ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

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Operational Decision Making under Uncertainty: Inferential, Sequential, and Adversarial Approaches

Modern security threats are characterized by a stochastic, dynamic, partially observable, and ambiguous operational environment. This dissertation addresses such complex security threats using operations research techniques for decision making under uncertainty in operations planning, analysis, and assessment. First, this research develops a new method for robust queue inference with partially observable, stochastic arrival and departure times, motivated by cybersecurity and terrorism applications. In the dynamic setting, this work develops a new variant of Markov decision processes and an algorithm for robust information collection in dynamic, partially observable and ambiguous environments, with an application to a cybersecurity detection problem. In the adversarial setting, this work presents a new application of counterfactual regret minimization and robust optimization to a multi-domain cyber and air defense problem in a partially observable environment

Real Options under Choquet-Brownian Ambiguitys

Real options models characterized by the presence of “ambiguity” (or “Knightian uncertainty”) have been recently proposed. But based on recursive multiple-priors preferences, they typically describe ambiguity through a range of Geometric Brownian motions and solve it by application of a maxmin expected utility criterion among them (worst case). This reduces acceptable individual preferences to the single case of an extreme form of pessimism. In contrast, by relying on dynamically consistent “Choquet-Brownian” motions to represent the ambiguous cash flows expected from a project, we show that a much broader spectrum of attitudes towards ambiguity may be accounted for, improving the explanatory and application potentials of these appealing expanded real options models. In the case of a perpetual real option to invest, ambiguity aversion may delay the moment of exercise of the option, while the opposite holds true for an ambiguity seeking decision maker. Furthermore, an intricate relationship between risk and ambiguity appears strikingly in our model.

Multi-Attribute Decision Tree Evaluation in Imprecise and Uncertain Domains

Abstract We present a decision tree evaluation method integrated with a common framework for analyzing multi-attribute decisions under risk, where information is numerically imprecise. The approach extends the use of additive and multiplicative utility functions for supporting evaluation of imprecise statements, relaxing requirements for precise estimates of decision parameters. Information is modeled in convex sets of utility and probability measures restricted by closed intervals. Evaluation is done relative to a set of rules, generalizing the concept of admissibility, computationally handled through optimization of aggregated utility functions. Pros and cons of two approaches, and tradeoffs in selecting a utility function, are discussed

Modeling fuzzy criteria preference to evaluate tradespace of system alternatives

2018 Summer.Includes bibliographical references.This dissertation explores techniques for evaluating system concepts using the point of diminishing marginal utility to determine a best value alternative with an optimal combination of risk, performance, reliability, and life cycle cost. The purpose of this research is to address the uncertainty of customer requirements and assess crisp and fuzzy design parameters to determine a best value system. At the time of this research, most commonly used decision analysis (DA) techniques use minimum and maximum values under a specific criterion to evaluate each alternative. These DA methods do not restrict scoring beyond the point of diminished marginal utility resulting in superfluous capabilities and overvalued system alternatives. Using these models, an alternative being evaluated could receive significantly higher scores when reported capabilities are greater than ideal customer requirements. This problem is pronounced whenever weights are applied to criteria where excessive capabilities are recorded. The techniques explored in this dissertation utilize fuzzy membership functions to restrict scoring for alternatives that provide excess capabilities beyond ideal customer requirements. This research investigates and presents DA techniques for evaluating system alternatives that determine an ideal compromise between risk, performance criteria, reliability and life cycle costs

Real Options under Choquet-Brownian Ambiguity

Real options models characterized by the presence of ambiguity have been recently proposed. But based on recursive multiple-priors approaches to solve ambiguity, these seminal models reduce individual preferences to extreme pessimism by considering only the worst case scenario. In contrast, by relying on dynamically consistent Choquet-Brownian motions to model the dynamics of ambiguous expected cash flows, we show that a much broader spectrum of attitudes towards ambiguity may be accounted for. In the case of a perpetual real option to invest, ambiguity aversion delays the moment of exercise of the option, while the opposite holds true for an ambiguity lover.Real Options; Ambiguity; Irreversible investment; Optimal stopping; Knightian uncertainty; Choquet-Brownian motions