Three essays in financial economics: asset pricing, optimal portfolio selection and financial integration

Executive Summary The unifying theme of this thesis is the pursuit of a satisfactory ways to quantify the riskureward trade-off in financial economics. First in the context of a general asset pricing model, then across models and finally across country borders. The guiding principle in that pursuit was to seek innovative solutions by combining ideas from different fields in economics and broad scientific research. For example, in the first part of this thesis we sought a fruitful application of strong existence results in utility theory to topics in asset pricing. In the second part we implement an idea from the field of fuzzy set theory to the optimal portfolio selection problem, while the third part of this thesis is to the best of our knowledge, the first empirical application of some general results in asset pricing in incomplete markets to the important topic of measurement of financial integration. While the first two parts of this thesis effectively combine well-known ways to quantify the risk-reward trade-offs the third one can be viewed as an empirical verification of the usefulness of the so-called "good deal bounds" theory in designing risk-sensitive pricing bounds. Chapter 1 develops a discrete-time asset pricing model, based on a novel ordinally equivalent representation of recursive utility. To the best of our knowledge, we are the first to use a member of a novel class of recursive utility generators to construct a representative agent model to address some long-lasting issues in asset pricing. Applying strong representation results allows us to show that the model features countercyclical risk premia, for both consumption and financial risk, together with low and procyclical risk free rate. As the recursive utility used nests as a special case the well-known time-state separable utility, all results nest the corresponding ones from the standard model and thus shed light on its well-known shortcomings. The empirical investigation to support these theoretical results, however, showed that as long as one resorts to econometric methods based on approximating conditional moments with unconditional ones, it is not possible to distinguish the model we propose from the standard one. Chapter 2 is a join work with Sergei Sontchik. There we provide theoretical and empirical motivation for aggregation of performance measures. The main idea is that as it makes sense to apply several performance measures ex-post, it also makes sense to base optimal portfolio selection on ex-ante maximization of as many possible performance measures as desired. We thus offer a concrete algorithm for optimal portfolio selection via ex-ante optimization over different horizons of several risk-return trade-offs simultaneously. An empirical application of that algorithm, using seven popular performance measures, suggests that realized returns feature better distributional characteristics relative to those of realized returns from portfolio strategies optimal with respect to single performance measures. When comparing the distributions of realized returns we used two partial risk-reward orderings first and second order stochastic dominance. We first used the Kolmogorov Smirnov test to determine if the two distributions are indeed different, which combined with a visual inspection allowed us to demonstrate that the way we propose to aggregate performance measures leads to portfolio realized returns that first order stochastically dominate the ones that result from optimization only with respect to, for example, Treynor ratio and Jensen's alpha. We checked for second order stochastic dominance via point wise comparison of the so-called absolute Lorenz curve, or the sequence of expected shortfalls for a range of quantiles. As soon as the plot of the absolute Lorenz curve for the aggregated performance measures was above the one corresponding to each individual measure, we were tempted to conclude that the algorithm we propose leads to portfolio returns distribution that second order stochastically dominates virtually all performance measures considered. Chapter 3 proposes a measure of financial integration, based on recent advances in asset pricing in incomplete markets. Given a base market (a set of traded assets) and an index of another market, we propose to measure financial integration through time by the size of the spread between the pricing bounds of the market index, relative to the base market. The bigger the spread around country index A, viewed from market B, the less integrated markets A and B are. We investigate the presence of structural breaks in the size of the spread for EMU member country indices before and after the introduction of the Euro. We find evidence that both the level and the volatility of our financial integration measure increased after the introduction of the Euro. That counterintuitive result suggests the presence of an inherent weakness in the attempt to measure financial integration independently of economic fundamentals. Nevertheless, the results about the bounds on the risk free rate appear plausible from the view point of existing economic theory about the impact of integration on interest rates.

Confinement of discrete breathers in inhomogeneously profiled nonlinear chains

We investigate numerically the scattering of a moving discrete breather on a pair of junctions in a Fermi-Pasta-Ulam chain. These junctions delimit an extended region with different masses of the particles. We consider (i) a rectangular trap, (ii) a wedge shaped trap, and (iii) a smoothly varying convex or concave mass profile. All three cases lead to DB confinement, with the ease of trapping depending on the profile of the trap. We also study the collision and trapping of two DBs within the profile as a function of trap width, shape, and approach time at the two junctions. The latter controls whether one or both DBs are trapped.

Accelerated Microstructure Imaging via Convex Optimization (AMICO) from diffusion MRI data.

Microstructure imaging from diffusion magnetic resonance (MR) data represents an invaluable tool to study non-invasively the morphology of tissues and to provide a biological insight into their microstructural organization. In recent years, a variety of biophysical models have been proposed to associate particular patterns observed in the measured signal with specific microstructural properties of the neuronal tissue, such as axon diameter and fiber density. Despite very appealing results showing that the estimated microstructure indices agree very well with histological examinations, existing techniques require computationally very expensive non-linear procedures to fit the models to the data which, in practice, demand the use of powerful computer clusters for large-scale applications. In this work, we present a general framework for Accelerated Microstructure Imaging via Convex Optimization (AMICO) and show how to re-formulate this class of techniques as convenient linear systems which, then, can be efficiently solved using very fast algorithms. We demonstrate this linearization of the fitting problem for two specific models, i.e. ActiveAx and NODDI, providing a very attractive alternative for parameter estimation in those techniques; however, the AMICO framework is general and flexible enough to work also for the wider space of microstructure imaging methods. Results demonstrate that AMICO represents an effective means to accelerate the fit of existing techniques drastically (up to four orders of magnitude faster) while preserving accuracy and precision in the estimated model parameters (correlation above 0.9). We believe that the availability of such ultrafast algorithms will help to accelerate the spread of microstructure imaging to larger cohorts of patients and to study a wider spectrum of neurological disorders.

Optimization of the sampling scheme for maps of physical and chemical properties estimated by kriging

The sampling scheme is essential in the investigation of the spatial variability of soil properties in Soil Science studies. The high costs of sampling schemes optimized with additional sampling points for each physical and chemical soil property, prevent their use in precision agriculture. The purpose of this study was to obtain an optimal sampling scheme for physical and chemical property sets and investigate its effect on the quality of soil sampling. Soil was sampled on a 42-ha area, with 206 geo-referenced points arranged in a regular grid spaced 50 m from each other, in a depth range of 0.00-0.20 m. In order to obtain an optimal sampling scheme for every physical and chemical property, a sample grid, a medium-scale variogram and the extended Spatial Simulated Annealing (SSA) method were used to minimize kriging variance. The optimization procedure was validated by constructing maps of relative improvement comparing the sample configuration before and after the process. A greater concentration of recommended points in specific areas (NW-SE direction) was observed, which also reflects a greater estimate variance at these locations. The addition of optimal samples, for specific regions, increased the accuracy up to 2 % for chemical and 1 % for physical properties. The use of a sample grid and medium-scale variogram, as previous information for the conception of additional sampling schemes, was very promising to determine the locations of these additional points for all physical and chemical soil properties, enhancing the accuracy of kriging estimates of the physical-chemical properties.

Use of information on the manufacture of samples for the optical characterization of multilayers through a global optimization

We present a procedure for the optical characterization of thin-film stacks from spectrophotometric data. The procedure overcomes the intrinsic limitations arising in the numerical determination of manyparameters from reflectance or transmittance spectra measurements. The key point is to use all theinformation available from the manufacturing process in a single global optimization process. The method is illustrated by a case study of solgel applications.

Computer-aided procedure for optimization of layer thickness uniformity in thermal evaporation physical vapor deposition chambers for lens coating

A computer-aided method to improve the thickness uniformity attainable when coating multiple substrates inside a thermal evaporation physical vapor deposition unit is presented. The study is developed for the classical spherical (dome-shaped) calotte and also for a plane sector reversible holder setup. This second arrangement is very useful for coating both sides of the substrate, such as antireflection multilayers on lenses. The design of static correcting shutters for both kinds of configurations is also discussed. Some results of using the method are presented as an illustration.

Optimization of preservation conditions of As (III) bioreporter bacteria.

Long-term preservation of bioreporter bacteria is essential for the functioning of cell-based detection devices, particularly when field application, e.g., in developing countries, is intended. We varied the culture conditions (i.e., the NaCl content of the medium), storage protection media, and preservation methods (vacuum drying vs. encapsulation gels remaining hydrated) in order to achieve optimal preservation of the activity of As (III) bioreporter bacteria during up to 12 weeks of storage at 4 degrees C. The presence of 2% sodium chloride during the cultivation improved the response intensity of some bioreporters upon reconstitution, particularly of those that had been dried and stored in the presence of sucrose or trehalose and 10% gelatin. The most satisfying, stable response to arsenite after 12 weeks storage was obtained with cells that had been dried in the presence of 34% trehalose and 1.5% polyvinylpyrrolidone. Amendments of peptone, meat extract, sodium ascorbate, and sodium glutamate preserved the bioreporter activity only for the first 2 weeks, but not during long-term storage. Only short-term stability was also achieved when bioreporter bacteria were encapsulated in gels remaining hydrated during storage.

Optimization of laser interferometers for the detection of gravitational waves from coalescing binaries

Coalescing compact binary systems are important sources of gravitational waves. Here we investigate the detectability of this gravitational radiation by the recently proposed laser interferometers. The spectral density of noise for various practicable configurations of the detector is also reviewed. This includes laser interferometers with delay lines and Fabry-Prot cavities in the arms, both in standard and dual recycling arrangements. The sensitivity of the detector in all those configurations is presented graphically and the signal-to-noise ratio is calculated numerically. For all configurations we find values of the detector's parameters which maximize the detectability of coalescing binaries, the discussion comprising Newtonian- as well as post-Newtonian-order effects. Contour plots of the signal-to-noise ratio are also presented in certain parameter domains which illustrate the interferometer's response to coalescing binary signals.

Optimization of Soil Stabilization with Class C Fly Ash, January 1987

Previous Iowa DOT sponsored research has shown that some Class C fly ashes are ementitious (because calcium is combined as calcium aluminates) while other Class C ashes containing similar amounts of elemental calcium are not (1). Fly ashes from modern power plants in Iowa contain significant amounts of calcium in their glassy phases, regardless of their cementitious properties. The present research was based on these findings and on the hyphothesis that: attack of the amorphous phase of high calcium fly ash could be initiated with trace additives, thus making calcium available for formation of useful calcium-silicate cements. Phase I research was devoted to finding potential additives through a screening process; the likely chemicals were tested with fly ashes representative of the cementitious and non-cementitious ashes available in the state. Ammonium phosphate, a fertilizer, was found to produce 3,600 psi cement with cementitious Neal #4 fly ash; this strength is roughly equivalent to that of portland cement, but at about one-third the cost. Neal #2 fly ash, a slightly cementitious Class C, was found to respond best with ammonium nitrate; through the additive, a near-zero strength material was transformed into a 1,200 psi cement. The second research phase was directed to optimimizing trace additive concentrations, defining the behavior of the resulting cements, evaluating more comprehensively the fly ashes available in Iowa, and explaining the cement formation mechanisms of the most promising trace additives. X-ray diffraction data demonstrate that both amorphous and crystalline hydrates of chemically enhanced fly ash differ from those of unaltered fly ash hydrates. Calciumaluminum- silicate hydrates were formed, rather than the expected (and hypothesized) calcium-silicate hydrates. These new reaction products explain the observed strength enhancement. The final phase concentrated on laboratory application of the chemically-enhanced fly ash cements to road base stabilization. Emphasis was placed on use of marginal aggregates, such as limestone crusher fines and unprocessed blow sand. The nature of the chemically modified fly ash cements led to an evaluation of fine grained soil stabilization where a wide range of materials, defined by plasticity index, could be stabilized. Parameters used for evaluation included strength, compaction requirements, set time, and frost resistance.

Artificial-Intelligence-Based Optimization of the Management of Snow Removal Assets and Resources Final Report, October 2002

Geographic information systems (GIS) and artificial intelligence (AI) techniques were used to develop an intelligent snow removal asset management system (SRAMS). The system has been evaluated through a case study examining snow removal from the roads in Black Hawk County, Iowa, for which the Iowa Department of Transportation (Iowa DOT) is responsible. The SRAMS is comprised of an expert system that contains the logical rules and expertise of the Iowa DOT’s snow removal experts in Black Hawk County, and a geographic information system to access and manage road data. The system is implemented on a mid-range PC by integrating MapObjects 2.1 (a GIS package), Visual Rule Studio 2.2 (an AI shell), and Visual Basic 6.0 (a programming tool). The system could efficiently be used to generate prioritized snowplowing routes in visual format, to optimize the allocation of assets for plowing, and to track materials (e.g., salt and sand). A test of the system reveals an improvement in snowplowing time by 1.9 percent for moderate snowfall and 9.7 percent for snowstorm conditions over the current manual system.

Discrete analysis of dividend payments in a non-life insurance portfolio

The process of free reserves in a non-life insurance portfolio as defined in the classical model of risk theory is modified by the introduction of dividend policies that set maximum levels for the accumulation of reserves. The first part of the work formulates the quantification of the dividend payments via the expectation of their current value under diferent hypotheses. The second part presents a solution based on a system of linear equations for discrete dividend payments in the case of a constant dividend barrier, illustrated by solving a specific case.

Optimization of analytical methods for the assessment of the quality of fats and oils used in continuous deep fat frying

La aplicabilidad, repetibilidad y capacidad de diferentes métodos de análisis para discriminar muestras de aceites con diferentes grados de oxidación fueron evaluadas mediante aceites recogidos en procesos de fritura en continuo en varias empresas españolas. El objetivo de este trabajo fue encontrar métodos complementarios a la determinación del índice de acidez para el control de calidad rutinario de los aceites de fritura empleados en estas empresas. La optimización de la determinación de la constante dieléctrica conllevó una clara mejora de la variabilidad. No obstante, excepto en el caso del índice del ATB, el resto de métodos ensayados mostraron una menor variabilidad. La determinación del índice del ATB fue descartada ya que su sensibilidad fue insuficiente para discriminar entre aceites con diferente grado de oxidación. Los diferentes parámetros de alteración determinados en los aceites de fritura mostraron correlaciones significativas entre el índice de acidez y varios parámetros de oxidación diferentes, como la constante dieléctrica, el índice de p-anisidina, la absorción al ultravioleta y el contenido en polímeros de los triacilgliceroles. El índice de acidez solo evalúa la alteración hidrolítica, por lo que estos parámetros aportan información complementaria al evaluar la alteración termooxidativa.

CT dose optimization when changing to CT multi-detector row technology

The purpose of this article was to review the strategies to control patient dose in adult and pediatric computed tomography (CT), taking into account the change of technology from single-detector row CT to multi-detector row CT. First the relationships between computed tomography dose index, dose length product, and effective dose in adult and pediatric CT are revised, along with the diagnostic reference level concept. Then the effect of image noise as a function of volume computed tomography dose index, reconstructed slice thickness, and the size of the patient are described. Finally, the potential of tube current modulation CT is discussed.