A comprehensive portfolio construction under stochastic environment

Prior research has established that idiosyncratic volatility of the securities prices exhibits a positive trend. This trend and other factors have made the merits of investment diversification and portfolio construction more compelling. ^ A new optimization technique, a greedy algorithm, is proposed to optimize the weights of assets in a portfolio. The main benefits of using this algorithm are to: (a) increase the efficiency of the portfolio optimization process, (b) implement large-scale optimizations, and (c) improve the resulting optimal weights. In addition, the technique utilizes a novel approach in the construction of a time-varying covariance matrix. This involves the application of a modified integrated dynamic conditional correlation GARCH (IDCC - GARCH) model to account for the dynamics of the conditional covariance matrices that are employed. ^ The stochastic aspects of the expected return of the securities are integrated into the technique through Monte Carlo simulations. Instead of representing the expected returns as deterministic values, they are assigned simulated values based on their historical measures. The time-series of the securities are fitted into a probability distribution that matches the time-series characteristics using the Anderson-Darling goodness-of-fit criterion. Simulated and actual data sets are used to further generalize the results. Employing the S&P500 securities as the base, 2000 simulated data sets are created using Monte Carlo simulation. In addition, the Russell 1000 securities are used to generate 50 sample data sets. ^ The results indicate an increase in risk-return performance. Choosing the Value-at-Risk (VaR) as the criterion and the Crystal Ball portfolio optimizer, a commercial product currently available on the market, as the comparison for benchmarking, the new greedy technique clearly outperforms others using a sample of the S&P500 and the Russell 1000 securities. The resulting improvements in performance are consistent among five securities selection methods (maximum, minimum, random, absolute minimum, and absolute maximum) and three covariance structures (unconditional, orthogonal GARCH, and integrated dynamic conditional GARCH). ^

Glycemic control: Risk factors, quality of life, workforce participation, and mortality among US adults with type 2 diabetes

Despite research showing the benefits of glycemic control, it remains suboptimal among adults with diabetes in the United States. Possible reasons include unaddressed risk factors as well as lack of awareness of its immediate and long term consequences. The objectives of this study were to, using cross-sectional data, (1) ascertain the association between suboptimal (Hemoglobin A1c (HbA1c) .7%), borderline (HbA1c 7-8.9%), and poor (HbA1c .9%) glycemic control and potentially new risk factors (e.g. work characteristics), and (2) assess whether aspects of poor health and well-being such as poor health related quality of life (HRQOL), unemployment, and missed-work are associated with glycemic control; and (3) using prospective data, assess the relationship between mortality risk and glycemic control in US adults with type 2 diabetes. Data from the 1988-1994 and 1999-2004 National Health and Nutrition Examination Surveys were used. HbA1c values were used to create dichotomous glycemic control indicators. Binary logistic regression models were used to assess relationships between risk factors, employment status and glycemic control. Multinomial logistic regression analyses were conducted to assess relationships between glycemic control and HRQOL variables. Zero-inflated Poisson regression models were used to assess relationships between missed work days and glycemic control. Cox-proportional hazard models were used to assess effects of glycemic control on mortality risk. Using STATA software, analyses were weighted to account for complex survey design and non-response. Multivariable models adjusted for socio-demographics, body mass index, among other variables. Results revealed that being a farm worker and working over 40 hours/week were risk factors for suboptimal glycemic control. Having greater days of poor mental was associated with suboptimal, borderline, and poor glycemic control. Having greater days of inactivity was associated with poor glycemic control while having greater days of poor physical health was associated with borderline glycemic control. There were no statistically significant relationships between glycemic control, self-reported general health, employment, and missed work. Finally, having an HbA1c value less than 6.5% was protective against mortality. The findings suggest that work-related factors are important in a person’s ability to reach optimal diabetes management levels. Poor glycemic control appears to have significant detrimental effects on HRQOL.^

Development and verification of control and protection strategies in hybrid AC/DC power systems for smart grid applications

Modern power networks incorporate communications and information technology infrastructure into the electrical power system to create a smart grid in terms of control and operation. The smart grid enables real-time communication and control between consumers and utility companies allowing suppliers to optimize energy usage based on price preference and system technical issues. The smart grid design aims to provide overall power system monitoring, create protection and control strategies to maintain system performance, stability and security. This dissertation contributed to the development of a unique and novel smart grid test-bed laboratory with integrated monitoring, protection and control systems. This test-bed was used as a platform to test the smart grid operational ideas developed here. The implementation of this system in the real-time software creates an environment for studying, implementing and verifying novel control and protection schemes developed in this dissertation. Phasor measurement techniques were developed using the available Data Acquisition (DAQ) devices in order to monitor all points in the power system in real time. This provides a practical view of system parameter changes, system abnormal conditions and its stability and security information system. These developments provide valuable measurements for technical power system operators in the energy control centers. Phasor Measurement technology is an excellent solution for improving system planning, operation and energy trading in addition to enabling advanced applications in Wide Area Monitoring, Protection and Control (WAMPAC). Moreover, a virtual protection system was developed and implemented in the smart grid laboratory with integrated functionality for wide area applications. Experiments and procedures were developed in the system in order to detect the system abnormal conditions and apply proper remedies to heal the system. A design for DC microgrid was developed to integrate it to the AC system with appropriate control capability. This system represents realistic hybrid AC/DC microgrids connectivity to the AC side to study the use of such architecture in system operation to help remedy system abnormal conditions. In addition, this dissertation explored the challenges and feasibility of the implementation of real-time system analysis features in order to monitor the system security and stability measures. These indices are measured experimentally during the operation of the developed hybrid AC/DC microgrids. Furthermore, a real-time optimal power flow system was implemented to optimally manage the power sharing between AC generators and DC side resources. A study relating to real-time energy management algorithm in hybrid microgrids was performed to evaluate the effects of using energy storage resources and their use in mitigating heavy load impacts on system stability and operational security.

Design optimization of modern machine drive systems for maximum fault tolerant and optimal operation

Modern electric machine drives, particularly three phase permanent magnet machine drive systems represent an indispensable part of high power density products. Such products include; hybrid electric vehicles, large propulsion systems, and automation products. Reliability and cost of these products are directly related to the reliability and cost of these systems. The compatibility of the electric machine and its drive system for optimal cost and operation has been a large challenge in industrial applications. The main objective of this dissertation is to find a design and control scheme for the best compromise between the reliability and optimality of the electric machine-drive system. The effort presented here is motivated by the need to find new techniques to connect the design and control of electric machines and drive systems. ^ A highly accurate and computationally efficient modeling process was developed to monitor the magnetic, thermal, and electrical aspects of the electric machine in its operational environments. The modeling process was also utilized in the design process in form finite element based optimization process. It was also used in hardware in the loop finite element based optimization process. The modeling process was later employed in the design of a very accurate and highly efficient physics-based customized observers that are required for the fault diagnosis as well the sensorless rotor position estimation. Two test setups with different ratings and topologies were numerically and experimentally tested to verify the effectiveness of the proposed techniques. ^ The modeling process was also employed in the real-time demagnetization control of the machine. Various real-time scenarios were successfully verified. It was shown that this process gives the potential to optimally redefine the assumptions in sizing the permanent magnets of the machine and DC bus voltage of the drive for the worst operating conditions. ^ The mathematical development and stability criteria of the physics-based modeling of the machine, design optimization, and the physics-based fault diagnosis and the physics-based sensorless technique are described in detail. ^ To investigate the performance of the developed design test-bed, software and hardware setups were constructed first. Several topologies of the permanent magnet machine were optimized inside the optimization test-bed. To investigate the performance of the developed sensorless control, a test-bed including a 0.25 (kW) surface mounted permanent magnet synchronous machine example was created. The verification of the proposed technique in a range from medium to very low speed, effectively show the intelligent design capability of the proposed system. Additionally, to investigate the performance of the developed fault diagnosis system, a test-bed including a 0.8 (kW) surface mounted permanent magnet synchronous machine example with trapezoidal back electromotive force was created. The results verify the use of the proposed technique under dynamic eccentricity, DC bus voltage variations, and harmonic loading condition make the system an ideal case for propulsion systems.^

Glycemic Control: Risk Factors, Quality of Life, Workforce Participation, and Mortality Among US Adults with Type 2 Diabetes

Despite research showing the benefits of glycemic control, it remains suboptimal among adults with diabetes in the United States. Possible reasons include unaddressed risk factors as well as lack of awareness of its immediate and long term consequences. The objectives of this study were to, using cross-sectional data, 1) ascertain the association between suboptimal (Hemoglobin A1c (HbA1c) ≥7%), borderline (HbA1c 7-8.9%), and poor (HbA1c ≥9%) glycemic control and potentially new risk factors (e.g. work characteristics), and 2) assess whether aspects of poor health and well-being such as poor health related quality of life (HRQOL), unemployment, and missed-work are associated with glycemic control; and 3) using prospective data, assess the relationship between mortality risk and glycemic control in US adults with type 2 diabetes. Data from the 1988-1994 and 1999-2004 National Health and Nutrition Examination Surveys were used. HbA1c values were used to create dichotomous glycemic control indicators. Binary logistic regression models were used to assess relationships between risk factors, employment status and glycemic control. Multinomial logistic regression analyses were conducted to assess relationships between glycemic control and HRQOL variables. Zero-inflated Poisson regression models were used to assess relationships between missed work days and glycemic control. Cox-proportional hazard models were used to assess effects of glycemic control on mortality risk. Using STATA software, analyses were weighted to account for complex survey design and non-response. Multivariable models adjusted for socio-demographics, body mass index, among other variables. Results revealed that being a farm worker and working over 40 hours/week were risk factors for suboptimal glycemic control. Having greater days of poor mental was associated with suboptimal, borderline, and poor glycemic control. Having greater days of inactivity was associated with poor glycemic control while having greater days of poor physical health was associated with borderline glycemic control. There were no statistically significant relationships between glycemic control, self-reported general health, employment, and missed work. Finally, having an HbA1c value less than 6.5% was protective against mortality. The findings suggest that work-related factors are important in a person’s ability to reach optimal diabetes management levels. Poor glycemic control appears to have significant detrimental effects on HRQOL.

Bayesian Inference in Large-scale Problems

Many modern applications fall into the category of "large-scale" statistical problems, in which both the number of observations n and the number of features or parameters p may be large. Many existing methods focus on point estimation, despite the continued relevance of uncertainty quantification in the sciences, where the number of parameters to estimate often exceeds the sample size, despite huge increases in the value of n typically seen in many fields. Thus, the tendency in some areas of industry to dispense with traditional statistical analysis on the basis that "n=all" is of little relevance outside of certain narrow applications. The main result of the Big Data revolution in most fields has instead been to make computation much harder without reducing the importance of uncertainty quantification. Bayesian methods excel at uncertainty quantification, but often scale poorly relative to alternatives. This conflict between the statistical advantages of Bayesian procedures and their substantial computational disadvantages is perhaps the greatest challenge facing modern Bayesian statistics, and is the primary motivation for the work presented here.

Two general strategies for scaling Bayesian inference are considered. The first is the development of methods that lend themselves to faster computation, and the second is design and characterization of computational algorithms that scale better in n or p. In the first instance, the focus is on joint inference outside of the standard problem of multivariate continuous data that has been a major focus of previous theoretical work in this area. In the second area, we pursue strategies for improving the speed of Markov chain Monte Carlo algorithms, and characterizing their performance in large-scale settings. Throughout, the focus is on rigorous theoretical evaluation combined with empirical demonstrations of performance and concordance with the theory.

One topic we consider is modeling the joint distribution of multivariate categorical data, often summarized in a contingency table. Contingency table analysis routinely relies on log-linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a reduced rank tensor factorization of the probability mass function for multivariate categorical data, while log-linear models achieve dimensionality reduction through sparsity. Little is known about the relationship between these notions of dimensionality reduction in the two paradigms. In Chapter 2, we derive several results relating the support of a log-linear model to nonnegative ranks of the associated probability tensor. Motivated by these findings, we propose a new collapsed Tucker class of tensor decompositions, which bridge existing PARAFAC and Tucker decompositions, providing a more flexible framework for parsimoniously characterizing multivariate categorical data. Taking a Bayesian approach to inference, we illustrate empirical advantages of the new decompositions.

Latent class models for the joint distribution of multivariate categorical, such as the PARAFAC decomposition, data play an important role in the analysis of population structure. In this context, the number of latent classes is interpreted as the number of genetically distinct subpopulations of an organism, an important factor in the analysis of evolutionary processes and conservation status. Existing methods focus on point estimates of the number of subpopulations, and lack robust uncertainty quantification. Moreover, whether the number of latent classes in these models is even an identified parameter is an open question. In Chapter 3, we show that when the model is properly specified, the correct number of subpopulations can be recovered almost surely. We then propose an alternative method for estimating the number of latent subpopulations that provides good quantification of uncertainty, and provide a simple procedure for verifying that the proposed method is consistent for the number of subpopulations. The performance of the model in estimating the number of subpopulations and other common population structure inference problems is assessed in simulations and a real data application.

In contingency table analysis, sparse data is frequently encountered for even modest numbers of variables, resulting in non-existence of maximum likelihood estimates. A common solution is to obtain regularized estimates of the parameters of a log-linear model. Bayesian methods provide a coherent approach to regularization, but are often computationally intensive. Conjugate priors ease computational demands, but the conjugate Diaconis--Ylvisaker priors for the parameters of log-linear models do not give rise to closed form credible regions, complicating posterior inference. In Chapter 4 we derive the optimal Gaussian approximation to the posterior for log-linear models with Diaconis--Ylvisaker priors, and provide convergence rate and finite-sample bounds for the Kullback-Leibler divergence between the exact posterior and the optimal Gaussian approximation. We demonstrate empirically in simulations and a real data application that the approximation is highly accurate, even in relatively small samples. The proposed approximation provides a computationally scalable and principled approach to regularized estimation and approximate Bayesian inference for log-linear models.

Another challenging and somewhat non-standard joint modeling problem is inference on tail dependence in stochastic processes. In applications where extreme dependence is of interest, data are almost always time-indexed. Existing methods for inference and modeling in this setting often cluster extreme events or choose window sizes with the goal of preserving temporal information. In Chapter 5, we propose an alternative paradigm for inference on tail dependence in stochastic processes with arbitrary temporal dependence structure in the extremes, based on the idea that the information on strength of tail dependence and the temporal structure in this dependence are both encoded in waiting times between exceedances of high thresholds. We construct a class of time-indexed stochastic processes with tail dependence obtained by endowing the support points in de Haan's spectral representation of max-stable processes with velocities and lifetimes. We extend Smith's model to these max-stable velocity processes and obtain the distribution of waiting times between extreme events at multiple locations. Motivated by this result, a new definition of tail dependence is proposed that is a function of the distribution of waiting times between threshold exceedances, and an inferential framework is constructed for estimating the strength of extremal dependence and quantifying uncertainty in this paradigm. The method is applied to climatological, financial, and electrophysiology data.

The remainder of this thesis focuses on posterior computation by Markov chain Monte Carlo. The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It has long been common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention has been paid to convergence and estimation error in these approximating Markov Chains. In Chapter 6, we propose a framework for assessing when to use approximations in MCMC algorithms, and how much error in the transition kernel should be tolerated to obtain optimal estimation performance with respect to a specified loss function and computational budget. The results require only ergodicity of the exact kernel and control of the kernel approximation accuracy. The theoretical framework is applied to approximations based on random subsets of data, low-rank approximations of Gaussian processes, and a novel approximating Markov chain for discrete mixture models.

Data augmentation Gibbs samplers are arguably the most popular class of algorithm for approximately sampling from the posterior distribution for the parameters of generalized linear models. The truncated Normal and Polya-Gamma data augmentation samplers are standard examples for probit and logit links, respectively. Motivated by an important problem in quantitative advertising, in Chapter 7 we consider the application of these algorithms to modeling rare events. We show that when the sample size is large but the observed number of successes is small, these data augmentation samplers mix very slowly, with a spectral gap that converges to zero at a rate at least proportional to the reciprocal of the square root of the sample size up to a log factor. In simulation studies, moderate sample sizes result in high autocorrelations and small effective sample sizes. Similar empirical results are observed for related data augmentation samplers for multinomial logit and probit models. When applied to a real quantitative advertising dataset, the data augmentation samplers mix very poorly. Conversely, Hamiltonian Monte Carlo and a type of independence chain Metropolis algorithm show good mixing on the same dataset.

Investigating the Tradespace between Increased Automation and Optimal Manning on Aircraft Carrier Decks

With increasing prevalence and capabilities of autonomous systems as part of complex heterogeneous manned-unmanned environments (HMUEs), an important consideration is the impact of the introduction of automation on the optimal assignment of human personnel. The US Navy has implemented optimal staffing techniques before in the 1990's and 2000's with a "minimal staffing" approach. The results were poor, leading to the degradation of Naval preparedness. Clearly, another approach to determining optimal staffing is necessary. To this end, the goal of this research is to develop human performance models for use in determining optimal manning of HMUEs. The human performance models are developed using an agent-based simulation of the aircraft carrier flight deck, a representative safety-critical HMUE. The Personnel Multi-Agent Safety and Control Simulation (PMASCS) simulates and analyzes the effects of introducing generalized maintenance crew skill sets and accelerated failure repair times on the overall performance and safety of the carrier flight deck. A behavioral model of four operator types (ordnance officers, chocks and chains, fueling officers, plane captains, and maintenance operators) is presented here along with an aircraft failure model. The main focus of this work is on the maintenance operators and aircraft failure modeling, since they have a direct impact on total launch time, a primary metric for carrier deck performance. With PMASCS I explore the effects of two variables on total launch time of 22 aircraft: 1) skill level of maintenance operators and 2) aircraft failure repair times while on the catapult (referred to as Phase 4 repair times). It is found that neither introducing a generic skill set to maintenance crews nor introducing a technology to accelerate Phase 4 aircraft repair times improves the average total launch time of 22 aircraft. An optimal manning level of 3 maintenance crews is found under all conditions, the point at which any additional maintenance crews does not reduce the total launch time. An additional discussion is included about how these results change if the operations are relieved of the bottleneck of installing the holdback bar at launch time.

Optimal Capital Requirements in Financial Networks with Fire Sales

I explore and analyze a problem of finding the socially optimal capital requirements for financial institutions considering two distinct channels of contagion: direct exposures among the institutions, as represented by a network and fire sales externalities, which reflect the negative price impact of massive liquidation of assets.These two channels amplify shocks from individual financial institutions to the financial system as a whole and thus increase the risk of joint defaults amongst the interconnected financial institutions; this is often referred to as systemic risk. In the model, there is a trade-off between reducing systemic risk and raising the capital requirements of the financial institutions. The policymaker considers this trade-off and determines the optimal capital requirements for individual financial institutions. I provide a method for finding and analyzing the optimal capital requirements that can be applied to arbitrary network structures and arbitrary distributions of investment returns.

In particular, I first consider a network model consisting only of direct exposures and show that the optimal capital requirements can be found by solving a stochastic linear programming problem. I then extend the analysis to financial networks with default costs and show the optimal capital requirements can be found by solving a stochastic mixed integer programming problem. The computational complexity of this problem poses a challenge, and I develop an iterative algorithm that can be efficiently executed. I show that the iterative algorithm leads to solutions that are nearly optimal by comparing it with lower bounds based on a dual approach. I also show that the iterative algorithm converges to the optimal solution.

Finally, I incorporate fire sales externalities into the model. In particular, I am able to extend the analysis of systemic risk and the optimal capital requirements with a single illiquid asset to a model with multiple illiquid assets. The model with multiple illiquid assets incorporates liquidation rules used by the banks. I provide an optimization formulation whose solution provides the equilibrium payments for a given liquidation rule.

I further show that the socially optimal capital problem using the ``socially optimal liquidation" and prioritized liquidation rules can be formulated as a convex and convex mixed integer problem, respectively. Finally, I illustrate the results of the methodology on numerical examples and

discuss some implications for capital regulation policy and stress testing.

A Comprehensive Portfolio Construction Under Stochastic Environment

Prior research has established that idiosyncratic volatility of the securities prices exhibits a positive trend. This trend and other factors have made the merits of investment diversification and portfolio construction more compelling. A new optimization technique, a greedy algorithm, is proposed to optimize the weights of assets in a portfolio. The main benefits of using this algorithm are to: a) increase the efficiency of the portfolio optimization process, b) implement large-scale optimizations, and c) improve the resulting optimal weights. In addition, the technique utilizes a novel approach in the construction of a time-varying covariance matrix. This involves the application of a modified integrated dynamic conditional correlation GARCH (IDCC - GARCH) model to account for the dynamics of the conditional covariance matrices that are employed. The stochastic aspects of the expected return of the securities are integrated into the technique through Monte Carlo simulations. Instead of representing the expected returns as deterministic values, they are assigned simulated values based on their historical measures. The time-series of the securities are fitted into a probability distribution that matches the time-series characteristics using the Anderson-Darling goodness-of-fit criterion. Simulated and actual data sets are used to further generalize the results. Employing the S&P500 securities as the base, 2000 simulated data sets are created using Monte Carlo simulation. In addition, the Russell 1000 securities are used to generate 50 sample data sets. The results indicate an increase in risk-return performance. Choosing the Value-at-Risk (VaR) as the criterion and the Crystal Ball portfolio optimizer, a commercial product currently available on the market, as the comparison for benchmarking, the new greedy technique clearly outperforms others using a sample of the S&P500 and the Russell 1000 securities. The resulting improvements in performance are consistent among five securities selection methods (maximum, minimum, random, absolute minimum, and absolute maximum) and three covariance structures (unconditional, orthogonal GARCH, and integrated dynamic conditional GARCH).

Essays in dynamic optimal taxation: working experience, unemployment scarring and poverty

This thesis investigates the design of optimal tax systems in dynamic environments. The first essay characterizes the optimal tax system where wages depend on stochastic shocks and work experience. In addition to redistributive and efficiency motives, the taxation of inexperienced workers depends on a second-best requirement that encourages work experience, a social insurance motive and incentive effects. Calibrations using U.S. data yield higher expected optimal marginal income tax rates for experienced workers for most of the inexperienced workers. They confirm that the average marginal income tax rate increases (decreases) with age when shocks and work experience are substitutes (complements). Finally, more variability in experienced workers' earnings prospects leads to increasing tax rates since income taxation acts as a social insurance mechanism. In the second essay, the properties of an optimal tax system are investigated in a dynamic private information economy where labor market frictions create unemployment that destroys workers' human capital. A two-skill type model is considered where wages and employment are endogenous. I find that the optimal tax system distorts the first-period wages of all workers below their efficient levels which leads to more employment. The standard no-distortion-at-the-top result no longer holds due to the combination of private information and the destruction of human capital. I show this result analytically under the Maximin social welfare function and confirm it numerically for a general social welfare function. I also investigate the use of a training program and job creation subsidies. The final essay analyzes the optimal linear tax system when there is a population of individuals whose perceptions of savings are linked to their disposable income and their family background through family cultural transmission. Aside from the standard equity/efficiency trade-off, taxes account for the endogeneity of perceptions through two channels. First, taxing labor decreases income, which decreases the perception of savings through time. Second, taxation on savings corrects for the misperceptions of workers and thus savings and labor decisions. Numerical simulations confirm that behavioral issues push labor income taxes upward to finance saving subsidies. Government transfers to individuals are also decreased to finance those same subsidies.

Integrated Optimal Power Flow for Distribution Networks in Local and Urban Scales

This paper develops an integrated optimal power flow (OPF) tool for distribution networks in two spatial scales. In the local scale, the distribution network, the natural gas network, and the heat system are coordinated as a microgrid. In the urban scale, the impact of natural gas network is considered as constraints for the distribution network operation. The proposed approach incorporates unbalance three-phase electrical systems, natural gas systems, and combined cooling, heating, and power systems. The interactions among the above three energy systems are described by energy hub model combined with components capacity constraints. In order to efficiently accommodate the nonlinear constraint optimization problem, particle swarm optimization algorithm is employed to set the control variables in the OPF problem. Numerical studies indicate that by using the OPF method, the distribution network can be economically operated. Also, the tie-line power can be effectively managed.

Managing Rentals with Usage-Based Loss

Motivated by new and innovative rental business models, this paper develops a novel discrete-time model of a rental operation with random loss of inventory due to customer use. The inventory level is chosen before the start of a finite rental season, and customers not immediately served are lost. Our analysis framework uses stochastic comparisons of sample paths to derive structural results that hold under good generality for demands, rental durations, and rental unit lifetimes. Considering different \recirculation" rules | i.e., which rental unit to choose to meet each demand | we prove the concavity of the expected profit function and identify the optimal recirculation rule. A numerical study clarifies when considering rental unit loss and recirculation rules matters most for the inventory decision: Accounting for rental unit loss can increase the expected profit by 7% for a single season and becomes even more important as the time horizon lengthens. We also observe that the optimal inventory level in response to increasing loss probability is non-monotonic. Finally, we show that choosing the optimal recirculation rule over another simple policy allows more rental units to be profitably added, and the profit-maximizing service level increases by up to 6 percentage points.

Estimating the effect of the 2008 financial crisis on GNI in Greece and Iceland: A synthetic control approach

The purpose of this thesis is to conduct a comparative study in order to estimate the impact of the financial crisis to the GNI of Greece and Iceland. By applying synthetic control matching (a relatively new methodology) the study intends to compare the two countries, thus deducting conclusions about good or bad measures adopted. The results indicate that in both cases the adopted measures were not the optimal ones, since the synthetic counterfactual appear to perform better than the actual Greece and Iceland. Moreover, it is shown that Iceland reacted better to the shock it was exposed. However, different characteristics of the two countries impede the application of Icelandic actions in the Greek case.

An iterative analytical design framework for the optimal designing of an off-grid renewable energy based hybrid smart micro-grid

Creative ways of utilising renewable energy sources in electricity generation especially in remote areas and particularly in countries depending on imported energy, while increasing energy security and reducing cost of such isolated off-grid systems, is becoming an urgently needed necessity for the effective strategic planning of Energy Systems. The aim of this research project was to design and implement a new decision support framework for the optimal design of hybrid micro grids considering different types of different technologies, where the design objective is to minimize the total cost of the hybrid micro grid while at the same time satisfying the required electric demand. Results of a comprehensive literature review, of existing analytical, decision support tools and literature on HPS, has identified the gaps and the necessary conceptual parts of an analytical decision support framework. As a result this research proposes and reports an Iterative Analytical Design Framework (IADF) and its implementation for the optimal design of an Off-grid renewable energy based hybrid smart micro-grid (OGREH-SμG) with intra and inter-grid (μG2μG & μG2G) synchronization capabilities and a novel storage technique. The modelling design and simulations were based on simulations conducted using HOMER Energy and MatLab/SIMULINK, Energy Planning and Design software platforms. The design, experimental proof of concept, verification and simulation of a new storage concept incorporating Hydrogen Peroxide (H2O2) fuel cell is also reported. The implementation of the smart components consisting Raspberry Pi that is devised and programmed for the semi-smart energy management framework (a novel control strategy, including synchronization capabilities) of the OGREH-SμG are also detailed and reported. The hybrid μG was designed and implemented as a case study for the Bayir/Jordan area. This research has provided an alternative decision support tool to solve Renewable Energy Integration for the optimal number, type and size of components to configure the hybrid μG. In addition this research has formulated and reported a linear cost function to mathematically verify computer based simulations and fine tune the solutions in the iterative framework and concluded that such solutions converge to a correct optimal approximation when considering the properties of the problem. As a result of this investigation it has been demonstrated that, the implemented and reported OGREH-SμG design incorporates wind and sun powered generation complemented with batteries, two fuel cell units and a diesel generator is a unique approach to Utilizing indigenous renewable energy with a capability of being able to synchronize with other μ-grids is the most effective and optimal way of electrifying developing countries with fewer resources in a sustainable way, with minimum impact on the environment while also achieving reductions in GHG. The dissertation concludes with suggested extensions to this work in the future.

Exact Solution of Bayes and Minimax Change-Detection Problems

The challenge of detecting a change in the distribution of data is a sequential decision problem that is relevant to many engineering solutions, including quality control and machine and process monitoring. This dissertation develops techniques for exact solution of change-detection problems with discrete time and discrete observations. Change-detection problems are classified as Bayes or minimax based on the availability of information on the change-time distribution. A Bayes optimal solution uses prior information about the distribution of the change time to minimize the expected cost, whereas a minimax optimal solution minimizes the cost under the worst-case change-time distribution. Both types of problems are addressed. The most important result of the dissertation is the development of a polynomial-time algorithm for the solution of important classes of Markov Bayes change-detection problems. Existing techniques for epsilon-exact solution of partially observable Markov decision processes have complexity exponential in the number of observation symbols. A new algorithm, called constellation induction, exploits the concavity and Lipschitz continuity of the value function, and has complexity polynomial in the number of observation symbols. It is shown that change-detection problems with a geometric change-time distribution and identically- and independently-distributed observations before and after the change are solvable in polynomial time. Also, change-detection problems on hidden Markov models with a fixed number of recurrent states are solvable in polynomial time. A detailed implementation and analysis of the constellation-induction algorithm are provided. Exact solution methods are also established for several types of minimax change-detection problems. Finite-horizon problems with arbitrary observation distributions are modeled as extensive-form games and solved using linear programs. Infinite-horizon problems with linear penalty for detection delay and identically- and independently-distributed observations can be solved in polynomial time via epsilon-optimal parameterization of a cumulative-sum procedure. Finally, the properties of policies for change-detection problems are described and analyzed. Simple classes of formal languages are shown to be sufficient for epsilon-exact solution of change-detection problems, and methods for finding minimally sized policy representations are described.