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This thesis is about insurance models and aspects of uncertainty pertaining to such models. The models we consider are insurance credibility models, arising from the need for accurate rate making based on past experience of claims in some portfolio of insurance policies. Classical credibility modelling is concerned with the use of a linear estimate to approximate the risk premium and was first studied by American actuaries at the start of the 20^th century. In the Bayesian paradigm the credibility premium is the optimal linear premium since it minimises the expected square loss based on current information. Here we focus on estimating the risk premium without using the linear estimator since the linear estimate is known to be an exact expression only in certain restricted cases such as the linear exponential family. Markov chain Monte Carlo (MCMC) has become a standard tool in statistical analysis. In this thesis we show how it can be used in a Bayesian setting applied to insurance credibility theory. Using MCMC methods, we can compute the premium to cover future risks to any degree of accuracy required by simulating directly from the posterior distribution of the unknown model risk parameters and then averaging the risk premium against this distribution. This is illustrated for a special case. We then consider the problem of model uncertainty and model selection in general credibility modelling. This is necessary especially when there are several competing models which seem to adequately describe the data. Most of our model selection techniques are based on the reversible jump MCMC algorithm of Green (1995, Biometrika). Recently Brooks et al. (2003, JRSSB) have proposed several implementational improvements for the vanilla reversible jump algorithm. In this thesis we apply these methods to various model selection problems in insurance credibility theory.

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The main purpose of the thesis is to extend the search literature by considering consumers who search for 'bundles' of commodities, rather than just a single good. It is shown that many of the results standard in the single commodity analysis, such as reservation prices and monopoly pricing, do not survive the transition to multi-commodity analysis. The thesis consists of three separate, but inter-related essays. Brief outlines of each essay follows. "Multi-Commodity Consumer Search." This paper considers the optimal strategy for a consumer who searches amongst firms for prices which will maximise an indirect utility function. The optimal search strategy cannot in general be represented by a 'reservation boundary', the multi-commodity extension of the 'reservation price'. Necessary and sufficient conditions are obtained for the optimal search strategy to be represented by a 'reservation boundary', and it is shown that an additively separable indirect utility function will satisfy these conditions. "Existence of Nash Equilibrium in Games with Discontinuous Payoffs." This paper extends the work by Dasgupta & Maskin and Simon to obtain a more general proof for the existence of mixed strategy Nash equilibria in games with discontinuous payoff functions. Following the method of analysis developed by Dasgupta & Maskin, I consider a sequence of finite games which converge to the discontinuous game in the limit. Sufficient conditions are obtained for the limit of a sequence of Nash equilibria from the finite games to be a Nash equilibrium of the limit game. The resulting conditions are not only more general than those from previous analyses but in many cases easier to apply. "Equilibrium Price Dispersion with Multi-Commodity Search." In this paper I develop a model of multi-commodity search where homogeneous consumers search sequentially, and with strictly positive search costs, to maximise an additively separable indirect utility function. Firms sell only one type of commodity, but within industries firms are identical and commodities are homogeneous.

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Epidemiologists have developed a vast range of models to describe the spread and control of epidemics. Most of these address critical issues such as invasion, persistence and variability of disease, though few have considered economic factors associated with control.  Conversely, economists have highlighted the importance of constraints imposed by limited resources, though few of these studies retained the vital dynamics and temporal progression that characterise epidemics. In this study we attempt to combine economic and epidemiological factors to create a framework within which optimal control strategies can be derived. Specifically, we address the following key questions: how can we incorporate economic constraints into an epidemiological framework?; can this be extended to more complex systems such as spatially explicit models?; and can we derive optimal control strategies in the presence of uncertainty? To address these questions we examine a range of systems, such as vaccination of emerging epidemics in human and animal populations, short and long-term application of fungicides to large-scale crop epidemics, and the timing of pest control measures in the presence of epidemic risk and uncertainty. Although we consider only a limited number of systems, the epidemiological models are generic and the methods from optimal control and option theory are applicable to a wide range of problems. The results can therefore be generalised to a number of epidemiological scenarios.

The study of a monetary economy requires concepts that are appropriate for this task. The essays in this dissertation study some of the concepts that Keynes used in this kind of analysis in The General Theory They have to do with the peculiarities of a monetary production economy and with the irreversibility of time. They also try to go beyond a history of economic theory and develop, where appropriate, the implications of Keynes's ideas for modern theory. Keynes argued that an essential feature of money was its zero elasticity of substitution. The first essay relates this idea to the 1930's debate on the recently introduced concept of elasticity of substitution, and shows its relation to the problems of multiplicity and stability of long-period equilibria. An economy in which there is a good with the essential features of money has multiple long-period unemployment equilibria. The essay also shows that some elements of the Cambridge controversies on the theory of capital were present in the substitution debate. The second essay traces the connection between the short period pricing in A Treatise on Money and the concepts Keynes used in order to link the present and the future in The General Theory. User cost and own rates of interest are generalizations for all assets of the theory of the Treatise on Money, with Fisherian elements that can be traced through Sraffa and Adarkar. This view of interest made it possible to understand the marginal efficiency of capital as something different from interest, and to reject its determination by marginal productivity. The third essay starts with the Keynesian concept of convention and builds an explanation in which investment decisions depend on individual expectations about the evolution of the economy. These individual expectations are based upon conventional knowledge and interactions among entrepreneurs. The interactions have macroeconomic effects which have, in turn, microeconomic consequences. Some of the results of the literature on the trade cycle can be obtained as a result of the introduction of conventions.

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