a été très dynamique au cours des dernières décennies. D'un point de vue théorique, les principaux objectifs sont de trouver des processus stochastiques adéquats permettant de modéliser le surplus d'une compagnie d'assurance non vie et d'analyser les mesures de risque, notamment le temps de ruine, la probabilité de ruine, l'espérance de la valeur actuelle de la fonction de pénalité et l'espérance de la valeur actuelle des dividendes et taxes. L'étude de ces mesures associées à la ruine fournit des informations cruciales pour les actuaires et les décideurs. Cette thèse consiste en l'étude des quatre différents modèles de risque d'assurance qui sont essentiellement liés. La ruine et les mesures qui y sont associées sont examinées à l'aide de différentes techniques, ce qui permet d'induire des expressions explicites ou asymptotiques du temps de ruine, de la probabilité de ruine, de l'espérance de la valeur actuelle de la fonction de pénalité et l'espérance de la valeur actuelle des dividendes et taxes.

Inter-limb coordination and energy cost in swimming.

OBJECTIVES: This study investigated the relationship between inter-arm coordination and the energy cost of locomotion in front crawl and breaststroke and explored swimmers' flexibility in adapting their motor organization away from their preferred movement pattern. DESIGN: Nine front-crawlers performed three 300-m in front crawl and 8 breaststrokers performed three 200-m in breaststroke at constant submaximal intensity and with 5-min rests. Each trial was performed randomly in a different coordination pattern: freely chosen, 'maximal glide' and 'minimal glide'. Two underwater cameras videotaped frontal and side views to analyze speed, stroke rate, stroke length and inter-limb coordination. METHODS: In front crawl, inter-arm coordination was quantified by the index of coordination (IdC) and the leg beat kicks were counted. In breaststroke, four time gaps quantified the arm to leg coordination (i.e., time between leg and arm propulsions; time between beginning, 90° flexion and end of arm and leg recoveries). The energy cost of locomotion was calculated from gas exchanges and blood lactate concentration. RESULTS: In both front crawl and breaststroke, the freely chosen coordination corresponded to glide pattern and showed the lowest energy cost (12.8 and 17.1Jkg(-1)m(-1), respectively). Both front-crawlers and breaststrokers were able to reach 'maximal glide' condition (respectively, +35% and +28%) but not 'minimal glide' condition for front crawl. CONCLUSIONS: The freely chosen pattern appeared more economic because more trained. When coordination was constrained, the swimmers had higher coordination flexibility in breaststroke than in front crawl, suggesting that breaststroke coordination was easier to regulate by changing glide time.

The Omega model: from bankruptcy to occupation times in the red

Ruin occurs the first time when the surplus of a company or an institution is negative. In the Omega model, it is assumed that even with a negative surplus, the company can do business as usual until bankruptcy occurs. The probability of bankruptcy at a point of time only depends on the value of the negative surplus at that time. Under the assumption of Brownian motion for the surplus, the expected discounted value of a penalty at bankruptcy is determined, and hence the probability of bankruptcy. There is an intrinsic relation between the probability of no bankruptcy and an exposure random variable. In special cases, the distribution of the total time the Brownian motion spends below zero is found, and the Laplace transform of the integral of the negative part of the Brownian motion is expressed in terms of the Airy function of the first kind.

Free-running 4D whole-heart self-navigated golden angle MRI: Initial results.

PURPOSE: To test the hypothesis that both coronary anatomy and ventricular function can be assessed simultaneously using a single four-dimensional (4D) acquisition. METHODS: A free-running 4D whole-heart self-navigated acquisition incorporating a golden angle radial trajectory was implemented and tested in vivo in nine healthy adult human subjects. Coronary magnetic resonance angiography (MRA) datasets with retrospective selection of acquisition window width and position were extracted and quantitatively compared with baseline self-navigated electrocardiography (ECG) -triggered coronary MRA. From the 4D datasets, the left-ventricular end-systolic, end-diastolic volumes (ESV & EDV) and ejection fraction (EF) were computed and compared with values obtained from conventional 2D cine images. RESULTS: The 4D datasets enabled dynamic assessment of the whole heart with isotropic spatial resolution of 1.15 mm(3) . Coronary artery image quality was very similar to that of the ECG-triggered baseline scan despite some SNR penalty. A good agreement between 4D and 2D cine imaging was found for EDV, ESV, and EF. CONCLUSION: The hypothesis that both coronary anatomy and ventricular function can be assessed simultaneously in vivo has been tested positive. Retrospective and flexible acquisition window selection allows to best visualize each coronary segment at its individual time point of quiescence. Magn Reson Med, 2014. © 2014 Wiley Periodicals, Inc.

The Feminization of Occupations and Change in Wages : a Panel Analysis of Britain, Germany, and Switzerland

In the past four decades, women have made major inroads into occupations previously dominated by men. This paper examines whether occupational feminization is accompanied by a decline in wages: Do workers suffer a wage penalty if they remain in, or move into, feminizing occupations? We analyze this question over the 1990s and 2000s in Britain, Germany, and Switzerland, using longitudinal panel data to estimate individual fixed effects for men and women. Moving from an entirely male to an entirely female occupation entails a loss in individual earnings of 13 percent in Britain, 7 percent in Switzerland, and 3 percent in Germany. The impact of occupational feminization on wages is not linear, but sets apart occupations holding more than 60 percent of women. Moving into such female occupations incurs a wage penalty. Contrary to the prevailing idea in economics, differences in productivity-human capital, job-specific skills, and time investment-do not fully explain the wage gap between male and female occupations. The wage penalty associated with working in a female occupation is also much larger where employer discretion is greater-in the private sector-than where wagesetting is guided by formal rules-the public sector. These findings suggest that wage disparities across male and female occupations are due to gender devaluation.

Dial M for Murder: A Case of Passion Killing, Criminal Evidence and Sultanic Power in Medieval India

This paper considers the structures and applications of the criminal judicial system in the Islamic Later Middle Period as it developed in India under the sultans of Delhi (1200-1400 CE). A fundamental issue in crime and punishment is the relationship between sultanic power and religious authority. Particularly at stake in this relationship is the question of who can sanction the highest form of punishment, i.e. the death penalty (siyāsa). Contemporary historians and scholars in the study of religion investigating the relationship between sharīʿa and siyāsa to reveal the extent and limits of sultanic power show a system of governance that allowed for the delegation of authority, particularly in the area of the judiciary, from the sultan down to viziers and judges. Some scholars depict the relationship between the ʿulamāʾ and the sultan as a kind of stand off. The actual dynamics of legal jurisdiction were much more complex. This study proposes a new interpretive framework for understanding the relationship between political power and religious authority through a critical analysis of the criminal judicial system, law, and historical narrative. In particular, I consider a murder case described by Shams al-dīn Sirāj ʿAfīf in one of the most significant histories written in the later Delhi Sultanate, the Tārīkh-i Fīrūzshāhī.