Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaves 200-206). Also available on the Internet.

<p>Essentially this project report is a discussion of mathematical modelling in pension funds, presenting sections from Cairns, A.J.D., Blake, D., Dowd, K., Stochastic lifestyling: Optimal dynamic asset allocation for defined contribution pension plans, Journal of Economic Dynamics and Control, Volume 30, Issue 2006, Pages 843-877, with added details and background material in order to demonstrate the mathematical methods. In the investigation of the management of the investment portfolio, we only use one risky asset together with a bond and cash as other assets in a&nbsp / continuous time framework. The particular model is very much designed according to the members&rsquo / preference and then the funds are invested by the fund manager in the financial market. At the end, we are going to show various simulations of these models. Our methods include stochastic control for utility maximisation among others. The optimisation problem entails the optimal&nbsp / investment portfolio to maximise a certain power utility function. We use MATLAB and MAPLE programming languages to generate results in the form of graphs and tables</p>

Thesis (Ph. D. in Interdisciplinary Studies: Civil and Environmental Engineering)--Vanderbilt University, Aug. 2009. / Title from title screen. Includes bibliographical references.

Thesis (M.S.) -- Mississippi State University. Department of Computer Science and Engineering. / Title from title screen. Includes bibliographical references.

Magister Scientiae - MSc / Essentially this project report is a discussion of mathematical modelling in pension funds, presenting sections from Cairns, A.J.D., Blake, D., Dowd, K., Stochastic lifestyling: Optimal dynamic asset allocation for defined contribution pension plans, Journal of Economic Dynamics and Control, Volume 30, Issue 2006, Pages 843-877, with added details and background material in order to demonstrate the mathematical methods. In the investigation of the management of the investment portfolio, we only use one risky asset together with a bond and cash as other assets in a continuous time framework. The particular model is very much designed according to the members’ preference and then the funds are invested by the fund manager in the financial market. At the end, we are going to show various simulations of these models. Our methods include stochastic control for utility maximisation among others. The optimisation problem entails the optimal investment portfolio to maximise a certain power utility function. We use MATLAB and MAPLE programming languages to generate results in the form of graphs and tables. / South Africa

Orientador: João Bosco Ribeiro do Val / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação / Made available in DSpace on 2018-08-16T02:55:02Z (GMT). No. of bitstreams: 1 Souto_RafaelFontes_M.pdf: 470367 bytes, checksum: 516cc5b88625a7d2e5142b69233188f5 (MD5) Previous issue date: 2010 / Resumo: Esta dissertação apresenta uma caracterização para sistemas estocásticos em tempo contínuo em que a variação da ação de controle aumenta a incerteza sobre o estado. Este tipo de sistema pode ser aplicado em diversas áreas da ciência e da engenharia, haja vista sua capacidade de modelar sistemas estocásticos complexos, cujas dinâmicas não são completamente conhecidas. Processos de difusão controlada de Itô são usados para descrever a trajetória do estado, e a otimização é realizada por meio do método da programação dinâmica, sendo, portanto, necessária a resolução da equação de Hamilton-Jacobi-Bellman. Adicionalmente, a utilização de ferramentas da análise de funções não suaves indicou a existência de uma região no espaço de estados onde a ação ótima de controle consiste na manutenção do controle que tem sido aplicado ao sistema, seja ele qual for. Intuitivamente, este resultado está de acordo com a natureza cautelosa do controle de sistemas subdeterminados. Finalmente, estudou-se analiticamente o caso particular de um sistema com custo quadrático. Este estudo revelou que a técnica desenvolvida permite o cálculo da solução ótima de maneira simples e eficaz para comportamentos assintóticos do sistema. Essa peculiaridade da solução vem de auxílio à obtenção da solução completa do problema via aproximações numéricas / Abstract: This dissertation presents a framework for continuous-time stochastic systems in which the control variations increase the state uncertainty. This type of system can be applied in several areas of science and engineering, due to its hability of modelling complex stochastic systems, for which the dynamics are not completely known. Controlled Itô diffusion processes are used in order to describe the state path, and the optimization was achieved by the dynamic programming method, so it was necessary to solve the Hamilton-Jacobi-Bellman equation. In addition, tools from nonsmooth analysis indicated the existence of a region in the state space in which the optimal control action is characterized by no variation, no matter the previous control were. Intuitively, this result is expected from the cautionary nature of controlling underdetermined systems. Finally, it was analytically studied the particular case of a system with quadratic running costs. This study revealed that the technique developed allows the computation of the optimal solution in a simple and effective way for asymptotic behavior of the system. This feature of the solution comes in hand to obtain the complete solution of the problem by means of numerical approximations / Mestrado / Automação / Mestre em Engenharia Elétrica

In this thesis we study two problems concerning probability. The first is stochastic control problem, which essentially amounts to find an optimal probability in order to optimize some reward function of probability. The second is to approximate the solution of the Boltzmann equation. Thanks to conservation of mass, the solution can be regarded as a family of probability indexed by time. In the first part, we prove a dynamic programming principle for stochastic optimal control problem with expectation constraint by measurable selection approach. Since state constraint, drawdown constraint, target constraint, quantile hedging and floor constraint can all be reformulated into expectation constraint, we apply our results to prove the corresponding dynamic programming principles for these five classes of stochastic control problems in a continuous but non-Markovian setting. In order to solve the Boltzmann equation numerically, in the second part, we propose a new model equation to approximate the Boltzmann equation without angular cutoff. Here the approximate equation incorporates Boltzmann collision operator with angular cutoff and the Landau collision operator. As a first step, we prove the well-posedness theory for our approximate equation. Then in the next step, we show the error estimate between the solutions to the approximate equation and the original equation. Compared to the standard angular cutoff approximation method, our method results in higher order of accuracy.

The ability to process and reason with causal information is fundamental in many aspects of human cognition and is pervasive in the way we probe reality in many of the empirical sciences. Given the centrality of causality through many aspects of human experience, we expect that the next generation of AI systems will need to represent causal knowledge, combine heterogeneous and biased datasets, and generalize across changing conditions and disparate domains to attain human-like intelligence. This dissertation investigates a problem in causal inference known as Data Fusion, which is concerned with inferring causal and statistical relationships from a combination of heterogeneous data collections from different domains, with various experimental conditions, and with nonrandom sampling (sampling selection bias). Despite the general conditions and algorithms developed so far for many aspects of the fusion problem, there are still significant aspects that are not well-understood and have not been studied together, as they appear in many challenging real-world applications. Specifically, this work advances our understanding of several dimensions of data fusion problems, which include the following capabilities and research questions: Reasoning with Soft Interventions. How to identify the effect of conditional and stochastic policies in a complex data fusion setting? Specifically, under what conditions can the effect of a new stochastic policy be evaluated using data from disparate sources and collected under different experimental conditions? Deciding Statistical Transportability. Under what conditions can statistical relationships (e.g., conditional distributions, classifiers) be extrapolated across disparate domains, where the target is somewhat related but not the same as the source domain where the data was initially collected? How to leverage additional data over a few variables in the target domain to help with the generalization process? Recovering from Selection Bias. How to determine whether a sample that was preferentially selected can be recovered so as to make a claim about the general underlying super-population? How can additional data over a subset of the variables, but sampled randomly, be used to achieve this goal? Instead of developing conditions and algorithms for each problem independently, this thesis introduces a computational framework capable of solving those research problems when appearing together. The approach decomposes the query and available heterogeneous distributions into factors with a canonical form. Then, the inference process is reduced to mapping the required factors to those available from the data, and then evaluating the query as a function of the input based on the mapping. The problems and methods discussed have several applications in the empirical sciences, statistics, machine learning, and artificial intelligence.

This thesis studies the decision-making of agents exhibiting time-inconsistent preferences and its implications in the context of contract theory. We take a probabilistic approach to continuous-time non-Markovian time-inconsistent stochastic control problems for sophisticated agents. By introducing a refinement of the notion of equilibrium, an extended dynamic programming principle is established. In turn, this leads to consider an infinite family of BSDEs analogous to the classical Hamilton–Jacobi–Bellman equation. This system is fundamental in the sense that its well-posedness is both necessary and sufficient to characterise equilibria and its associated value function. In addition, under modest assumptions, the existence and uniqueness of a solution is established. With the previous results in mind, we then study a new general class of multidimensional type-I backward stochastic Volterra integral equations. Towards this goal, the well-posedness of a system of an infinite family of standard backward stochastic differential equations is established. Interestingly, its well-posedness is equivalent to that of the type-I backward stochastic Volterra integral equation. This result yields a representation formula in terms of semilinear partial differential equation of Hamilton–Jacobi–Bellman type. In perfect analogy to the theory of backward stochastic differential equations, the case of Lipschitz continuous generators is addressed first and subsequently the quadratic case. In particular, our results show the equivalence of the probabilistic and analytic approaches to time-inconsistent stochastic control problems. Finally, this thesis studies the contracting problem between a standard utility maximiser principal and a sophisticated time-inconsistent agent. We show that the contracting problem faced by the principal can be reformulated as a novel class of control problems exposing the complications of the agent’s preferences. This corresponds to the control of a forward Volterra equation via constrained Volterra type controls. The structure of this problem is inherently related to the representation of the agent’s value function via extended type-I backward stochastic differential equations. Despite the inherent challenges of this class of problems, our reformulation allows us to study the solution for different specifications of preferences for the principal and the agent. This allows us to discuss the qualitative and methodological implications of our results in the context of contract theory: (i) from a methodological point of view, unlike in the time-consistent case, the solution to the moral hazard problem does not reduce, in general, to a standard stochastic control problem; (ii) our analysis shows that slight deviations of seminal models in contracting theory seem to challenge the virtues attributed to linear contracts and suggests that such contracts would typically cease to be optimal in general for time-inconsistent agents; (iii) in line with some recent developments in the time-consistent literature, we find that the optimal contract in the time-inconsistent scenario is, in general, non-Markovian in the state process X.

<p>As the economy recovered with the winding down of the pandemic, businesses with complex supply chains could not bring their inventories back to optimal levels as their production was susceptible to disruption due to supply outages. Deriving optimal ordering policies as a way to mitigate the impact of production disruption represents a challenge in multi-stage decision problems given the complexity of the network and the uncertainty in the demand.</p> <p><br></p> <p>In the first part of the thesis, we formulate a stochastic inventory control problem for a general supply network model. Using the Bellman’s recursion and properties of the cost function at each stage, we characterize the optimal request decision as a threshold policy where the threshold computation is based on the marginal cost. Lastly, we validate that the policy developed minimizes the inventory cost and meets an exogenous random demand. However, the policy does not guarantee that the inventory level for each firm satisfies the constraints when a supply disruption occurs in the network.</p> <p><br></p> <p>In the second part of the thesis, we consider a serial network in which firms engage in production subject to disruption risk and they look to maximize their profit. We propose an algorithm to characterize a stationary optimal policy based on the closed-form solutions obtained from a discounted finite horizon problem for profit maximization. Finally, by computing the policy proposed as a function of the tier’s location and its disruption probability, we provide simulation results of the disruption effect in the supply network.</p>