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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published_or_final_version / abstract / toc / Business / Master / Master of Philosophy

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R&D can be considered the driving force of the modern economy. The economy is organized to utilize scarce resources. R&D through technological change results in a transformation of scarcities, in the creation of new resources, new products and new prices. "The central stupendous truth about developed economies today is that they can have the kind and scale of resources...they decide to have. It is no longer resources that limit decisions, it is the decision that makes the resources" (Toffler, 1971, p. 15). In technological society resources are created. Yet recent publications indicate a universal decline in R&D investment. This dissertation focuses upon some important aspects of R&D decision making in Canada. The first chapter analyzes available information about determinants and practices of R&D investment decisions, describes the inventory of normative models developed to improve decision making, and identifies empirical studies investigating their implementation. A review of the state of the art leads to the identification of the following four areas of information which are deficient: 1. information about the nature of selective perception processes of R&D decision making, 2. the objective functions (explicit and latent) which guide choices among alternative R&D investment opportunities, 3. the impact of R&D upon the positions of prime bargaining units organizations, and 4. the impacts of organizational structure and processes upon implementation of investment decisions. The first two categories of information relate to the question of what different decision units consider relevant in defining their problems and what they value. The last two categories relate to the organizational impact of R&D and the processes by which decisions are reached and implemented. These areas provide a focus for required additional research aimed at improvements in R&D decision making. This dissertation attempts to contribute to the first three areas of research outlined above. The focus in Chapter 2 is upon the impact of R&D in shifting resource shares of labour, capital and energy in the total output. Chapter 3 focuses upon processes of information selection in R&D decision making, identifying what environmental conditions are important to whom in making R&D investment decisions. Chapter 4 investigates multi-attribute preferences in R&D project selection. Each chapter draws some normative implications for R&D public policy, and the postscript identifies, promising areas for future research. Some of the major findings of this sequence of studies are: 1. Accepting a neoclassical framework of analysis, in most sectors, R&D has had no impact on input shares, indicating that scale and price effects dominate the structure of technology. Where R&D has had impact on the structure, it has sometimes had a labour using and sometimes a capital using bias. 2. Significant differences in patterns of attention to environmental conditions were identified. These differences are related to executive attributes and firm characteristics. 3. High concensus exists with respect to tradeoffs among project attributes across all firm-executive groupings. 4. Compensatory actuarial models provide a good fit with observations of R&D investment judgments. Some normative implications of the study for public policy include the following: 1. As R&D impact upon the economic objectives of the major bargaining units in firms is neutral in most cases, perhaps an effort should be made to eliminate technological development as part of the traditional arena of labour-management bargaining. 2. In creating favourable R&D investment climates, government ought to develop a sensitive strategy which recognizes explicitly the selective impact of single dimension interventions on alternative target populations. 3. The role of government as an independent insurance agent for R&D ventures is recommended to replace direct participation in project funding. / Business, Sauder School of / Graduate

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