Forward contracting can deliver benefits in terms of risk hedging, price discovery, and market power mitigation. Aiming to advance the understanding of its role in market design, I examine how the introduction of a forward market changes the strategic and hedging incentives of participants. I challenge the two common literature assumptions of (i) one-sided market power: the assumption that only sellers exercise market power and (ii) perfect arbitrage: the equivalence of forward and (expected) spot price. I provide a framework in which oligopolists face oligopsonists in two sequential markets and allow for a price premium to arise endogenously as the result of hedging and strategic considerations. The introduction of a forward market is found to increase efficiency but does not necessarily do so in a Pareto improving way. The distribution of potential benefits to sellers and buyers depends on their risk aversion and market power. Policy implications are discussed.

A majority of infectious disease models are compartmental models, due to their simplicity and interpretability. However the assumption of homogeneous mixing in compartmental models does not hold in general, and for certain diseases or subpopulations the heterogeneity in mixing behavior is particularly prominent. With more and more data becoming available to shed light on the heterogeneous mixing of population, network model has emerged as an alternative solution. This dissertation focuses on developing and applying network models to study infectious diseases with readily available data. In Chapter 2, we propose a mathematical framework to study the spread of blood-borne diseases among people who inject drugs (PWID). The prevalence rate of blood-borne diseases is higher among PWID as compared to the general population, due to unprotected sex and needle-sharing. To accurately account for transmissions via both types of risky contact, we build a bi-layer network model. We present methodology for inferring model parameters from readily available data sources. The model can be used to evaluate interventions that exploit the structure of the contact network to contain infectious diseases in PWID. To illustrate, we instantiate a network model with data collected by a needle and syringe program in Chicago, then we use the model to evaluate the potential effects of a peer education (PE) program on averting new HIV and HCV infections over the next ten years. We show that a targeted PE program would avert significantly more HIV and HCV infections than an untargeted program, highlighting the importance of reaching individuals who are centrally located in contact networks. In Chapter 3, we adapt the network model of Chapter 2 to evaluate the cost-effectiveness of a pre-exposure prophylaxis (PrEP) program for PWID. Inspired by the illustrative example of targeted PE program in Chapter 2, we sought to improve the cost-effectiveness of PrEP program by enrolling high risk PWID. Specifically we investigate four strategies: 1) random PWID are enrolled (Unselected Enrollment); 2) individuals are randomly selected and enrolled together with their partners (Enroll Partners); 3) individuals with the highest number of sexual and needle-sharing partnerships are enrolled (Most Partners); 4) individuals with the greatest number of infected partners are enrolled (Most Positive Partners). We measure costs and QALYs associated with each strategy, and find that all strategies except the Unselected Enrollment strategy are cost-effective, indicating that selection of high risk PWID for PrEP can indeed improve the cost-effectiveness of PrEP for PWID. In Chapter 4, we explore a household model to study the circulation of poliovirus in a community.The Polio Eradication and Endgame Strategic Plan 2013-2018 calls for the gradual withdrawal of OPV from routine immunization. Little is understood regarding the transmission potential of Sabin virus when it is reintroduced in the post-cessation era. In view of this, we develop an individual-based stochastic epidemic model and use the model to investigate two scenarios: 1) an outbreak response using OPV takes place to interrupt wild poliovirus transmission; 2) a case actively shedding Sabin virus is released into the community and sparks an undetected circulation. We find that inactivated poliovirus vaccine (IPV) alone is insufficient to prevent long term circulation of Sabin virus under current level of sanitation and contact patterns in Mexican communities if OPV is reintroduced. Our result highlights the need for aggressive OPV use in outbreak response, vigilant poliovirus surveillance, improvement in hygiene and sanitation, as well as development of new vaccines that protect against fecal shedding and reinfection. We conclude with a summary of our findings and a discussion of future research directions in Chapter 5.

This thesis covers several applications of Operations Research in the domains of finance and healthcare. There are three chapters, each covering a different application. Chapter 1 applies techniques from deep learning to estimate mortgage risk. The near-elimination of feature engineering is substituted by models with several thousand parameters that require large amounts of training data. The predictive performance of these models strongly exceeds that of baseline models, especially for predicting prepayments. This increased accuracy, however, comes at the cost of a more opaque model which is harder for a human to interpret than simpler models like logistic regression, which are currently the industry standard. The work in Chapter 2 explores the design of policies for biometric authentication. It first develops a model for the joint distribution of similarity scores associated with different fingers and irises. In the second step, this model is harnessed to design near-optimal multi-stage policies that would be used for authentication, and are robust to gaming, can be computed in real-time and are personalized for optimal performance. The work shows that a reduction of several orders of magnitude in the error rates is achievable by solely changing the authentication policies -- and leaving the hardware unchanged. Chapter 3 is motivated by a humanitarian cause geared towards helping developing countries -- to reduce mortality in children by identifying effective interventions at the planning stage. It takes a descriptive health model (called LiST), which estimates mortality of children given coverage of interventions, and embeds that into an optimization engine in order to minimize mortality under a fixed budget. In doing so, it allows LiST to be used in a prescriptive framework, where policymakers can identify the optimal intervention set at a fixed budget as well as recognize the trade-off of mortality reduction and budget allocation. We find that a greedy strategy offers near-optimal performance with ease of implementation. The findings also highlight the critical role that optimization plays in mortality reduction.

Better understanding energy, how to harness and utilise it effectively, and what the implications of its use in these ways means from an individual to a more aggregate level are important topics for business, policy making, and research. Growing evidence pointing to the serious global consequences of society's energy usage further increases the importance of these goals. Furthermore it is increasingly clear that the costs and benefits of energy use are experienced disproportionately across the population. The changing nature of individual decision-making and how the actions of individuals affect an entire economic system also play important roles in our effort to implement effective energy and environmental policy. Both on the demand-side and the supply-side, trends of decentralisation and the increased adoption of more granular technologies are making it increasingly important to understand the role of the individual and their behaviour within the broader energy-economic-environmental system. This dissertation contributes to the intersection of the energy, environmental, and behavioural economics literatures with an emphasis on policy efficacy. It considers questions of efficient retail electricity pricing, externality-correcting policies, the role of behavioural bias in consumer decision making, and the implications of such bias for policy efficacy. Its approach is grounded in neoclassical economics, but it brings the newer field of behavioural economics into the fold where its inclusion strengthens the ability to answer the question at hand. There are two main projects in this dissertation. The first is an in-depth evaluation of the rooftop solar pricing policy of Net Energy Metering (NEM) from both an economic efficiency and distributional equity approach. Treatment of this topic is approached first theoretically and then complemented with a suite of numerical simulations. The second project represents an attempt to codify and unify considerations of behavioural bias in individual decision making and what implications they have for optimal policy efficacy. In this way it showcases behavioural economics as an extension of, rather than a challenge to, neoclassical theory.

Consider a farm of robots operating concurrently, learning to carry out a task, and sharing data with one another in real time. There are clear benefits to scale, since a larger number of robots can gather and share more data in the same amount of time that enables each robot in the group to learn faster than it would learn on its own. However, the benefits of parallelization can be greatly magnified if the robots explore the environment in a coordinated fashion, diversifying their experience and adapting appropriately as data is gathered. We identify three properties which are necessary for efficient coordinated exploration -- adaptivity, commitment, diversity -- and demonstrate that straightforward extensions of statistically efficient optimistic and posterior sampling approaches from single-agent to concurrent reinforcement learning fail to satisfy them. As an alternative, we propose seed sampling, which extends posterior sampling in a manner that meets these requirements. We proceed to design concurrent reinforcement learning algorithms that achieve the three properties of efficient coordinated exploration in real systems with potentially enormous state spaces, to which tabular methods do not scale. This is achieved by coupling the seed sampling concept with learning general value function or policy function representations that allow the agents to generalize and operate in arbitrarily large scale environments. Overall, this dissertation presents a concept that enables rapid learning of effective policies in the presence of complex goals, when we have multiple agents who learn to operate in parallel in a common, unknown environment and collaborate in real time. There is a multitude of applications that can benefit from this algorithmic framework, ranging from recommendation systems, to robot automation, to autonomous vehicles.

The last decade of American politics has been marked by an increasingly polarized electorate and a subsequent ideological schism in political discourse. In this climate, it is imperative for research to focus on quantitative methods, and to provide inherently objective views on topics under public scrutiny. In this study, we explore various ways in which modern computational models can help in examining political topics and presenting impartial conclusions. We begin by investigating the accuracy of election polls through an empirical analysis of polls conducted during the final three weeks of the campaigns. We establish that the average survey error is approximately twice as large as that implied by most reported margins of error. Using a Bayesian hierarchical model, we find that average absolute election-level bias is about 2 percentage points, indicating that polls for a given election often share a common component of error. We discuss how these results can help to explain polling failures in the 2016 U.S. presidential election. Next, we focus on voter fraud and show how a probabilistic birthdate model can be used to estimate the number of double votes in U.S. presidential elections. Refuting commonly asserted allegations of rampant double voting, we estimate that fewer than 0.03% of votes cast in 2012 were double votes, and we show that almost all of these cases can be explained by a plausible rate of error in marking registration records. Finally, we leverage a variant of model-based post-stratification (MP) to measure the effects of sentiment and turnout on electoral change between two elections. We use this model to explain the Republican surge in the House in 2010 and 2014, and to critique the narrative that young people have tilted Republican in these two elections. The findings of our study reveal the presence of polling error, the negligibility of voter fraud, and the advantage of using an MP-based approach to investigate electoral change, and reinforce the necessity of applying computational models to difficult topics in political science.

Cardiovascular disease (CVD) is the leading cause of morbidity and mortality in the United States (US). In addition, CVD remains a major cause of health disparities and rising health care costs. Because cardiovascular outcomes depend highly on multiple patient characteristics that evolve stochastically over time, this dissertation focuses on developing novel mathematical models to capture heterogeneous population characteristics, and to support actionable policy recommendations and informed decision-making in CVD prevention and control. Efficient prevention and control of CVD includes two types of interventions: primary prevention to prevent the onset of disease, such as lifestyle interventions, and secondary prevention with drug treatment to reduce the progression of disease. In Chapter 2, given recent data on the relationship between sodium intake, hypertension, and associated cardiovascular diseases, we examine the impact of population-wide expansion of the National Salt Reduction Initiative (NSRI), in which food producers agree to lower sodium to levels deemed feasible for different foods. We developed and validated a stochastic microsimulation model of hypertension, myocardial infarction (MI) and stroke in the US population. The model follows individual dietary intakes and CVD risk factors of the population stratified by demographic characteristics. We find that expanding the NSRI nationwide is expected to significantly reduce hypertension and hypertension-related CVD morbidity and mortality among the majority of the population, even in the context of compensatory consumer behaviors. But older women in particular may be at risk for excessively low sodium intake. This suggests that careful consideration should be made of how to target such large-scale population-wide policy interventions to minimize adverse effects among the most vulnerable. Large socioeconomic disparities exist in US dietary habits and CVD morbidity and mortality. While high fruits and vegetable (F& V) consumption is thought to reduce the risk of chronic diseases, dietary patterns and intakes of F& Vs are particularly lower among low-socioeconomic groups. Providing financial incentives for F& V purchases among low-income households has been demonstrated to increase F& V consumption. In Chapter 3, we extend the microsimulation model developed in Chapter 2 to evaluate lifetime costs and health outcomes of subsidizing F& V purchases among Supplemental Nutrition Assistance Program (SNAP) participants in the US, and to assess its impact on CVD disparities. In this model, type II diabetes and obesity were included in addition to MI and stroke to capture the complex interrelationship between changes in F& V prices and its effects on health outcomes. We find that nationwide expansion of the F& V subsidy among SNAP participants would be expected to significantly lower incidence of long-term chronic diseases in the US and would be cost-saving under a wide range of scenarios. The benefits would be accumulated the most among demographic groups for whom healthcare interventions alone have not been sufficient to reduce large disparities in CVD incidence that have been attributed in part to poor nutrition. Moreover, these benefits would likely persist even if the incentive is imperfectly implemented. As a secondary CVD prevention, hypertension management has traditionally been guided by a treat-to-target strategy focusing on achieving specific levels of blood pressure. Because treatment benefits depend on multiple patient characteristics, it has been recommended to personalize blood pressure treatment decisions. In Chapter 4, we develop a Markov decision process (MDP) model for determining the optimal blood pressure treatment for an individual, incorporating a complex variety of individual-level covariates, treatment effect modifiers, and risks and benefits of treatment alternatives. We find that the MDP-based treatment approach would improve overall population health compared to current blood pressure treatment guidelines, and it would be cost-saving. In order to improve usability and interpretability of the MDP model developed in Chapter 4, we use data analytic techniques to approximate the optimal blood pressure treatment policies derived from the MDP model in Chapter 5. We create a more easily interpretable treatment planning framework that offer comparable results to the optimal decisions rules determined by the MDP. In this dissertation, we present the use of data-driven methods in modeling health policy and healthcare decisions, focusing on CVD prevention and control. The methods we used can be adapted to other diseases and settings to promote informed-decision making.

How do large-scale shocks affect individuals and firms? Answering that question has been a motivating theme in my research agenda, which is taken up here through the lens of foreclosures on home mortgages during the financial crisis. Foreclosures grew by 200-400% across counties and foreclosures per open mortgage grew by a factor of five between 2006 and 2011. The surge in foreclosures was unprecedented—far above levels observed in the post-war U.S. era. This dissertation examines the causal effects of these foreclosures on the real economy in several dimensions. The first chapter examines how county foreclosures affect local labor market outcomes, such as employment and hiring, and the mechanism behind these declines. Foreclosures are instrumented using quasi-experimental variation in the timing and magnitude of interest rate changes on adjustable rate mortgages, which involve contractually and pre-determined changes in monthly mortgage payments based on national interest rates. These interest rate changes generate substantial movement in the frequency of foreclosures, but are plausibly exogenous because of their idiosyncratic and discontinuous nature. I find declines in labor market operates operating primarily through a banking sector channel. The second chapter examines how zipcode foreclosures affect individual well-being and community dynamism. Measures of well-being are obtained based on a partnership with Gallup over their U.S. Daily Poll, capturing overall sentiment. Using the same identification strategy, I show that increases in foreclosures are associated with declines in well-being even among individuals who do not experience foreclosure themselves, consistent with spillover effects. The third chapter examines what happened to these individuals who were foreclosed upon and why. How did they fare and why did they move where they move? An important theme in this paper is the importance of local factors—for example, if local factors deteriorate, then individuals are less likely to move to a better subsequent location, reflecting the importance of bargaining power in the job search process. Much more work is required to understand how mortgage markets interact with firm outcomes and the underlying mobility decisions among individuals. I look forward to pursuing further work in these areas in the years that follow.

This thesis includes four self-contained essays on marketing, economics, and optimization, all sharing a common theme: creating numerical models and algorithms to tackle computationally challenging optimization problems. The first essay considers geographic sub-branding via manufacture location in marketing. Manufacture location, as part of geographic product identity, is becoming a significant differential factor among a variety of products and a sub-branding element in various markets, but there is little empirical research on how manufacture location influences consumer preference and purchase choices. The first barrier comes naturally from the market. Most of the time, manufacture location is completely correlated with product characteristics. I was fortunately able to acquire both data and a whole year research grant from Ford Motor Company. New car buyer data in the Chinese automobile market makes possible the analysis of manufacture location as a geographic sub-branding element. Hedonic price analysis gives us a quick and intuitive view of how much consumers are willing to pay for geographic sub-branding products, and also motivates our new brand and sub-brand definition for a BLP-type random coefficient discrete choice model. However, using General Method of Moments (GMM) to estimate the variance-covariance matrix of consumer brand taste coefficients poses another challenge for all existing optimization solvers. To prevent indefinite unknown variance-covariance matrices in the constraints of the optimization problem from terminating the solver, I reformulate the optimization program and successfully solve the problem. If the computation becomes more difficult, we can also apply our new algorithm NCL, which is described in details in the third essay. Our results reveal the strong substitution patterns in the market and confirm our definition and framework of brand and geographic identity. Furthermore, our method can be helpful in the analysis of branding and sub-branding in other empirical settings. The second essay studies optimal income taxation with multidimensional taxpayer types in economics. This engendered the subject of the third essay: stabilized optimization via an NCL algorithm in numerical optimization. The income taxation literature has generally focused on economies where individuals differ only in their productivity, i.e., income. In reality, people differ in many ways. In our models, we consider people's productivity, basic needs, distaste for work, the elasticity of labor supply, and the elasticity of demand for consumption. We find that extra dimensions give us substantially different and interesting results. In certain cases, high-productivity people may pay negative tax. Therefore, considering income taxation in multiple dimensions is essential, and again is computationally challenging. All existing optimization solvers fail to find optimal solutions. Eventually, we transformed the model, created a new algorithm (NCL), and solved the high-dimension difficult optimization problems. The nonlinearly constrained augmented Lagrangian algorithm (NCL) we created was motivated by the bound-constrained and the linearly constrained augmented Lagrangian algorithms (BCL and LCL). To facilitate implementation, we take advantage of the mathematical programming language AMPL. We did not have to write fifty thousand lines of Fortran code to implement NCL. The third essay on algorithm NCL was published this year in Numerical Analysis and Optimization. The taxation part remains as a working paper. I am excited about not only solving the complex income taxation models, but also creating a general algorithm that can be applied to tough mathematical models in different fields. For instance, our algorithm NCL can be easily adapted to nonlinear pricing in economics and marketing. The fourth essay considers reliable and efficient solution of genome-scale models of metabolism and macromolecular expression. For many years, scientific computing has advanced in two complementary ways: improved algorithms and improved hardware. In order to solve the large and complicated biochemical network of metabolism in systems biology, we made use of improved machine precision and created algorithms utilizing software-simulated quadruple precision arithmetic and successfully solved both original and reformulated optimization models. This essay is published in Scientific Reports. Today, our linear and non-linear quadruple precision solver quadMINOS is supporting the research of systems biologists in their COBRA (COnstraint-Based Reconstruction and Analysis) Toolbox, and it can also help researchers in many other areas. As my advisor Professor Michael Saunders predicts: ``Just as double precision floating-point hardware revolutionized scientific computing in the 1960s, the advent of the quadruple precision data type, even in software, brings us to a new era of greatly improved reliability in optimization solvers.''.

The opioid abuse epidemic in the United States calls for new and cost-effective policies to address the rise of morbidity and mortality associated with drug injection. This dissertation explores how, and the extent to which, mathematical modeling can inform policy interventions surrounding HIV for people who inject drugs (PWID). First, we develop a dynamic compartmental model empirically calibrated to the US HIV epidemic to assess the cost-effectiveness of HIV preexposure chemoprophylaxis (PrEP) for PWID. We identify the optimal delivery scenario for PrEP but nonetheless find that it is not likely to be cost-effective. Next, we consider PrEP within a context of other HIV interventions. We find that an optimal portfolio of opioid agonist therapy (OAT), needle syringe exchange programs, and test and treat programs can deliver greater health benefit for less cost than PrEP. Although PrEP averts more infection than OAT, OAT provides more value because of its immediate quality of life improvements for an individual with high competing mortality risks. Finally, to explore how structural modeling assumptions influence policy conclusions, we perform a case study of a potential HIV vaccination across a family of linked models. We find that aggregating individuals into compartments biases us towards intervention, an effect most pronounced when targeting to smaller populations. Parameter complexity, although it has little effect on network models in this context, can mitigate overestimation effects in compartmental models.

Every person has hundreds and thousands of habits that they rarely think about having. Every time a person exercises a habit, they automatically choose a course of action. Every time that choice is made is an opportunity to apply decision analysis. However, normal decision analysis is too costly to use for all of a person's habits. In this dissertation I look at ways that decision analysis can be applied to a person's habits to ensure they are good ones. If they are not, they must be updated to match an ever-changing environment, new information, and preferences that evolve over time. Expanding decision analysis to include the numerous tiny decisions that are made with habits opens up the opportunity for massive gains in value when each tiny improvement is aggregated over many habits and a lifetime of use.

Over the last several decades, the world has become increasingly reliant on the space domain. With the insertion of new spacecraft in various orbits, the risk of collisions with spacecraft or debris has increased. Currently, several space surveillance systems provide signals of such impending collisions and opportunities for owners and operators to respond to these alerts. The monitoring systems, however, are imperfect, and the current number of sensors of different types, costs, and levels of accuracy may need to be increased to allow better space traffic management. The objective of this dissertation is to estimate and optimize the benefits of such improvements. We present first, a general model to evaluate sensor systems based on a Bayesian updating of the prior probability of collision given two types of independent signals: some from more accurate but more expensive sensors, and some from less accurate but cheaper sensors. We use this model to evaluate the risks of collision of space assets given the current monitoring systems. We then assess the risk of losing a satellite constellation, which is where the satellites' values reside. Next, we assess the risk reduction value of adding one or more sensors of either type to the current monitoring systems, based on the classic notion of value of information. For simplicity, we assume a constant risk aversion in rational decisions, both for the sensor system managers and for the satellite operators. We illustrate the model by a fictionalized version of the United States Space Surveillance Network operated by the United States Air Force, and other sensor systems of lesser accuracy. Together, these networks collect optical and radar data, which allow synthesis of observations into a coherent picture of space. The results of this analysis can be used to support the selection of an optimal number of additional space surveillance sensors, either "large" or "small, " under resource constraints. This choice is sensitive to the risk aversion of both the users of the signals and the managers of the monitoring systems. The method can be extended to other types of monitoring system with similar structures.

This dissertation consists of two parts, with a central focus on modeling and approximating non-stationarities in stochastic systems. The first part revolves around the statistical and stochastic modeling of the non-stationary arrivals that serve as inputs to such systems. The second part revolves around approximating performances for stochastic systems with non-stationary dynamics or non-stationary inputs.

Populations comprising individuals with varying characteristics and needs presents a challenge to public health decision making, as people may benefit from (or be harmed by) policies to differing extents. This dissertation focuses on mathematical modeling approaches to assess the differential effects of public health interventions across heterogeneous populations and inform policy decisions. First, we develop a microsimulation model to project the impact of increased meat price on dietary consumption, obesity and mortality by sex and race. We find that increased meat price would likely reduce obesity prevalence for white males, black males, and black females, far more than for white females. We also identify black males as least likely to experience gains in life expectancy from such a price increase. Next, we create a dynamic compartmental model of the population, stratified by pain, opioid use, and opioid addiction status, to estimate the ten-year impact of 11 interventions in response to the US opioid epidemic. We find that policies that reduce the prescription opioid supply may increase heroin use and reduce quality of life in the short term, but in the long term could generate positive health benefits. Policies focused on treating addiction (or mitigating its impact) improve health without causing harm, but alone, these will not stem the epidemic. A portfolio of interventions will be needed for eventual mitigation. Finally, we offer a framework for categorizing health interventions according to the expected distribution of benefit and harm to aid decision makers in identifying tradeoffs between efficiency, equity, and harm avoidance.

How does a seller's local environment affect their behavior on digital platforms? The digitization of the economy has drastically lowered the costs of data storage, access, and transmission. Leveraging digital technologies, platform companies such as Amazon and Airbnb have created online marketplaces that have extended an unprecedented level of market access to individual entrepreneurs, whom we often refer to as sellers. Much of the existing research on digital platforms shows that platforms can dictate sellers' behavior through a variety of reward and punishment mechanisms, e.g., search ranking algorithms and surge pricing. However, a great amount of variation in sellers' behavior can be attributed to factors in their local environment -- factors outside the platform's control. Upon closer examination, one may realize that local factors could potentially explain many perplexing seller actions faced by platforms and their engineers. For instance, why do Uber drivers protest surge pricing? Why do e-commerce sellers continue to sell counterfeit products despite strict regulation? Why do Airbnb hosts refuse to interact with users even with algorithms rewarding host-user interactions? In this dissertation, I argue that factors such as sellers' cultural customs, local interactions, and perception of the law may serve to explain many of their behavioral patterns. These factors strongly affect sellers' behavior on digital platforms. Their behavior, in turn, influences a platform's growth trajectory and contains major social implications. Therefore, it is important for both platform designers and policymakers to pay attention to sellers' heterogeneous local environments in order to anticipate sellers' behavior, create appropriate designs, and devise sound policy.

We study three related applications, in the field of finance, and in particular of multi-period investment management, of convex optimization and model predictive control. First, we look at the classical multi-period trading problem, consisting in trading assets within a certain universe for a sequence of periods in time. We develop a framework for single- and multi-period optimization: the trades in each period are found by solving a convex optimization problem that trades off expected return, risk, transaction cost and holding cost. Second, we look at the classical Kelly gambling problem, consisting in repeatedly allocating wealth among bets so as to maximize the expected growth rate of wealth. We develop a convex constraint that controls the risk of drawdown, i.e., the risk of losing a certain (high) amount of wealth. Third, we look at an optimal execution problem, consisting in buying, or selling, a given quantity of some asset on a limit-order book market. We study the case when the execution is benchmarked to the market volume weighted average price, and the objective is to minimize the mean-variance of the slippage. In all three cases, we provide extensive numerical simulations (using real-world data, whenever possible), developed as open-source software. In practice, these problems are solved to high accuracy in little time on commodity hardware, thanks to strong theoretical guarantees from modern convex optimization and a rich and growing ecosystem of open source software.

This research develops a quantitative risk analytic method to assess the risk of deterrence failure given modern nuclear weapon arsenals and policies. The model includes multiple antagonist behaviors, levels of conflict escalation, weapon capabilities and effects, and a spectrum of policies, both for protagonists and antagonists. It is based on infinite-horizon, risk-sensitive Interactive Partially Observable Markov Decision Processes. This model allows multiple agents to identify optimal policies in the management of conflict scenarios given the trade-offs between their political goals and the consequences of various forms of conflict. We develop a set of metrics for deterrence effectiveness based on the probability of specific opponent actions and on the evaluation of different conflict outcomes. The model and analysis capture complex behaviors and escalation dynamics, identify approximately optimal policies in specific conflicts, and can be extended to a large spectrum of possible scenarios. An illustration is presented, based on the analysis of fictitious data for a bilateral conflict scenario between two nuclear-armed, peer states. In this example, we evaluate various nuclear arsenals and stated policies about their use, based on the results of the model, including optimal conflict management and comparison of deterrence-effectiveness metrics. The results can provide valuable insights to policy and decision makers by allowing them to consider a spectrum of consequences involved in various alternatives.

This research enables decision makers to use time strategically in real-life games. At its core, it is pushing back against the assumption of an obvious decision time that is implicitly made when real-life situations are modeled as turn-based games with no sense of time. When analysts model real-life situations as turn-based, timing-free games, the application of the model's insight is stunted. The analyst has derived an optimal policy for what to do, but not when to do it, and since real-life situations rarely come with turns, a lot of the value can be lost. In every game, a first-person perspective is taken, since the model's main objective is to provide normative advice to a single decision maker. Throughout the game, a focus on the passage of time, which is discretized into time intervals, allows for players to better understand how their actions and choice of timing affect the situation. Players will often have a chance to act now or employ strategic patience, in which case they decide that waiting is their best alternative. If a player waits, the model considers the possibility of the environment changing, of a player learning more about an uncertainty, of a player's alternatives changing with time, and of an opponent taking the initiative. Players also have the ability to affect the timing of their opponents' actions, which is called controlling the tempo of the game. A player can control the tempo by control- ling the information available to other players, using hard constraints like deadlines that remove future alternatives, or providing incentives for quick or slow action. The ability to indirectly increase one's own expected utility through an opponent's tim- ing will prove to be very powerful, which is shown in three intentionally diverse case studies. The first case study explores how a coach can use the clock strategically in a basketball game. A coach can be strategically patient by instructing his team to shoot the ball later in the shot clock and can control the tempo of the game by having his team foul intentionally. The model uses a team's historical play-by-play data to construct a distribution over possession lengths and outcomes, which allows for specific team matchups to be explored. Here, the Indiana Pacers will be the decision maker and the Chicago Bulls will be the opponent. The model constructs an optimal offensive and defensive policy for the Pacers that could help them win an extra game per NBA season. The second case study explores how an investment banking firm can improve the results of its recruitment process for juniors interns by incentivizing quick responses from students. Multiple ways that a firm can control the tempo of the game are explored. Exploding offers prove to be ineffective since the best students will be strategically patient. Offers of decreasing value prove to be more effective since they both incentivize quick action and also do not expire when a student is patient. The specific decision maker explored here is the investment bank JP Morgan, who could see improvements in recruiting by using time strategically. The third case study explores how the United States could have used time strate- gically in the Cuban Missile Crisis. The work reconstructs from historical primary sources what was known/believed at the time by President Kennedy and his advisors. As the President waits, he learns more about the number of offensive weapons in Cuba and the feasibility of a diplomatic solution, but the Soviet surface-to-surface missiles are more likely to become operational. Both the US and the USSR are also uncertain about the other's willingness to escalate to a nuclear exchange/full-scale war. In this context, the model provides normative advice on both what to do and when to do it despite uncertainty over what the opponents wants, knows, and has. The effect of modeling the Soviet Union as less than rational is also discussed. The value of the case study is the framework through which an optimal policy for the United States can be derived; this framework could potentially be applied to a modern-day crisis in which timing plays a key role.

A common problem for all applied fields is the practicality gap, which is the disconnect between academia and practice, and decision analysis is no exception. Two qualitative studies conducted with the members of the field led to three main conclusions. First, the practicality gap is there for decision analysis, and the gap is wide. Second, there is no common definition of what decision analysis is. Third, practitioners, despite knowing the art of application, have lost the wisdom of certain parts of the process. This dissertation proposes that a pattern language framework will be able to combine and capture explicit and tacit knowledge in the field in a format that is clear and shareable. To verify this claim, I developed a catalog of patterns and tested them in a case study with students of decision analysis. As part of this case study, a qualitative study was conducted for which interviews with students, materials they submitted as part of the exercise, and notes from and recording of their discussions were used as data sources. There were three findings from the case study. First, students stated that the catalog was a helpful guideline that combined all relevant knowledge and presented it in a package that provided them with how to apply decision analysis. Second, the patterns helped students apply the decision analysis processes in their projects successfully. Third, they were able to conduct a quality decision conversation, which helped decision-makers get to the clarity of action. In summary, this dissertation showed that it is possible for a pattern language for decision analysis to gather the collective wisdom of the practice by reviving the lost wisdom and demystifying the art of application. This language can be shared so that both students of decision analysis can apply what they learn and professionals can enrich their skill set.

This dissertation aims to advance the application of mathematical modelling and computing, in particular optimisation methods, to the planning of solutions to energy and climate problems. The work first addresses two applied modelling problems relating to the electricity sector, a sector that is a major global source of greenhouse gas emissions, but also a potential provider of low carbon energy throughout the global economy. The dissertation then closes with an investigation into the appropriate formulation of the normative models used in planning, focusing on the choosing of model detail. At a high level, this work can be summarised as the development of tractable methods to incorporate necessary detail in models, followed by the introduction of a framework to understand when detail is necessary more generally. The first technical portion of this dissertation investigates how to represent intra-annual temporal variability in models of optimum electricity capacity investment. The mechanisms are shown by which inappropriate aggregation of temporal resolution can introduce substantial error into model outputs and associated economic insight, particularly in systems where variable renewable power sources are cost competitive and/or policy supported. For a sample dataset, a scenario-robust aggregation of hourly (8760) resolution is possible in the order of 10 representative hours when electricity demand is the only source of variability. The inclusion of wind and solar supply variability increases the resolution of the robust aggregation to the order of 1000. A similar scale of expansion is shown for representative days and weeks. These concepts, and underlying methods, can be applied to any such temporal dataset, providing a benchmark that any other aggregation method can aim to emulate. To the author's knowledge, this is the first time that the impact of variable renewable power sources on appropriate temporal representation has been quantified in this way. The next stage of the work considers the potential impact of emerging smart grid technologies, particularly those that enable electricity consumers to shift, automatically and optimally, their electricity demand in response to a price signal. In so doing, a model of a competitive electricity market, where consumers exhibit optimal load shifting behaviour to maximise utility and producers/suppliers maximise their profit under supply capacity constraints, is formulated and analysed. The associated computationally tractable convex optimisation formulation can be used to inform market design or policy analysis in the context of increasing availability of the smart grid technologies that enable optimal load shifting. Analytic and numeric assessment of the model allows assessment of the equilibrium value of optimal electricity load shifting, including how the value reduces as more electricity consumers adopt associated technologies. The sensitivity of the value to the flexibility of load is assessed, along with its relationship to the deployment of renewables. Additionally, a formulation of the model based on the Alternating Direction Method of Multipliers is presented. This particular optimisation method is desirable for its potential to scale to large problems. The applied modelling exercises provide examples for the final portion of the dissertation, a systematic assessment of model formulation, particularly relating to model detail. The normative models used for energy and climate planning explore long term pathways into uncharted territory. The test of predictive power used in other fields to evaluate model formulation is frequently not possible to apply in this long term context, nor necessarily makes sense in the normative context. This work introduces a conceptual framework that can potentially augment the necessary expert judgement in model formulation. It is based on the idea that some modelling decisions are testable, including the choice of model detail under certain conditions. The framework uses information theoretic principles to demonstrate the tradeoff between model detail and model accuracy for a given question, and can specifically aid with representing heterogenous spatial, temporal or population characteristics in models. This section of the dissertation represents an early attempt in a domain where limited systematic analysis has been undertaken to date.