In this thesis, we develop partial differential equation (PDE) based numerical methods to solve certain optimal stochastic control problems in finance. The value of a stochastic control problem is normally identical to the viscosity solution of a Hamilton-Jacobi-Bellman (HJB) equation or an HJB variational inequality. The HJB equation corresponds to the case when the controls are bounded while the HJB variational inequality corresponds to the unbounded control case. As a result, the solution to the stochastic control problem can be computed by solving the corresponding HJB equation/variational inequality as long as the convergence to the viscosity solution is guaranteed. We develop a unified numerical scheme based on a semi-Lagrangian timestepping for solving both the bounded and unbounded stochastic control problems as well as the discrete cases where the controls are allowed only at discrete times. Our scheme has the following useful properties: it is unconditionally stable; it can be shown rigorously to converge to the viscosity solution; it can easily handle various stochastic models such as jump diffusion and regime-switching models; it avoids Policy type iterations at each mesh node at each timestep which is required by the standard implicit finite difference methods. In this thesis, we demonstrate the properties of our scheme by valuing natural gas storage facilities---a bounded stochastic control problem, and pricing variable annuities with guaranteed minimum withdrawal benefits (GMWBs)---an unbounded stochastic control problem. In particular, we use an impulse control formulation for the unbounded stochastic control problem and show that the impulse control formulation is more general than the singular control formulation previously used to price GMWB contracts.

In this thesis, we develop partial differential equation (PDE) based numerical methods to solve certain optimal stochastic control problems in finance. The value of a stochastic control problem is normally identical to the viscosity solution of a Hamilton-Jacobi-Bellman (HJB) equation or an HJB variational inequality. The HJB equation corresponds to the case when the controls are bounded while the HJB variational inequality corresponds to the unbounded control case. As a result, the solution to the stochastic control problem can be computed by solving the corresponding HJB equation/variational inequality as long as the convergence to the viscosity solution is guaranteed. We develop a unified numerical scheme based on a semi-Lagrangian timestepping for solving both the bounded and unbounded stochastic control problems as well as the discrete cases where the controls are allowed only at discrete times. Our scheme has the following useful properties: it is unconditionally stable; it can be shown rigorously to converge to the viscosity solution; it can easily handle various stochastic models such as jump diffusion and regime-switching models; it avoids Policy type iterations at each mesh node at each timestep which is required by the standard implicit finite difference methods. In this thesis, we demonstrate the properties of our scheme by valuing natural gas storage facilities---a bounded stochastic control problem, and pricing variable annuities with guaranteed minimum withdrawal benefits (GMWBs)---an unbounded stochastic control problem. In particular, we use an impulse control formulation for the unbounded stochastic control problem and show that the impulse control formulation is more general than the singular control formulation previously used to price GMWB contracts.

Local electricity markets can be defined broadly as 'future electricity market designs involving domestic customers, demand-side response and energy storage'. Like current deregulated electricity markets, these localised derivations present specific stochastic optimisation problems in which the dynamic and random nature of the market is intertwined with the physical needs of its participants. Moreover, the types of contracts and constraints in this setting are such that 'games' naturally emerge between the agents. Advanced modelling techniques beyond classical mathematical finance are therefore key to their analysis. This thesis aims to study contracts in these local electricity markets using the mathematical theories of stochastic optimal control and games. Chapter 1 motivates the research, provides an overview of the electricity market in Great Britain, and summarises the content of this thesis. It introduces three problems which are studied later in the thesis: a simple control problem involving demand-side management for domestic customers, and two examples of games within local electricity markets, one of them involving energy storage. Chapter 2 then reviews the literature most relevant to the topics discussed in this work. Chapter 3 investigates how electric space heating loads can be made responsive to time varying prices in an electricity spot market. The problem is formulated mathematically within the framework of deterministic optimal control, and is analysed using methods such as Pontryagin's Maximum Principle and Dynamic Programming. Numerical simulations are provided to illustrate how the control strategies perform on real market data. The problem of Chapter 3 is reformulated in Chapter 4 as one of optimal switching in discrete-time. A martingale approach is used to establish the existence of an optimal strategy in a very general setup, and also provides an algorithm for computing the value function and the optimal strategy. The theory is exemplified by a numerical example for the motivating problem. Chapter 5 then continues the study of finite horizon optimal switching problems, but in continuous time. It also uses martingale methods to prove the existence of an optimal strategy in a fairly general model. Chapter 6 introduces a mathematical model for a game contingent claim between an electricity supplier and generator described in the introduction. A theory for using optimal switching to solve such games is developed and subsequently evidenced by a numerical example. An optimal switching formulation of the aforementioned game contingent claim is provided for an abstract Markovian model of the electricity market. The final chapter studies a balancing services contract between an electricity transmission system operator (SO) and the owner of an electric energy storage device (battery operator or BO). The objectives of the SO and BO are combined in a non-zero sum stochastic differential game where one player (BO) uses a classic control with continuous effects, whereas the other player (SO) uses an impulse control (discontinuous effects). A verification theorem proving the existence of Nash equilibria in this game is obtained by recursion on the solutions to Hamilton-Jacobi-Bellman variational PDEs associated with non-zero sum controller-stopper games.

Indiana University-Purdue University Indianapolis (IUPUI) / Prior research indicated a high prevalence of problematic drinking among college students, suggesting a need for more effective screening approaches and treatments. The tendency to act rashly in face of strong emotions (e.g. positive and negative urgency), alcohol cravings, and cue reactivity all have been associated with problematic alcohol use. However, no studies have examined the interactive effects of alcohol cravings, urgency, and cue reactivity. I hypothesized that alcohol cravings will be associated with greater problematic drinking among individuals with higher levels of (1) urgency, (2) cue reactivity, and (3) cue reactivity and urgency. Data were collected from a sample (final n = 240) of college students through a survey, which consisted of measures of urgency, problematic drinking, and alcohol cravings. On the survey, participants were also exposed to alcohol and non-alcohol pictures, after which they assessed their level of cue reactivity. Results were examined using multiple regression and simple slope analyses. Results provided partial support for our hypotheses. Alcohol cravings were associated with greater problematic drinking at lower levels of negative urgency (b = 7.36, p< 0.001). Furthermore, alcohol cravings were most strongly associated with problematic drinking at high levels of cue reactivity and low levels of negative urgency (b = 8.69, p<0.001), and at low levels of cue reactivity and high levels of positive urgency (b = 6.56, p<0.001). These findings emphasize the importance of considering urgency and cue reactivity in understanding how alcohol cravings create risk for problematic drinking.

Indiana University-Purdue University Indianapolis (IUPUI) / Hypothalamic-pituitary-adrenal (HPA) axis dysfunction is found in heavy alcohol users. Negative urgency is a personality trait reflecting the tendency to act rashly in response to negative emotional states, and is associated with problematic alcohol consumption. The current study examined the relationship between negative urgency and HPA axis functioning following (1) negative mood induction and (2) intravenous alcohol administration among heavy social drinkers (proposed n = 40). I hypothesized the following: (1) Negative mood induction would result in an increase of cortisol release as compared to neutral mood induction; (1a) Negative urgency would be related to increased cortisol release in response to negative mood induction; (1b) Negative urgency would partially mediate the relationship between mood induction and cortisol release; (2) Acute IV alcohol administration would result in increased cortisol levels in the neutral mood condition, but decreased cortisol levels in the negative mood condition; and (2a) Negative urgency would be related to the suppression of cortisol release in the negative mood condition in response to acute IV alcohol administration. Repeated measures analyses of variance, the PROCESS macro, and paired samples t-tests were used to examine study hypotheses. Hypotheses were largely unsupported. Writing mood induction procedures reduced salivary cortisol levels in negative mood (t(35)= 2.49, p= 0.02) and there was a trend decrease in neutral mood (t(35)= 1.87, p= 0.07). Alcohol administration also reduced salivary cortisol levels in both negative mood (t(35)= 3.99, p< 0.01) and neutral mood (t(35)= 2.60, p= 0.01). However, salivary cortisol changes were no different than typical circadian patterns in response to mood induction (t(231)= 0.37, p=0.71) or in response to acute alcohol administration (t(231)= 0.44, p= 0.64). Negative urgency had a trend main effect on salivary cortisol level in response to acute IV alcohol administration, such that those higher in negative urgency were more similar to typical circadian patterns (F(19,28)= 1.59, p=0.13). This could serve as preliminary support for a psychological mechanism for the alcohol sensitivity hypothesis. Overall these findings suggest the current study failed to sufficiently manipulate salivary cortisol levels. Future studies should consider methodological techniques when exploring these relationships, including IV compared to oral alcohol administration, mood compared to stress manipulations, and cortisol compared to other HPA axis biomarkers.

L’impulsivité est une séquelle fréquente suite à un traumatisme cranio-cérébral (TCC) à laquelle sont associées de nombreuses conséquences néfastes et qui nécessite un investissement considérable de ressources. En ce sens, une évaluation adéquate de l’impulsivité est de mise dans un contexte de réadaptation. Par contre, malgré son importance, il n’existe pas de définition consensuelle de l’impulsivité post-TCC ni de mesure spécifique permettant de l’évaluer. Il est généralement admis, dans la littérature récente, que l’impulsivité est un construit multidimensionnel. Notamment, le modèle UPPS-P de l’impulsivité gagne un appui significatif et pourrait permettre une compréhension plus spécifique de l’impulsivité post-TCC. Selon ce modèle, il existe quatre dimensions à l’impulsivité soit l’urgence (tendance à agir ses impulsions dans un contexte d’émotions intenses), le manque de persévérance (difficulté au niveau du maintien de l’attention sur une tâche complexe et ennuyante et une susceptibilité à l’ennui), le manque de préméditation (difficulté de prévoir les conséquences d’un comportement avant de le poser) et la recherche de sensations (tendance à préconiser des activités jugées excitantes et l’ouverture à essayer de nouvelles expériences qui peuvent ou non, être dangereuses). Il a été proposé que l’urgence, le manque de persévérance et le manque de préméditation sont associés à des difficultés à inhiber la réponse automatique, à résister à l’interférence proactive et de la prise de décision, respectivement (Bechara et Van der Linden, 2005). Une telle conceptualisation offre une avenue prometteuse quant à l’évaluation de l’impulsivité post-TCC. Le présent projet vise à clarifier le construit de l’impulsivité post-TCC, à déterminer si les mêmes mécanismes cognitifs sont en lien avec les dimensions de l’impulsivité dans un contexte de réadaptation fonctionnelle intensive puis de déterminer quelles tâches de performance prédisent le mieux les comportements impulsifs dans ce milieu. D’abord, une recension des écrits portant sur l’impulsivité post-TCC donne un appui à la conceptualisation multidimensionnelle de l’impulsivité et fait ressortir les obstacles qui nuisent à l’étude de l’impulsivité post-TCC. Ensuite, l’utilisation de diverses tâches de performance permet d’évaluer le lien entre les dimensions de l’UPPS-P et les mécanismes cognitifs. Les résultats indiquent des atteintes sur les mécanismes liés à l’inhibition de la réponse automatique, à la résistance à l’interférence proactive ainsi qu’à la prise de décision. Toutefois, ils ne permettent pas de supporter les propositions de Bechara et Van der Linden quant aux mécanismes sous-jacents aux dimensions de l’impulsivité post-TCC chez les patients en réadaptation intensive. Finalement, les résultats permettent de faire ressortir la pertinence des tâches de performance écologiques dans la prédiction de comportements impulsifs dans la vie quotidienne. Les portées théoriques et cliniques des résultats sont discutées. / Impulsivity is a common sequela following traumatic brain injury (TBI) to which are associated many negative consequences and necessitates important resources. A thorough assessment of impulsivity is therefore necessary in a rehabilitation setting. However, there is no consensual definition of post TBI impulsivity nor is there a specific measure allowing its assessment. It is generally acknowledged, in recent literature, that impulsivity is a multidimensional construct. The UPPS-P model is gaining a significant amount of support and could allow a better understanding of post-TBI impulsivity. According to this model, there are four dimensions to impulsivity, namely urgency (tendency to experience and act on strong impulses frequently under conditions of strong affect), lack of perseverance (inability to remain focused on a task that may be boring or difficult), lack of premeditation (inability to think and reflect on the consequences of an act before engaging in that act) and sensation seeking (tendency to enjoy activities that are exciting and a willingness to try new experiences). It has been suggested that urgency, lack of perseverance and lack of premeditation are linked to impairments on prepotent response inhibition, on resistance to proactive interference and on decision making, respectively (Bechara and Van der Linden, 2005). This conceptualisation offers a promising avenue as to the assessment of post-TBI impulsivity. This project aims to clarify the construct of post-TBI impulsivity, to determine whether the same cognitive mechanisms come into play in the different dimensions of impulsivity in an intensive functional rehabilitation setting and to determine which performance tasks allow the prediction of impulsive behaviors in that setting. Firstly, a literature review among studies on post-TBI impulsivity gives support to a multidimensional conceptualisation of impulsivity and allows to bring out the obstacles which make the study of post-TBI impulsivity more complicated. Secondly, the use of different performance tasks is used to assess the links between UPPS-P dimensions and cognitive mechanisms. Results indicate impairments on the mechanisms linked to prepotent response inhibition, to resistance to proactive interference and to decision making. However, they do not support Bechara and Van der Linden’s (2005) propositions as to the underlying mechanisms to the dimensions of post-TBI impulsivity in an acute rehabilitation setting. Thirdly, the results show the relevance of ecological performance tasks as to the prediction of impulsive behaviors in everyday life. The theoretical and clinical implications of the results are discussed.

INTRODUÇÃO: A dependência química engloba alterações comportamentais, cognitivas e fisiológicas. A impulsividade está presente em muitos transtornos psiquiátricos. Sobre a impulsividade na dependência química de cocaína, os estudos existentes são relativamente novos. A Estimulação Magnética Transcraniana de repetição (EMTr) é um método capaz de neuromodular o cérebro. Este estudo avaliou os efeitos da EMTr sobre a impulsividade em dependentes de cocaína. MÉTODOS: Em um estudo randomizado, duplamente encoberto, 25 pacientes diagnosticados pelo DSM-IV-TR foram tratados com EMTr de alta frequência ativa (1250 pulsos/dia) ou EMTr placebo. O tratamento consistiu em 1 mês de aplicação de EMTr seguido de 2 meses em acompanhamento ambulatorial semanal em um grupo de prevenção de recaídas. Os pacientes foram avaliados antes do início do tratamento com EMTr (T0) e após o término das aplicações (T1), através dos instrumentos: The Shorter PROMIS Questionnaire, The Schalling Impulsivity Scale e The Leeds Dependence Questionnaire. RESULTADOS: 25 pacientes foram tratados e a análise dos dados demonstraram redução nos índices de impulsividade em ambos os grupos ao longo do tempo, porém, quando comparados entre si, os valores de interação não se mostraram significativos. CONCLUSÃO: Os efeitos da EMTr não diferiram em eficácia terapêutica na redução da impulsividade em dependentes de cocaína, com o efeito ativo correspondendo com o placebo / INTRODUCTION: Chemical addiction involves behavioral, cognitive and physiological alterations. Impulsivity is present in many psychiatric disorders. Studies about impulsivity and cocaine chemical addiction are relatively new. Transcranial Magnetic Stimulation (EMTr) is a method capable of neuromodulation the brain. This study evaluated the effects of EMTr over impulsivity in cocaine addicts. METHODS: This is a randomized doubly covert study with 25 patients diagnosed by the DSM-IV-TR who were treated with active high frequency EMTr (1250 pulses/day) or placebo. Treatment was consisted of one month of application of EMTr followed by 2 months of clinical follow-up in a relapse prevention group. Patients were evaluated before the treatment with EMTr (T0) and after the end of the applications (T1), through the instruments: The Shorter PROMIS Questionnaire, The Schalling Impulsivity Scale and The Leeds Dependence Questionnaire. RESULTS: 25 patients were treated and data analysis showed a reduction in the levels of impulsivity in both groups throughout the time. However, group comparisons did not show statistical differences. CONCLUSION: EMTr\'s effects did not differ in terms of therapeutical efficacy in the reduction of impulsivity in cocaine addicts

INTRODUÇÃO: A dependência química engloba alterações comportamentais, cognitivas e fisiológicas. A impulsividade está presente em muitos transtornos psiquiátricos. Sobre a impulsividade na dependência química de cocaína, os estudos existentes são relativamente novos. A Estimulação Magnética Transcraniana de repetição (EMTr) é um método capaz de neuromodular o cérebro. Este estudo avaliou os efeitos da EMTr sobre a impulsividade em dependentes de cocaína. MÉTODOS: Em um estudo randomizado, duplamente encoberto, 25 pacientes diagnosticados pelo DSM-IV-TR foram tratados com EMTr de alta frequência ativa (1250 pulsos/dia) ou EMTr placebo. O tratamento consistiu em 1 mês de aplicação de EMTr seguido de 2 meses em acompanhamento ambulatorial semanal em um grupo de prevenção de recaídas. Os pacientes foram avaliados antes do início do tratamento com EMTr (T0) e após o término das aplicações (T1), através dos instrumentos: The Shorter PROMIS Questionnaire, The Schalling Impulsivity Scale e The Leeds Dependence Questionnaire. RESULTADOS: 25 pacientes foram tratados e a análise dos dados demonstraram redução nos índices de impulsividade em ambos os grupos ao longo do tempo, porém, quando comparados entre si, os valores de interação não se mostraram significativos. CONCLUSÃO: Os efeitos da EMTr não diferiram em eficácia terapêutica na redução da impulsividade em dependentes de cocaína, com o efeito ativo correspondendo com o placebo / INTRODUCTION: Chemical addiction involves behavioral, cognitive and physiological alterations. Impulsivity is present in many psychiatric disorders. Studies about impulsivity and cocaine chemical addiction are relatively new. Transcranial Magnetic Stimulation (EMTr) is a method capable of neuromodulation the brain. This study evaluated the effects of EMTr over impulsivity in cocaine addicts. METHODS: This is a randomized doubly covert study with 25 patients diagnosed by the DSM-IV-TR who were treated with active high frequency EMTr (1250 pulses/day) or placebo. Treatment was consisted of one month of application of EMTr followed by 2 months of clinical follow-up in a relapse prevention group. Patients were evaluated before the treatment with EMTr (T0) and after the end of the applications (T1), through the instruments: The Shorter PROMIS Questionnaire, The Schalling Impulsivity Scale and The Leeds Dependence Questionnaire. RESULTS: 25 patients were treated and data analysis showed a reduction in the levels of impulsivity in both groups throughout the time. However, group comparisons did not show statistical differences. CONCLUSION: EMTr\'s effects did not differ in terms of therapeutical efficacy in the reduction of impulsivity in cocaine addicts

Indiana University-Purdue University Indianapolis (IUPUI) / Drug addiction is a behavioral disorder characterized by impulsive behavior and continued intake of drug in the face of adverse consequences. Millions of people suffer the financial and social consequences of addiction, and yet many of the current therapies for addiction treatment have limited efficacy. Therefore, there is a critical need to characterize the neurobiological substrates of addiction in order to formulate better treatment options. In the first chapter, the striatal dopamine system is interrogated with [11C]raclopride PET to assess differences between chronic cannabis users and healthy controls. The results of this chapter indicate that chronic cannabis use is not associated with a reduction in striatal D2/D3 receptor availability, unlike many other drugs of abuse. Additionally, recent cannabis consumption in chronic users was negatively correlated with D2/D3 receptor availability. Chapter 2 describes a retrospective analysis in which striatal D2/D3 receptor availability is compared between three groups of alcohol-drinking and tobacco-smoking subjects: nontreatment-seeking alcoholic smokers, social-drinking smokers, and social-drinking non-smokers. Results showed that smokers had reduced D2/D3 receptor availability throughout the striatum, independent of drinking status. The results of the first two chapters suggest that some combustion product of marijuana and tobacco smoke may have an effect on striatal dopamine concentration. Furthermore, they serve to highlight the effectiveness of using baseline PET imaging to characterize dopamine dysfunction in addictions. The final chapter explores the use of [18F]fallypride PET in a proof-of-concept study to determine whether changes in cortical dopamine can be detected during a response inhibition task. We were able to detect several cortical regions of significant dopamine changes in response to the task, and the amount of change in three regions was significantly associated with task performance. Overall, the results of Chapter 3 validate the use of [18F]fallypride PET to detect cortical dopamine changes during a impulse control task. In summary, the results reported in the current document demonstrate the effectiveness of PET imaging as a tool for probing resting and activated dopamine systems in addiction. Future studies will expand on these results, and incorporate additional methods to further elucidate the neurobiology of addiction.

Indiana University-Purdue University Indianapolis (IUPUI) / Losing a job or a significant other are examples of incentive shifts that result in negative emotional reactions. The occurrence of negative life events is associated with increased drinking, and alleviation of negative emotions has been cited as a drinking motive for individuals with problematic drinking patterns (Keyes et al., 2011; Adams et al., 2012). Further, there is evidence that certain genotypes drink alcohol in response to stressful negative life events (Blomeyer et al., 2008; Covault et al., 2007). It is possible that shared genetic factors contribute to both alcohol drinking and emotional reactivity, but there is a critical need for this relationship to be understood. The first aim of this proposal will use an incentive downshift paradigm to address whether emotional reactivity is elevated in mice predisposed to drink alcohol. The second aim of this proposal will address if reactivity to an incentive shift can result in rash action using a differential reinforcement of low rates of responding task, and whether this response is also associated with a predisposition for high drinking. The third aim of this proposal will investigate if experimenter administered ethanol reduces contrast effects, and if an incentive shift increases ethanol consumption in a high drinking line. The overall goal of this proposal is to investigate whether reactivity to incentive shift is an important mechanism underlying alcohol drinking in these mice, and the role an incentive shift may play in producing rash action and influencing ethanol consumption.