Optimal trade execution aims at balancing price impact and timing risk. With respect to the mathematical formulation of the optimization problem, we primarily focus on Mean Variance (MV) optimization, in which the two conflicting objectives are maximizing expected revenue (the flip side of trading impact) and minimizing variance of revenue (a measure of timing risk). We also consider the use of expected quadratic variation of the portfolio value process as an alternative measure of timing risk, which leads to Mean Quadratic Variation (MQV) optimization. We demonstrate that MV-optimal strategies are quite different from MQV-optimal strategies in many aspects. These differences are in stark contrast to the common belief that MQV-optimal strategies are similar to, or even the same as, MV-optimal strategies. These differences should be of interest to practitioners since we prove that the classic Almgren-Chriss strategies (industry standard) are MQV-optimal, in contrary to the common belief that they are MV-optimal. From a computational point of view, we extend theoretical results in the literature to prove that the mean variance efficient frontier computed using our method is indeed the complete Pareto-efficient frontier. First, we generalize the result in Li (2000) on the embedding technique and develop a post-processing algorithm that guarantees Pareto-optimality of numerically computed efficient frontier. Second, we extend the convergence result in Barles (1990) to viscosity solution of a system of nonlinear Hamilton Jacobi Bellman partial differential equations (HJB PDEs). On the numerical aspect, we combine the techniques of similarity reduction, non-standard interpolation, and careful grid construction to significantly improve the efficiency of our numerical methods for solving nonlinear HJB PDEs.

Piezoelectric actuators have proven to be useful in suppressing disturbances and shape control of flexible structures. Large space structures such as solar arrays are susceptible to large amplitude vibrations while in orbit. Moreover, Shape control of many high precision structures such as large membrane mirrors and space antenna is of great importance. Since most of these structures need to be ultra-light-weight, only a limited number of actuators can be used. Consequently, in order to obtain the most effcient control system, the locations of the piezoelectric elements as well as the feedback gain should be optimized. These optimization problems are generally non-convex. In addition, the models for these systems typically have a large number of degrees of freedom. Researchers have used numerous optimization criteria and optimization techniques to find the optimal actuator locations in structural shape and vibration control. Due to the non-convex nature of the problem, evolutionary optimization techniques are extensively used. However, One drawback of these methods is that they do not use the gradient information and so convergence can be very slow. Classical gradient-based techniques, on the other hand, have the advantage of accurate computation; however, they may be computationally expensive, particularly since multiple initial conditions are typically needed to ensure that a global optimum is found. Consequently, a fast, yet global optimization method applicable to systems with a large number of degrees of freedom is needed. In this study, the feedback control is chosen to be an optimal linear quadratic regulator. The optimal actuator location problem is reformulated as a convex optimization problem. A subgradient-based optimization scheme which leads to the global solution of the problem is introduced to optimize the actuator locations. The optimization algorithm is applied to optimize the placement of piezoelectric actuators in vibration control of flexible structures. This method is compared with a genetic algorithm, and is observed to be faster in finding the global optimum. Moreover, by expanding the desired shape into the structure’s modes of vibration, a methodology for shape control of structures is presented. Applying this method, locations of piezoelectric actuators on flexible structures are optimized. Very few experimental studies exist on shape and vibration control of structures. To the best knowledge of the author, optimal actuator placement in shape control has not been experimentally studied in the past. In this work, vibration control of a cantilever beam is investigated for various actuator locations and the effect of optimal actuator placement is studied on suppressing disturbances to the beam. Also using the proposed shape control method, the effect of optimal actuator placement is studied on the same beam. The final shape of the beam and input voltages of actuators are compared for various actuator placements.

A large radiological accident will result in the contamination of surrounding people, animal, vegetation etc. In such a situation assessing of the level of contamination becomes necessary to plan for the decontamination. There are plans existing for evaluating contamination on people. However, there are limited to no plans to evaluate animals. It is the responsibility of the United States Department of Agriculture (USDA) to decontaminate animals. So the objective of this thesis work was to design a scalable gamma radiation portal monitor (RPM) which can be used to assess the level of contamination on large animals like cattle. This work employed a Monte Carlo N-Particle (MCNP) radiation transport code for the purpose. A virtual system of cow, radiation source representing the contamination, cattle chute and different detector configurations were modeled. NaI scintillation detectors were modeled for this work. To find the optimal detector size and configuration, different detector orientations were simulated for different source positions using the MCNP code. Also simulations were carried out using different number and size of the detectors. It was found that using 2" x 4" x 16" detector yielded a minimum detectable activity (MDA) value of 0.4 microCi for 137Cs source.

We study the infinite time ruin probability for an insurance company in the classical Cramér-Lundberg model with finite exponential moments. The additional non-classical feature is that the company is also allowed to invest in some stock market, modeled by geometric Brownian motion. We obtain an exact analogue of the classical estimate for the ruin probability without investment, i.e., an exponential inequality. The exponent is larger than the one obtained without investment, the classical Lundberg adjustment coefficient, and thus one gets a sharper bound on the ruin probability. A surprising result is that the trading strategy yielding the optimal asymptotic decay of the ruin probability simply consists in holding a fixed quantity (which can be explicitly calculated) in the risky asset, independent of the current reserve. This result is in apparent contradiction to the common believe that 'rich' companies should invest more in risky assets than 'poor' ones. The reason for this seemingly paradoxical result is that the minimization of the ruin probability is an extremely conservative optimization criterion, especially for 'rich' companies. (author's abstract) / Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

My PhD research focuses on the recommendation of optimal designs for two-colour microarray experiments. Two-colour microarrays are a technology used to investigate the behaviour of many thousands of genes in a single experiment. This technology has created the potential for making significant advances in the field of bioinformatics. Careful statistical design is crucial to realize the full potential of microarray technology. My research has focused on the recommendation of designs that are optimal in terms of precision for effects that are of scientific interest, making the most effective use of available resources. Based on statistical efficiency, the optimality criterion used is Pareto optimality. A design is defined to be Pareto optimal if there is no other design that leads to equal or greater precision for each effect of scientific interest and strictly greater precision for at least one. My PhD thesis was submitted in June and key aspects of my research are summarised below. Pareto optimality enables the recommendation of designs that are particularly efficient for the effects that are of scientific interest. I have developed methodology to cater for effects of interest that correspond to contrasts rather than solely considering parameters of the statistical linear model. My approach also caters for additional experimental considerations such as contrasts that are of equal scientific interest. During my PhD, I have provided advice regarding the design of two-colour microarray experiments aimed at discovering the genetic basis of medical conditions. For large experiments, it is not feasible to examine all possible designs in an exhaustive search for Pareto optimal designs. I have adapted the multiple objective metaheuristic method of Pareto simulated annealing to the microarray context. The aim of Pareto simulated annealing is to generate an approximation to the set of Pareto optimal designs in a relatively short time. At each iteration, a sample of generating designs is used to explore the design space in an efficient way. This involves the setting of a number of Pareto simulated annealing parameters and the development of appropriate quality measures. I have developed algorithms to search systematically for the optimal values of the tuning parameters based on Pareto simulated annealing and response surface methodology. / Thesis (Ph.D.) -- University of Adelaide, School of Mathematical Sciences, 2010

Research Doctorate - Doctor of Philosophy (PhD) / This Thesis addresses the problem of robust experiment design, i.e., how to design an input signal to maximise the amount of information obtained from an experiment given limited prior knowledge of the true system. The majority of existing literature on experiment design specifically considers optimal experiment design, which, typically depends on the true system parameters, that is, the very thing that the experiment is intended to find. This obviously gives rise to a paradox. The results presented in this Thesis, on robust experiment design, are aimed at resolving this paradox. In the robust experiment design problem, we assume that the parameter vector is a-priori known to belong to a given compact set, and study the design of an input spectrum which maximises the worst case scenario over this set. We also analyse the problem from a different perspective where, given the same assumption on the parameter vector, we examine cost functions that give rise to an optimal input spectrum independent of the true system features. As a first approach to this problem we utilise an asymptotic (in model order) expression for the variance of the system transfer function estimator. To enable the extension of these results to finite order models, we digress from the main topic and develop several fundamental integral limitations on the variance of estimated parametric models. Based on these results, we then return to robust experiment design, where the input design problems are reformulated using the fundamental limitations as constraints. In this manner we establish that our previous results, obtained from asymptotic variance formulas, are valid also for finite order models. Robustness issues in experiment design also arise in the area of `identification for (robust) control'. In particular, a new paradigm has recently been developed to deal with experiment design for control, namely `least costly experiment design'. In the Thesis we analyse least costly experiment design and establish its equivalence with the standard formulation of experiment design problems. Next we examine a problem involving the cost of complexity in system identification. This problem consists of determining the minimum amount of input power required to estimate a given system with a prescribed degree of accuracy, measured as the maximum variance of its frequency response estimator over a given bandwidth. In particular, we study the dependence of this cost on the model order, the required accuracy, the noise variance and the size of the bandwidth of interest. Finally, we consider the practical problem of how to optimally generate an input signal given its spectrum. Our solution is centered around a Model Predictive Control (MPC) based algorithm, which is straightforward to implement and exhibits fast convergence that is empirically verified.

Research Doctorate - Doctor of Philosophy (PhD) / This Thesis addresses the problem of robust experiment design, i.e., how to design an input signal to maximise the amount of information obtained from an experiment given limited prior knowledge of the true system. The majority of existing literature on experiment design specifically considers optimal experiment design, which, typically depends on the true system parameters, that is, the very thing that the experiment is intended to find. This obviously gives rise to a paradox. The results presented in this Thesis, on robust experiment design, are aimed at resolving this paradox. In the robust experiment design problem, we assume that the parameter vector is a-priori known to belong to a given compact set, and study the design of an input spectrum which maximises the worst case scenario over this set. We also analyse the problem from a different perspective where, given the same assumption on the parameter vector, we examine cost functions that give rise to an optimal input spectrum independent of the true system features. As a first approach to this problem we utilise an asymptotic (in model order) expression for the variance of the system transfer function estimator. To enable the extension of these results to finite order models, we digress from the main topic and develop several fundamental integral limitations on the variance of estimated parametric models. Based on these results, we then return to robust experiment design, where the input design problems are reformulated using the fundamental limitations as constraints. In this manner we establish that our previous results, obtained from asymptotic variance formulas, are valid also for finite order models. Robustness issues in experiment design also arise in the area of `identification for (robust) control'. In particular, a new paradigm has recently been developed to deal with experiment design for control, namely `least costly experiment design'. In the Thesis we analyse least costly experiment design and establish its equivalence with the standard formulation of experiment design problems. Next we examine a problem involving the cost of complexity in system identification. This problem consists of determining the minimum amount of input power required to estimate a given system with a prescribed degree of accuracy, measured as the maximum variance of its frequency response estimator over a given bandwidth. In particular, we study the dependence of this cost on the model order, the required accuracy, the noise variance and the size of the bandwidth of interest. Finally, we consider the practical problem of how to optimally generate an input signal given its spectrum. Our solution is centered around a Model Predictive Control (MPC) based algorithm, which is straightforward to implement and exhibits fast convergence that is empirically verified.

Thesis (Ph. D.)--University of Chicago, Dept. of Statistics, June 2002. / Includes bibliographical references (p. 123-132) Also available on the Internet.

This thesis uses an experimental approach to explore optimal gender assignment theory, an approach to gender assignment housed in Optimality Theory (Prince & Smolensky 1993/2004). Optimal gender assignment theory was proposed by Curt Rice (2006) and stipulates that grammatical gender is assigned based on a set of crucially non-ranked gender features constraints and markedness constraints. Thirty-seven participants who were bilingual in English and German received 40 sentences containing English loanwords with the definite article removed and asked to provide the appropriate gender marker and a lexical equivalency. The study found that the constraints employed and developed for optimal gender assignment theory are not applicable to English loanwords in German.

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