This thesis, consisting of six papers and a summary, studies the area of continuous time financial mathematics. A unifying theme for many of the problems studied is the implications of possible mis-specifications of models. Intimately connected with this question is, perhaps surprisingly, convexity properties of option prices. We also study qualitative behavior of different optimal stopping boundaries appearing in option pricing. In Paper I a new condition on the contract function of an American option is provided under which the option price increases monotonically in the volatility. It is also shown that American option prices are continuous in the volatility. In Paper II an explicit pricing formula for the perpetual American put option in the Constant Elasticity of Variance model is derived. Moreover, different properties of this price are studied. Paper III deals with the Russian option with a finite time horizon. It is shown that the value of the Russian option solves a certain free boundary problem. This information is used to analyze the optimal stopping boundary. A study of perpetual game options is performed in Paper IV. One of the main results provides a condition under which the value of the option is increasing in the volatility. In Paper V options written on several underlying assets are considered. It is shown that, within a large class of models, the only model for the stock prices that assigns convex option prices to all convex contract functions is geometric Brownian motion. Finally, in Paper VI it is shown that the optimal stopping boundary for the American put option is convex in the standard Black-Scholes model.

Models are important tools for understanding the hydrological processes that govern water transport in the landscape and for prediction at times and places where no observations are available. The degree of trust placed on models, however, should not exceed the quality of the data they are fed with. The overall aim of this thesis was to tune the modeling process to account for the uncertainty in the data, by identifying robust parameter values using methods from computational geometry. The methods were developed and tested on data from the Choluteca River basin in Honduras. Quality control of precipitation and discharge data resulted in a rejection of 22% percent of daily raingage data and the complete removal of one out of the seven discharge stations analyzed. The raingage network was not found sufficient to capture the spatial and temporal variability of precipitation in the Choluteca River basin. The temporal variability of discharge was evaluated through a Monte Carlo assessment of the rating-equation parameter values over a moving time window of stage-discharge measurements. Al hydrometric stations showed considerable temporal variability in the stage-discharge relationship, which was largest for low flows, albeit with no common trend. The problem with limited data quality was addressed by identifying robust model parameter values within the set of well-performing (behavioral) parameter-value vectors with computational-geometry methods. The hypothesis that geometrically deep parameter-value vectors within the behavioral set were hydrologically robust was tested, and verified, using two depth functions. Deep parameter-value vectors tended to perform better than shallow ones, were less sensitive to small changes in their values, and were better suited to temporal transfer. Depth functions rank multidimensional data. Methods to visualize the multivariate distribution of behavioral parameters based on the ranked values were developed. It was shown that, by projecting along a common dimension, the multivariate distribution of behavioral parameters for models of varying complexity could be compared using the proposed visualization tools. This has a potential to aid in the selection of an adequate model structure considering the uncertainty in the data. These methods allowed to quantify observational uncertainties. Geometric methods have only recently begun to be used in hydrology. It was shown that they can be used to identify robust parameter values, and some of their potential uses were highlighted. / Modeller är viktiga verktyg för att förstå de hydrologiska processer som bestämmer vattnets transport i landskapet och för prognoser för tider och platser där det saknas mätdata. Graden av tillit till modeller bör emellertid inte överstiga kvaliteten på de data som de matas med. Det övergripande syftet med denna avhandling var att anpassa modelleringsprocessen så att den tar hänsyn till osäkerheten i data och identifierar robusta parametervärden med hjälp av metoder från beräkningsgeometrin. Metoderna var utvecklade och testades på data från Cholutecaflodens avrinningsområde i Honduras. Kvalitetskontrollen i nederbörds- och vattenföringsdata resulterade i att 22 % av de dagliga nederbördsobservationerna måste kasseras liksom alla data från en av sju analyserade vattenföringsstationer. Observationsnätet för nederbörd befanns otillräckligt för att fånga upp den rumsliga och tidsmässiga variabiliteten i den övre delen av Cholutecaflodens avrinningsområde. Vattenföringens tidsvariation utvärderades med en Monte Carlo-skattning av värdet på parametrarna i avbördningskurvan i ett rörligt tidsfönster av vattenföringsmätningar. Alla vattenföringsstationer uppvisade stor tidsvariation i avbördningskurvan som var störst för låga flöden, dock inte med någon gemensam trend. Problemet med den måttliga datakvaliteten bedömdes med hjälp av robusta modellparametervärden som identifierades med hjälp av beräkningsgeometriska metoder. Hypotesen att djupa parametervärdesuppsättningar var robusta testades och verifierades genom två djupfunktioner. Geometriskt djupa parametervärdesuppsättningar verkade ge bättre hydrologiska resultat än ytliga, var mindre känsliga för små ändringar i parametervärden och var bättre lämpade för förflyttning i tiden. Metoder utvecklades för att visualisera multivariata fördelningar av välpresterande parametrar baserade på de rangordnade värdena. Genom att projicera längs en gemensam dimension, kunde multivariata fördelningar av välpresterande parametrar hos modeller med varierande komplexitet jämföras med hjälp av det föreslagna visualiseringsverktyget. Det har alltså potentialen att bistå vid valet av en adekvat modellstruktur som tar hänsyn till osäkerheten i data. Dessa metoder möjliggjorde kvantifiering av observationsosäkerheter. Geometriska metoder har helt nyligen börjat användas inom hydrologin. I studien demonstrerades att de kan användas för att identifiera robusta parametervärdesuppsättningar och några av metodernas potentiella användningsområden belystes.

Wireless sensor networks (WSNs) have recently attracted a great deal of attention due to their numerous attractive applications in many different fields. Sensors and WSNs possess a number of special characteristics that make them very promising in a wide range of applications, but they also put on them lots of constraints that make issues in sensor network particularly challenging. These issues may include topology control, routing, coverage, security, data management and many others. Among them, coverage problem is one of the most fundamental ones for which a WSN has to watch over the environment such as a forest (area coverage) or set of subjects such as collection of precious renaissance paintings (target of point coverage) in order for the network to be able to collect environment parameters, and maybe further monitor the environment. In this dissertation, we highly focus on the area coverage problem. With no assumption of sensors’ locations (i.e., the sensor network is randomly deployed), we only consider distributed and parallel scheduling methods with the ultimate objective of maximizing network lifetime. Additionally, the proposed solutions (including algorithms, a scheme, and a framework) have to be energy-efficient. Generally, we investigate numerous generalizations and variants of the basic coverage problem. Those problems of interest include k-coverage, composite event detection, partial coverage, and coverage for adjustable sensing range network. Various proposed algorithms. In addition, a scheme and a framework are also suggested to solve those problems. The scheme, which is designed for emergency alarming applications, specifies the guidelines for data and communication patterns that significantly reduce the energy consumption and guarantee very low notification delay. For partial coverage problem, we propose a universal framework (consisting of four strategies) which can take almost any complete-coverage algorithm as an input to generate an algorithm for partial coverage. Among the four strategies, two pairs of strategies are trade-off in terms of network lifetime and coverage uniformity. Extensive simulations are conducted to validate the efficiency of each of our proposed solutions.

Essay 1: (with Henrik Jordahl and Panu Poutvaara) We present and test a theory of prospective and retrospective pocketbook voting. Focusing on two large reforms in Sweden, we establish a causal chain from policies to sizeable individual gains and losses and then to voting. The Social Democrats proposed budget cuts affecting parents with young children before the 1994 election, but made generous promises to the same group before the 1998 election. Since parents with older children were largely unaffected we use a difference-in-differences strategy for identification. We find clear evidence of prospective pocketbook voting. Voters respond to campaign promises but not to the later implementation of the reforms. / Essay 2: This essay presents a detailed analysis of voters' response to municipality and regional level unemployment and economic growth, in Swedish general elections from 1985 to 2002, using data on 284 municipalities and 9 regions. The preferred specification suggests that an increase in regional growth or a reduction in regional unemployment by one percentage point is associated with an increase in the support for the national government by about 0.6 and 1.0 percentage points. Changes in unemployment and growth at the municipality level seem to have muchsmaller effects on government support. / Essay 3: One prediction from cognitive dissonance theory is that the act of voting makes people more positive toward the party or candidate they have voted for. Following Mullainathan and Washington (2008), I test this prediction by using exogenous variation in turnout provided by the voting age restriction. I improve on previous studies by investigating political attitudes, measured just before elections, when they are highly predictive of voting. In contrast to earlier studies I find no effect of voting on political attitudes. This result holds for a variety of political attitudes and data from both Sweden and the United States. / Essay4: (with Niclas Berggren and Henrik Jordahl) We conduct an extensive robustness analysis of the relationship between trust and growth by investigating a later time period and a bigger sample than in previous studies. In addition to robustness tests that focus on model uncertainty, we systematize the investigation of outlier influence on the results by using the robust estimation technique Least Trimmed Squares. We find that when outliers (especially China) are removed, the trust-growth relationship is no longer robust. On average, the trust coefficient is half as large as in previous findings.

This dissertation studies models for locating facilities in time varying demand environments. We describe the characteristics of the time varying demand that motivate the analysis of our location models in terms of total demand and the change in value and location of the demand of each customer. The first part of the dissertation is devoted to the dynamic location model, which determines the optimal time and location for establishing capacitated facilities when demand and cost parameters are time varying. This model minimizes the total cost over a discrete and finite time horizon for establishing, operating, and closing facilities, including the transportation costs for shipping demand from facilities to customers. The model is solved using Lagrangian relaxation and Benders? decomposition. Computational results from different time varying total demand structures demonstrate, empirically, the performance of these solution methods. The second part of the dissertation studies two location models where relocation of facilities is not allowed and the objective is to determine the optimal location of capacitated facilities that will have a good performance when demand and cost parameters are time varying. The first model minimizes the total cost for opening and operating facilities and the associated transportation costs when demand and cost parameters are time varying. The model is solved using Benders? decomposition. We show that in the presence of high relocation costs of facilities (opening and closing costs), this model can be solved as a special case by the dynamic location model. The second model minimizes the maximum regret or opportunity loss between a robust configuration of facilities and the optimal configuration for each time period. We implement local search and simulated annealing metaheuristics to efficiently obtain near optimal solutions for this model.

Investments in space systems are substantial, indivisible, and irreversible, characteristics that make them high-risk, especially when coupled with an uncertain demand environment. Traditional approaches to system design and acquisition, derived from a performance- or cost-centric mindset, incorporate little information about the spacecraft in relation to its environment and its value to its stakeholders. These traditional approaches, while appropriate in stable environments, are ill-suited for the current, distinctly uncertain and rapidly changing technical, and economic conditions; as such, they have to be revisited and adapted to the present context. This thesis proposes that in uncertain environments, decision-making with respect to space system design and acquisition should be value-based, or at a minimum value-informed. This research advances the value-centric paradigm by providing the theoretical basis, foundational frameworks, and supporting analytical tools for value assessment of priced and unpriced space systems. For priced systems, stochastic models of the market environment and financial models of stakeholder preferences are developed and integrated with a spacecraft-sizing tool to assess the system's net present value. The analytical framework is applied to a case study of a communications satellite, with market, financial, and technical data obtained from the satellite operator, Intelsat. The case study investigates the implications of the value-centric versus the cost-centric design and acquisition choices. Results identify the ways in which value-optimal spacecraft design choices are contingent on both technical and market conditions, and that larger spacecraft for example, which reap economies of scale benefits, as reflected by their decreasing cost-per-transponder, are not always the best (most valuable) choices. Market conditions and technical constraints for which convergence occurs between design choices under a cost-centric and a value-centric approach are identified and discussed. In addition, an innovative approach for characterizing value uncertainty through partial moments, a technique used in finance, is adapted to an engineering context and applied to priced space systems. Partial moments disaggregate uncertainty into upside potential and downside risk, and as such, they provide the decision-maker with additional insights for value-uncertainty management in design and acquisition. For unpriced space systems, this research first posits that their value derives from, and can be assessed through, the value of information they provide. To this effect, a Bayesian framework is created to assess system value in which the system is viewed as an information provider and the stakeholder an information recipient. Information has value to stakeholders as it changes their rational beliefs enabling them to yield higher expected pay-offs. Based on this marginal increase in expected pay-offs, a new metric, Value-of-Design (VoD), is introduced to quantify the unpriced system's value. The Bayesian framework is applied to the case of an Earth Science satellite that provides hurricane information to oil rig operators using nested Monte Carlo modeling and simulation. Probability models of stakeholders' beliefs, and economic models of pay-offs are developed and integrated with a spacecraft payload generation tool. The case study investigates the information value generated by each payload, with results pointing to clusters of payload instruments that yielded higher information value, and minimum information thresholds below which it is difficult to justify the acquisition of the system. In addition, an analytical decision tool, probabilistic Pareto fronts, is developed in the Cost-VoD trade space to provide the decision-maker with additional insights into the coupling of a system's probable value generation and its associated cost risk.

Im Beitrag werden drei Methoden für den Entwurf und die Bemessung von Textilbetonverstärkungen vorgestellt. Für eine Vorbemessung wird die Variantenuntersuchung angewendet, z.B. für die Bestimmung der Anzahl an Textillagen. Für die Festlegung von Realisierungen mehrerer kontinuierlicher Entwurfsvariablen unter Berücksichtigung unterschiedlicher Entwurfsziele und Entwurfsnebenbedingungen werden die Fuzzy-Optimierung und die direkte Lösung der Entwurfsaufgabe skizziert. Mit der Fuzzy-Optimierung werden Kompromisslösungen für die multikriterielle Entwurfsaufgabe ermittelt. Die direkte Lösung basiert auf der explorativen Datenanalyse von Punktmengen, die als Ergebnis einer unscharfen Tragwerksanalyse vorliegen, und liefert Bereiche – sog. Entwurfsteilräume – als Grundlage für die Auswahl des Entwurfs.

<p>Industrial robot manipulators are general-purpose machines used for industrial automation in order to increase productivity, flexibility, and quality. Other reasons for using industrial robots are cost saving, and elimination of heavy and health-hazardous work. Robot motion control is a key competence for robot manufacturers, and the current development is focused on increasing the robot performance, reducing the robot cost, improving safety, and introducing new functionalities. Therefore, there is a need to continuously improve the models and control methods in order to fulfil all conflicting requirements, such as increased performance for a robot with lower weight, and thus lower mechanical stiffness and more complicated vibration modes. One reason for this development of the robot mechanical structure is of course cost-reduction, but other benefits are lower power consumption, improved dexterity, safety issues, and low environmental impact.</p><p>This thesis deals with three different aspects of modeling and control of flexible, i.e., elastic, manipulators. For an accurate description of a modern industrial manipulator, the traditional flexible joint model, described in literature, is not sufficient. An improved model where the elasticity is described by a number of localized multidimensional spring-damper pairs is therefore proposed. This model is called the extended flexible joint model. This work describes identification, feedforward control, and feedback control, using this model.</p><p>The proposed identification method is a frequency-domain non-linear gray-box method, which is evaluated by the identification of a modern six-axes robot manipulator. The identified model gives a good description of the global behavior of this robot.</p><p>The inverse dynamics control problem is discussed, and a solution methodology is proposed. This methodology is based on a differential algebraic equation (DAE) formulation of the problem. Feedforward control of a two-axes manipulator is then studied using this DAE approach.</p><p>Finally, a benchmark problem for robust feedback control of a single-axis extended flexible joint model is presented and some proposed solutions are analyzed.</p>

This paper deals with the computation of OC- and ASN-function of sequential probability ratio tests in the multi-parameter case. In generalization of the method of conjugated parameter pairs Wald-like approximations are presented for the OC- and ASN-function. These characteristics can be used describing robustness properties of a sequential test in case of nuisance parameters. As examples tests are considered for the mean and the variance of a normal distribution.

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