Over the past decades, researchers in economics, financial mathematics and actuarial science have introduced results to the concept of comonotonicity in their respective fields of interest. Comonotonicity is a very strong dependence structure and is very often mistaken as a dependence structure that is too extreme and unrealistic. However, the concept of comonotonicity is actually a useful tool for solving several research and practical problems in capital allocation, risk sharing and optimal allocation. The first topic of this thesis is focused on the application of comonotonicity in optimal capital allocation. The Enterprise Risk Management process of a financial institution usually contains a procedure to allocate the total risk capital of the company into its different business units. Dhaene et al. (2012) proposed a unifying capital allocation framework by considering some general deviation measures. This general framework is extended to a more general optimization problem of minimizing separable convex function with a linear constraint and box constraints. A new approach of solving this constrained minimization problem explicitly by the concept of comonotonicity is developed. Instead of the traditional Kuhn-Tucker theory, a method of expressing each convex function as the expected stop-loss of some suitable random variable is used to solve the optimization problem. Then, some results in convex analysis with infimum-convolution are derived using the result of this new approach. Next, Borch's theorem is revisited from the perspective of comonotonicity. The optimal solution to the Pareto optimal risk-sharing problem can be obtained by the Lagrangian method or variational arguments. Here, I propose a new method, which is based on a Breeden-Litzanbeger type integral representation formula for increasing convex functions. It enables the transform of the objective function into a sum of mixtures of stop-losses. Necessary conditions for the existence of optimal solution are then discussed. The explicit solution obtained allows us to show that the risk-sharing problem is indeed a “point-wise” problem, and hence the value function can be obtained immediately using the notion of supremum-convolution in convex analysis. In addition to the above classical risk-sharing and capital allocation problems, the problem of minimizing a separable convex objective subject to an ordering restriction is then studied. Best et al. (2000) proposed a pool adjacent violators algorithm to compute the optimal solution. Instead, we show that using the concept of comonotonicity and the technique of dynamic programming the solution can be derived in a recursive manner. By identifying the right-hand derivative of the convex functions with distribution functions of some suitable random variables, we rewrite the objective function into a sum of expected deviations. This transformation and the fact that the expected deviation is a convex function enable us to solve the minimizing problem. / published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

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Disruption Management in the airline industry plays an important role in airline operations. The goal of disruption management is to minimize the costs associated with disruptions while returning to the original schedule. Methodologies using advanced tabu search (TS) were investigated to solve two flight rescheduling problems: the aircraft grounding problem and the reduced station capacity problem. The objectives of both problems were to minimize the schedule recovery costs associated with flight schedule modifications and deviations from the original route, which are composed of the sum of delay costs, cancellation costs and aircraft route swap costs. Reflecting the cost of the deviation from the original route, the swap cost was modeled as a non-linear function of the swaps of aircraft between routes. In each problem, a stand-alone tabu search approach was constructed to holistically minimize the sum of the cost of delays, cancellations and swaps. Next a hybrid method which combined a time-space network flow model with side constraints and a limited tabu search was created which attacked the problem in two steps: first, the total cost of delays and cancellations was minimized by the network flow model; second, a limited tabu search was conducted to minimize the number of swaps. A second hybrid method was then developed, which utilized the result from the first hybrid method as starting solution for the stand-alone tabu search. The results of the experiments performed with the hybrid methods clearly indicate that integrating TS with classical optimization methods has marked potential for improving the results of a disruption management technique.

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D. Tech. Civil Engineering / Construction contracts have provisional clauses to control financial risks, but studies have shown that cost overruns are still common, which require the inclusion of additional management techniques to improve cost estimates. The research investigated, analysed and identified the shortcomings that exist within the current mechanisms to manage financial risk. A new risk ranking model that can be used to eliminate construction cost overruns in South Africa was developed. The study sought the views from a variety of construction professionals, based on knowledge and experiences within their own organisations, to explore new mechanisms to limit the risk impact of persistent cost overruns.

University-built satellite programs are prone to failure because these projects are performed by inexperienced student-engineers during the early parts of the satellite-building “learning curve”. However, with sufficient attention on risk management, students should be able to identify what risk avoidance actions should be taken, and when. By applying risk mitigation strategies, university built satellite programs will not only contribute students to learn space systems engineering, but also accomplish their scientific missions with higher rates of success. This thesis study is aimed to provide risk management guidelines that could be adapted to university built satellite programs to increase the risk awareness. Besides indicating the key strategies for risk mitigation, a set of risk management procedures are prepared to help students during the university-built satellite projects. / text

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