Optimal stopping and mathematical finance are intimately connected since the value of an American option is given as the solution to an optimal stopping problem. Such a problem can be viewed as a game in which we are trying to maximize an expected reward. The solution involves finding the best possible strategy, or equivalently, an optimal stopping time for the game. Moreover, the reward corresponding to this optimal time should be determined. It is also of interest to know how the solution depends on the model parameters. For example, when pricing and hedging an American option, the volatility needs to be estimated and it is of great practical importance to know how the price and hedging portfolio are affected by a possible misspecification. The first paper of this thesis investigates the performance of the delta hedging strategy for a class of American options with non-convex payoffs. It turns out that an option writer who overestimates the volatility will obtain a superhedge for the option when using the misspecified hedging portfolio. In the second paper we consider the valuation of a so-called stock loan when the lender is allowed to issue a margin call. We show that the price of such an instrument is equivalent to that of an American down-and-out barrier option with a rebate. The value of this option is determined explicitly together with the optimal repayment strategy of the stock loan. The third paper considers the problem of how to optimally stop a Brownian bridge. A finite horizon optimal stopping problem like this can rarely be solved explicitly. However, one expects the value function and the optimal stopping boundary to satisfy a time-dependent free boundary problem. By assuming a special form of the boundary, we are able to transform this problem into one which does not depend on time and solving this we obtain candidates for the value function and the boundary. Using stochastic calculus we then verify that these indeed satisfy our original problem. In the fourth paper we consider an investor wanting to take advantage of a mispricing in the market by purchasing a bull spread, which is liquidated in case of a market downturn. We show that this can be formulated as an optimal stopping problem which we then, using similar techniques as in the third paper, solve explicitly. In the fifth and final paper we study convexity preservation of option prices in a model with jumps. This is done by finding a sufficient condition for the no-crossing property to hold in a jump-diffusion setting.

This paper is concerned with the problem of finding an experimental design for discrimination between two rival models and for model robustness that minimizing the maximum bias simultaneously in binary response experiments. The criterion for model discrimination is based on the $T$-optimality criterion proposed in Atkinson and Fedorov (1975), which maximizes the sum of squares of deviations between the two rival models while the criterion for model robustness is based on minimizing the maximum probability bias of the two rival models. In this paper we obtain the optimum designs satisfy the above two criteria for some commonly used rival models in binary response experiments such as the probit and logit models etc.

The mobility of people, freight and information is fundamental to economic and social activities such as commuting, manufacturing, distributing consumer goods and supplying energy. There are two major problems that arise as a result of mobility. The first is economic cost and the second is environmental impact which is of increasing concern in sustainable development due to emission levels, particularly as a result of car use. This study focuses on constructing a network of induced emissions (NOIEs) by using three models and checking the robustness of NOIEs under varying parameters and models. The three models are Stead’s model, the NAEI model, and Oguchi’s model. This study uses the Swedish city of Borlänge as the case study. Calculating CO2 emissions by constructing the NOIEs using Stead’s model appears to give an underestimation when compared to results from a NOIEs which applies Oguchi’s model. Results when applying the NAEI model in constructing a NOIEs also give an underestimation compared to a NOIEs applying Oguchi’s model. Applying the NAEI model is, however, more accurate than applying Stead’s model in constructing a NOIEs. The outcomes of this study show that constructing a NOIEs is robust using Oguchi’s model. This model is preferable since it takes into account more important variables such as driving behavior and the length of the road segments which have a significant impact when estimating CO2 emissions.

abstract: In this dissertation two research questions in the field of applied experimental design were explored. First, methods for augmenting the three-level screening designs called Definitive Screening Designs (DSDs) were investigated. Second, schemes for strategic subdata selection for nonparametric predictive modeling with big data were developed. Under sparsity, the structure of DSDs can allow for the screening and optimization of a system in one step, but in non-sparse situations estimation of second-order models requires augmentation of the DSD. In this work, augmentation strategies for DSDs were considered, given the assumption that the correct form of the model for the response of interest is quadratic. Series of augmented designs were constructed and explored, and power calculations, model-robustness criteria, model-discrimination criteria, and simulation study results were used to identify the number of augmented runs necessary for (1) effectively identifying active model effects, and (2) precisely predicting a response of interest. When the goal is identification of active effects, it is shown that supersaturated designs are sufficient; when the goal is prediction, it is shown that little is gained by augmenting beyond the design that is saturated for the full quadratic model. Surprisingly, augmentation strategies based on the I-optimality criterion do not lead to better predictions than strategies based on the D-optimality criterion. Computational limitations can render standard statistical methods infeasible in the face of massive datasets, necessitating subsampling strategies. In the big data context, the primary objective is often prediction but the correct form of the model for the response of interest is likely unknown. Here, two new methods of subdata selection were proposed. The first is based on clustering, the second is based on space-filling designs, and both are free from model assumptions. The performance of the proposed methods was explored visually via low-dimensional simulated examples; via real data applications; and via large simulation studies. In all cases the proposed methods were compared to existing, widely used subdata selection methods. The conditions under which the proposed methods provide advantages over standard subdata selection strategies were identified. / Dissertation/Thesis / Doctoral Dissertation Statistics 2020

<p dir="ltr">In the realm of deep learning and neural networks, there has been substantial advancement, but the persistent DNN vulnerability to adversarial attacks has prompted the search for more efficient defense strategies. Unfortunately, this becomes an arms race. Stronger attacks are being develops, while more sophisticated defense strategies are being proposed, which either require modifying the model's structure or incurring significant computational costs during training. The first part of the work makes a significant progress towards breaking this arms race. Let’s consider natural images, where all the feature values are discrete. Our proposed metrics are able to discover all the vulnerabilities surrounding a given natural image. Given sufficient computation resource, we are able to discover all the adversarial examples given one clean natural image, eliminating the need to develop new attacks. For remedial measures, our approach is to introduce a random factor into DNN classification process. Furthermore, our approach can be combined with existing defense strategy, such as adversarial training, to further improve performance.</p>

Artificial intelligence (AI) and machine learning (ML) present some application opportunities and challenges that can be framed as learning problems. The performance of machine learning models depends on algorithms and the data. Moreover, learning algorithms create a model of reality through learning and testing with data processes, and their performance shows an agreement degree of their assumed model with reality. ML algorithms have been successfully used in numerous classification problems. With the developing popularity of using ML models for many purposes in different domains, the validation of such predictive models is currently required more formally. Traditionally, there are many studies related to model evaluation, robustness, reliability, and the quality of the data and the data-driven models. However, those studies do not consider the concept of the applicability domain (AD) yet. The issue is that the AD is not often well defined, or it is not defined at all in many fields. This work investigates the robustness of ML classification models from the applicability domain perspective. A standard definition of applicability domain regards the spaces in which the model provides results with specific reliability. The main aim of this study is to investigate the connection between the applicability domain approach and the classification model performance. We are examining the usefulness of assessing the AD for the classification model, i.e. reliability, reuse, robustness of classifiers. The work is implemented using three approaches, and these approaches are conducted in three various attempts: firstly, assessing the applicability domain for the classification model; secondly, investigating the robustness of the classification model based on the applicability domain approach; thirdly, selecting an optimal model using Pareto optimality. The experiments in this work are illustrated by considering different machine learning algorithms for binary and multi-class classifications for healthcare datasets from public benchmark data repositories. In the first approach, the decision trees algorithm (DT) is used for the classification of data in the classification stage. The feature selection method is applied to choose features for classification. The obtained classifiers are used in the third approach for selection of models using Pareto optimality. The second approach is implemented using three steps; namely, building classification model; generating synthetic data; and evaluating the obtained results. The results obtained from the study provide an understanding of how the proposed approach can help to define the model’s robustness and the applicability domain, for providing reliable outputs. These approaches open opportunities for classification data and model management. The proposed algorithms are implemented through a set of experiments on classification accuracy of instances, which fall in the domain of the model. For the first approach, by considering all the features, the highest accuracy obtained is 0.98, with thresholds average of 0.34 for Breast cancer dataset. After applying recursive feature elimination (RFE) method, the accuracy is 0.96% with 0.27 thresholds average. For the robustness of the classification model based on the applicability domain approach, the minimum accuracy is 0.62% for Indian Liver Patient data at r=0.10, and the maximum accuracy is 0.99% for Thyroid dataset at r=0.10. For the selection of an optimal model using Pareto optimality, the optimally selected classifier gives the accuracy of 0.94% with 0.35 thresholds average. This research investigates critical aspects of the applicability domain as related to the robustness of classification ML algorithms. However, the performance of machine learning techniques depends on the degree of reliable predictions of the model. In the literature, the robustness of the ML model can be defined as the ability of the model to provide the testing error close to the training error. Moreover, the properties can describe the stability of the model performance when being tested on the new datasets. Concluding, this thesis introduced the concept of applicability domain for classifiers and tested the use of this concept with some case studies on health-related public benchmark datasets. / Ministry of Higher Education in Libya