Model uncertainty in financial markets is prevalent by the very nature of how models are constructed and used by financial practitioners. As such, a proper characterization of model uncertainty should be paramount in the eyes of every practitioner, and furthermore, a proper framework for implementing such a characterization towards financial activities should be implicit. While model uncertainty is acknowledged by practitioners, a cohesive and robust framework for determining a model uncertainty risk measure that is broadly accepted by practitioners is missing. We acknowledge this deficiency and provide a practitioner's guide for evaluating a modern characterization of model uncertainty, specifically that of Li and Kwon, as applied to a subset of derivative related calculations, with the goal of promoting its implementation by practitioners. We promote its implementation by demonstrating the utility and flexibility of such a characterization relative to another modern model uncertainty risk measure, specifically that of Cont.

Model uncertainty in financial markets is prevalent by the very nature of how models are constructed and used by financial practitioners. As such, a proper characterization of model uncertainty should be paramount in the eyes of every practitioner, and furthermore, a proper framework for implementing such a characterization towards financial activities should be implicit. While model uncertainty is acknowledged by practitioners, a cohesive and robust framework for determining a model uncertainty risk measure that is broadly accepted by practitioners is missing. We acknowledge this deficiency and provide a practitioner's guide for evaluating a modern characterization of model uncertainty, specifically that of Li and Kwon, as applied to a subset of derivative related calculations, with the goal of promoting its implementation by practitioners. We promote its implementation by demonstrating the utility and flexibility of such a characterization relative to another modern model uncertainty risk measure, specifically that of Cont.

Master of Science / Department of Industrial & Manufacturing Systems Engineering / John R. English / Inventory accuracy is critical for almost all industrial environments such as distribution, warehousing, and retail. It is quite common for companies with exceptional inventory accuracy to use a technique called cycle counting. For many organizations, the time and resources to complete cycle counting are limited or not available. In this work, we promote statistical process control (SPC) to monitor inventory accuracy. Specifically, we model the complex underlying environments with mixture distributions to demonstrate sampling from a mixed but stationary process. For our particular application, we concern ourselves with data that result from inventory adjustments at the stock keeping unit (SKU) level when a given SKU is found to be inaccurate. We provide estimates of both the Type I and Type II errors when a classic c chart is used. In these estimations, we use both analytical as well as simulation results, and the findings demonstrate the environments that might be conducive for SPC approaches.

In this thesis, we first study delay systems with different classes of impatient customers. We analyze the M/GI/1+M queue serving two priority classes under the static non-preemptive priority discipline. We also study the multi-server priority queue considering two cases depending on the time-to-abandon distribution being exponentially distributed or deterministic. In all models, we obtain the Laplace transforms of the virtual waiting time for each class by exploiting the level-crossing method. This enables us to obtain the steady-state system performance measures. In the second part, we consider the steady-state waiting time distributions of a two class M/GI/1 queue operating under a dynamic priority discipline. We find an accurate approximation for the steady-state waiting time distribution of the low-priority customers which allows us to study how they are penalized as the priority parameter increases. We also obtain bounds for the variance of the waiting time of high-priority customers.

In this thesis, we first study delay systems with different classes of impatient customers. We analyze the M/GI/1+M queue serving two priority classes under the static non-preemptive priority discipline. We also study the multi-server priority queue considering two cases depending on the time-to-abandon distribution being exponentially distributed or deterministic. In all models, we obtain the Laplace transforms of the virtual waiting time for each class by exploiting the level-crossing method. This enables us to obtain the steady-state system performance measures. In the second part, we consider the steady-state waiting time distributions of a two class M/GI/1 queue operating under a dynamic priority discipline. We find an accurate approximation for the steady-state waiting time distribution of the low-priority customers which allows us to study how they are penalized as the priority parameter increases. We also obtain bounds for the variance of the waiting time of high-priority customers.

Pairs trading has been a popular statistical arbitrage strategy among hedge funds. One important research field in pairs trading is to maximize the return under differential constraints and assumptions. In this thesis, we develop two models to optimize the performance of pairs trading. In the static model, we find the analytic solution of optimal thresholds for pairs trading to maximize the long run profit per unit time. Comparison is made between the optimal rules we developed and the common practice. To overcome limitations of the static model, we extend our research to dynamic pairs trading, where a continuous time Markov chain is used to model the change of parameters. Our objective is to maximize the expected return in the finite horizon under the Constant Relative Risk Aversion (CRRA) utility. Numerical examples are presented to illustrate the impact of price limits, risk aversion rate and regime switching on consumers' investment decision.

In joint human-automation systems, operators must often supervise the automation and adapt their reliance on it based on judgments of its context-specific reliability. For this to occur, operators should trust the automation appropriately. In the design of a water monitoring decision aid’s display, Ecological Interface Design was used to satisfy design guidelines for supporting appropriate trust. Design focused upon a visualization that made the aid’s use of the Dempster-Shafer theory directly perceptible. The display was evaluated using a signal detection theory-based approach that measured reliance on automation. Results indicated that the ecological display yielded less appropriate reliance and poorer performance than a conventional display for a highly reliable decision aid. However, the experimental task prevented participants from adapting to the aid’s context-specific reliabilities, reducing the validity of the findings. A subsequent study is proposed to further study the effects of ecological displays on automation reliance.

In joint human-automation systems, operators must often supervise the automation and adapt their reliance on it based on judgments of its context-specific reliability. For this to occur, operators should trust the automation appropriately. In the design of a water monitoring decision aid’s display, Ecological Interface Design was used to satisfy design guidelines for supporting appropriate trust. Design focused upon a visualization that made the aid’s use of the Dempster-Shafer theory directly perceptible. The display was evaluated using a signal detection theory-based approach that measured reliance on automation. Results indicated that the ecological display yielded less appropriate reliance and poorer performance than a conventional display for a highly reliable decision aid. However, the experimental task prevented participants from adapting to the aid’s context-specific reliabilities, reducing the validity of the findings. A subsequent study is proposed to further study the effects of ecological displays on automation reliance.

Master of Science / Department of Industrial & Manufacturing Systems Engineering / Todd W. Easton / Integer Programs (IP) are a class of discrete optimization problems that are utilized commercially to improve the function of various systems. Implementation is often aimed at reaching optimal financial objectives with constraints on resources and operation. While incredibly beneficial, IPs are NP-complete, with many IP models being unsolvable. Branch and bound (BB) is the primary method employed to solve IPs to optimality. BB is an exhaustive approach to enumerating all potential integer solutions for a given IP. By utilizing a hierarchical tree structure to tabulate progression of enumeration, BB can guarantee an optimal solution in finite time. However, BB can take an exponential number of iterations to solve an IP. Computationally, this can result in a tree structure that exceeds a computer’s memory capacity, or a prohibitively long solution time. This thesis introduces a modified version of BB call the Quaternary Hyperplane Branching Algorithm (QHBA). QHBA employs a quaternary branching scheme, utilizes hyperplane branching constraints, and generates internal cutting planes to increase efficiency. Implementation of these advancements theoretically improves QHBA in comparison to traditional BB. It can also be shown that QHBA guarantees an optimal solution in a finite number of iterations. A short computational study shows that QHBA results in a 26.7% decrease in solution times when compared to CPLEX, a commercially available IP solver.

Master of Science / Department of Industrial & Manufacturing Systems Engineering / Todd W. Easton / Baseball is an incredibly complex game where the managers of the baseball teams have numerous decisions to make. The managers are in control of the offense and defense of a team. Some managers have ruined their teams’ chances of a victory by removing their star pitcher too soon in a game or leaving them in too long; managers also choose to pinch hit for batters or pinch run for base runners in order to set up a “favorable match-up” such as a left handed pitcher versus a right handed batter. This research’s goal is to aid managers by providing an optimal positioning of defensive players on the field for a particular batter. In baseball, every ball that is hit onto the field of play can be an out if the fielders are positioned correctly. By positioning the fielders in an optimal manner a team will directly reduce the number of runs that it gives up, which increases the chances of a win. This research describes an integer program that can determine the optimal location of defensive players. This integer program is based off of a random set of hits that the player has produced in the past. The integer program attempts to minimize the expected costs associated with each hit where the cost is defined by a penalty (single, double or triple) or benefit (out) of the person’s hit. By solving this integer program in Opl Studio 4.2, a commercial integer programming software, an optimal defensive positioning is derived for use against this batter. To test this defense against other standard defenses that teams in the MLB currently use, a simulation was created. This simulation uses Derek Jeter’s actual statistics; including his 2009 regular season hit chart. The simulation selects a hit at random according to his hit chart and determines the outcome of the hit (single, double, out, double play, etc.). Once this simulation is complete a printout shows the batter’s statistics; including his average and slugging percentage. VI By comparing the optimized defensive alignment with some commonly used major league alignments, it can be shown that this optimal alignment would decrease Jeter’s average by nearly 13% and decrease his slugging by 35%. It is my opinion that managers should use this tool to help them win more games. These defenses can be seamlessly implemented by any coach or team.