This was a study on the Utah cattle industry which compared five different feeding enterprises. These feeding enterprises included feeding cull cows, finishing beef yearling steers, finishing Holstein yearling steers, backgrounding beef steer calves, and backgrounding Holstein steer calves. The main purpose of this study was to determine which feeding enterprise was the most profitable for Utah cattle producers. Another objective of the study was to determine if LRP insurance lowered the volatility in the returns to these feeding enterprises. In order to answer these two questions of interest, a historical analysis of Utah cattle and feed prices was conducted from 1990 through 2009. Weekly sales data were used, and seasonality and price trends were determined. Next, enterprise budgets were created for each feeding enterprise to establish historical returns. Then, using the historical data as a foundation, a simulation analysis was run to forecast future returns and determine the risk associated with each feeding enterprise. LRP insurance was also added to the model to simulate the effects it had on lowering risk. After completing a simulation analysis and comparing means and standard deviations of the expected returns, portfolio theory was used to put the feeding enterprises into different portfolios to attempt to lower risk. Then stochastic dominance was used to conclude which feeding enterprise was the most preferred for Utah cattle producers. The results of the study depend upon the producer's level of risk. The majority of producers have an ARAC value between -0.0002 and 0.0012. With that knowledge, the results suggested that the majority of Utah cattle producers should finish Holstein yearling steers. If a producer was highly risk seeking, then he or she was better off to feed cull cows. If the producer was highly risk averse, then he or she preferred a portfolio of cull cows and backgrounding both Holstein and beef steers with LRP insurance. The results of the study also indicated that LRP insurance was an effective tool for lowering the variability in expected returns. However, the results suggested that the most preferred option for Utah cattle producers was to feed either cull cows or Holstein yearling steers without LRP insurance.

This work focuses on measuring the quality of stochastic dominance approx- imation. A measure of non-dominance is developed to quantify the error caused by assuming that a stochastic dominance relationship holds even when it does not. It is computed exactly for uniform, normal, and exponential distribution, and a numerical study is performed to estimate its values for log-normal and gamma distribution. Portfolio optimization problems involving stochastic dom- inance constraints are also presented. They are applied to real-life data using monthly returns of twelve assets captured by the German stock index DAX. The end of this work focuses on the computation of the measure of non-dominance for the optimal portfolio with respect to the second-order stochastic dominance. 1

The thesis deals with high-order stochastic dominance of random variables and portfolios. The summary of findings about high-order stochastic dominance and portfolio efficiency is presented. As a main part of the thesis it is proven that under assumption of both normal and gamma distribution the infinite-order stochastic dominance is equivalent to the second-order stochastic dominance. The necessary and sufficient condition for the infinite-order stochastic dominance portfolio efficiency is derived under the assumption of normality. The condition is used in the empirical part of the thesis where parametrical approach to the portfolio efficiency is compared to the nonparametric scenario approach. The derived necessary and sufficient condition is based on the assumption of normality; therefore we use two sets of data, one with fulfilled assumption of normality and the other for which the assumption of normality was unambigously rejected. Consequently, the influence of fulfillment of the normality assumption on the results of the necessary and sufficient condition for portfolio efficiency is estimated.

<div>Life cycle cost analysis (LCCA) has been defined as a method to assess the total cost of a project. It is a simple tool to use when a single project has different alternatives that fulfill the original requirements. Different alternatives could differ in initial investment, operational and maintenance costs among other long term costs. The cost involved in building a bridge depends upon many different factors. Moreover, long-term cost needs to be considered to estimate the true overall cost of the project and determine its life-cycle cost. Without watchful consideration of the long-term costs and full life cycle costing, current investment decisions that look attractive could result in a waste of economic resources in the future. This research is focused on short and medium span bridges (between 30-ft and 130-ft) which represents 65\% of the NBI INDIANA bridge inventory. </div><div><br></div><div>Bridges are categorized in three different groups of span ranges. Different superstructure types are considered for both concrete and steel options. Types considered include: bulb tees, AASHTO prestressed beams, slab bridges, prestressed concrete box beams, steel beams, steel girders, folded plate girders and simply supported steel beams for dead load and continuous for live load (SDCL). A design plan composed of simply supported bridges and continuous spans arrangements was carried out. Analysis for short and medium span bridges in Indiana based on LCCA is presented for different span ranges and span configurations. </div><div><br></div><div>Deterministic and stochastic analysis were done for all the span ranges considered. Monte Carlo Simulations (MCS) were used and the categorization of the different superstructure alternatives was done based on stochastic dominance. First, second, almost first and almost second stochastic dominance rules were used to determined the efficient set for each span length and all span configurations. Cost-effective life cycle cost profiles for each superstructure type were proposed. Additionally, the top three cost-effective alternatives for superstructure types depending on the span length are presented as well as the optimum superstructure types set for both simply supported and continuous beams. Results will help designers to consider the most cost-effective bridge solution for new projects, resulting in cost savings for agencies involved.</div>

Asset and Liability Management (ALM) models have become well established decision tools for pension funds. ALMs are commonly modelled as multi-stage, in which a large terminal wealth is required, while at intermediate time periods, constraints on the funding ratio, that is, the ratio of assets to liabilities, are imposed. Underfunding occurs when the funding ratio is too low; a target value for funding ratios is pre-specified by the decision maker. The risk of underfunding has been usually modelled by employing established risk measures; this controls one single aspect of the funding ratio distributions. For example, controlling the expected shortfall below the target has limited power in controlling shortfall under worst-case scenarios. We propose ALM models in which the risk of underfunding is modelled based on the concept of Second Order Stochastic Dominance (SSD). This is a criterion of ranking random variables - in our case funding ratios - that takes the entire distributions of interest into account and works under the widely accepted assumptions of decision makers being rational and risk averse. In the proposed SSD models, investment decisions are taken such that the resulting short-term distribution of the funding ratio is non-dominated with respect to SSD, while a constraint is imposed on the expected terminal wealth. This is done by considering progressively larger tails of the funding ratio distribution and considering target levels for them; a target distribution is thus implied. Different target distributions lead to different SSD efficient solutions. Improved distributions of funding ratios may be thus achieved, compared to the existing risk models for ALM. This is the first contribution of this thesis. Interesting results are obtained in the special case when the target distribution is deterministic, specified by one single outcome. In this case, we can obtain equivalent risk minimisation models, with risk defined as expected shortfall or as worst case loss. This represents the second contribution. The third contribution is a framework for scenario generation based on the "Birth, Immigration, Death, Emigration" (BIDE) population model and the Empirical copula; the scenarios are used to evaluate the proposed models and their special cases both in-sample and out-of-sample. As an application, we consider the planning problem of a large DB pension fund in Saudi Arabia.

In this dissertation we study several non-convex and stochastic optimization problems. The common theme is the use of mixed-integer programming (MIP) techniques including valid inequalities and reformulation to solve these problems. We first study a strategic capacity planning model which captures the trade-off between the incentive to delay capacity installation to wait for improved technology and the need for some capacity to be installed to meet current demands. This problem is naturally formulated as a MIP with a bilinear objective. We develop several linear MIP formulations, along with classes of strong valid inequalities. We also present a specialized branch-and-cut algorithm to solve a compact concave formulation. Computational results indicate that these formulations can be used to solve large-scale instances. We next study methods for optimization with joint probabilistic constraints. These problems are challenging because evaluating solution feasibility requires multidimensional integration and the feasible region is not convex. We propose and analyze a Monte Carlo sampling scheme to simplify the probabilistic structure of such problems. Computational tests of the approach indicate that it can yield good feasible solutions and reasonable bounds on their quality. Next, we study a MIP formulation of the non-convex sample approximation problem. We obtain two strengthened formulations. As a byproduct of this analysis, we obtain new results for the previously studied mixing set, subject to an additional knapsack inequality. Computational results indicate that large-scale instances can be solved using the strengthened formulations. Finally, we study optimization problems with stochastic dominance constraints. A stochastic dominance constraint states that a random outcome which depends on the decision variables should stochastically dominate a given random variable. We present new formulations for both first and second order stochastic dominance which are significantly more compact than existing formulations. Computational tests illustrate the benefits of the new formulations.

Stochastic methods are present in our daily lives, especially when we need to make a decision based on uncertain events. In this thesis, we present basic approaches used in stochastic tasks. In the first chapter, we define the stochastic problem and introduce basic methods and tasks which are present in the literature. In the second chapter, we present various problems which are non-linearly dependent on the probability measure. Moreover, we introduce deterministic and non-deterministic multicriteria tasks. In the third chapter, we give an insight on the concept of stochastic dominance and we describe the methods that are used in tasks with multidimensional stochastic dominance. In the fourth chapter, we capitalize on the knowledge from chapters two and three and we try to solve the role of portfolio optimization on real data using different approaches. 1

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Title: Semi-infinite programming: theory and portfolio efficiency application Author: Bc. Lukáš Klouda Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Ing. Miloš Kopa, PhD. Supervisor's e-mail address: kopa@karlin.mff.cuni.cz Abstract: The thesis deals with application of semi-infinite programming to a portfolio efficiency testing. The summary of semi-infinite programming, first and second order optimality conditions and duality in linear semi-infinite programming is presented. The optimization problem for a portfolio efficiency testing with respect to the second order stochastic dominance under assumption of discrete, normal, Students and general elliptical distribution is formulated. Conditional value at risk(CVaR) is used as the risk measure, because of its consistency with the second order stochastic dominance relation. Efficiency of index PX with respect to the second order stochastic dominance is tested. The tests are performed using the program GAMS.

Prioritätensetzung in der Agrarforschung ist ein komplexes Entscheidungsproblem angesichts der Unsicherheit in der Abschätzung der erwarteten Wirkungen von Forschung und Technologien und den vielfältigen sozialen und wirtschaftlichen Zielen, die mit der Generierung von Wissen und neuen Technologien in landwirtschaftlichen Forschungsinstitutionen in Entwicklungsländern verbunden sind. Diese Arbeit versucht durch die Anwendung von formalen und quantitativen Evaluierungs- und Entscheidungsmethoden mit der besonderen Berücksichtigung von Unsicherheit und multiplen Zielen einen Beitrag zur Methodenverbesserung in der Prioritätensetzung zu leisten. Zur Darstellung dieser Methoden wurde als Fallstudie das nationale Milchviehforschungsprogramm des "Kenyan Agricultural Research Institute" (KARI) ausgewählt. Gegenstand der Analyse sind 19 geplante Forschungsprojekte, die anhand eines stochastischen Evaluierungsansatzes ("Economic Surplus" und Monte Carlo Simulation) hinsichtlich ihrer ökonomischen Wirkungen auf den kenianischen Milchmarkt untersucht wurden. Die Evaluierungsergebnisse der Forschungsprojekte und anschließende Bewertung anhand verschiedener stochastischer Dominanztests zeigen, daß die Ableitung einer klaren Präferenzstruktur und Rangordnung innerhalb der Projekte nach ökonomischen Kriterien, z.B. Gegenwartswert und Kosten-Nutzenrelation, in vielen Fällen nicht möglich ist, sondern vielmehr von den unterstellten Risikopräferenzen abhängt. Dies bedeutet, daß aus der Sicht eines Planers eine differenzierte und vorsichtige Interpretation und Beratung des Forschungsmanagements vorzunehmen ist. Dies steht im Gegensatz zu einer deterministischen Investitionsanalyse. Mehrere mathematische Programmierungsmodelle wurden zur Analyse von multiplen Zielen, der Untersuchung der Wirkungen von Verteilungsaspekten und unterschiedlicher Risikopräferenzen auf die Zusammensetzung eines optimalen Forschungsportfolios entwickelt und angewandt. Obwohl in den meisten Fällen eine Änderung der Risikoeinstellung auch eine Änderung des optimalen Portfolios bewirken würde, sind die ökonomischen Unterschiede gemessen am Gegenwartswert der alternativen Portfolios unbedeutend. Die Analyse der Zielkonflikte zwischen Effizienz- und Verteilungsziel wurde unter zwei unterschiedlichen Blickwinkeln für das Verteilungsziel untersucht: zum einen als räumliche und regionale Allokation des Forschungsnutzens, und zum anderen zwischen kenianischen Konsumenten und Produzenten von Milch. Aus den Modellergebnissen wird deutlich, daß eine spezielle Förderung von Produzenten- sowie Konsumenteninteressen nur beschränkt möglich ist, d.h. die jeweiligen Planungsoptionen nur geringe Umverteilungswirkungen erzielen. Ganz anders stellt sich die Situation bei einer regionalen Differenzierung dar. Dort würden je nach relativer Bedeutung einzelner Regionen starke Umverteilungswirkungen in den regionalen Einkommen auftreten. Allerdings sind diese Optionen im Vergleich zu einer "neutralen", d.h. regional indifferenten Ausrichtung mit großen Effizienzverlusten verbunden. / Priority setting in agricultural research is a complex decision making problem due to the inherent uncertainty surrounding the impact of research activities and the multiple social and economic research objectives under which research institutions in developing countries have to operate. This study attempts to apply formal and quantitative evaluation and decision making methods for a more rigorous and explicit analysis of the uncertainty and multiple research objectives. These methods are illustrated by applying them to a priority setting exercise for the National Dairy Research Program of the Kenyan Agricultural Research Institute (KARI) conducted in 1996. A set of 19 planned dairy research projects was proposed and specified by KARI scientists and the economic impact assessed based on a stochastic evaluation framework using economic surplus methods and Monte Carlo simulation. Results show that comparing these projects by stochastic dominance criteria with respect to the expected net present value and cost-benefit ratio the final rank order is very much subject to assumed risk preferences of the decision- makers. Thus, decision advice on the type of prioritised projects for implementation and fund raising is much less clear-cut than a deterministic evaluation would suggest. Mathematical programming techniques were applied to analyse the trade-off between multiple research objectives, to examine the distributional consequences of research, and to explore how different risk strategies (from risk aversion to risk proneness) would affect the selection of a optimal research portfolio from the planned dairy research projects. Although risk has a strong bearing on the composition of a research portfolio for various different funding levels the economic implications are not significant in terms of net present value. In a Multiple-objective programming framework the trade-off between efficiency and equity was examined. Equity concern was looked at two different angles: first, by a spatial distribution of the research benefits, and second by the distributions among consumer and producer groups. Results show a limited scope of directing the dairy research plan either for the sake of consumers or producers while the scope of targeting different production zones in Kenya is much larger although the trade-offs in terms of foregone welfare between different zones are very pronounced.