This dissertation comprises three chapters on the question of how individuals make choices in situations of uncertainty. In chapter 1 we develop an axiomatic model of choice in which the decision-maker acts on the anticipation of regret. Our representation is analogous to a representation from classic regret theory but we consider transitive preferences over act profiles rather than intransitive preferences over single acts. We consider the behavioural implications of our theory, in particular the decision-maker’s attitude to statewise dominated acts, the responsibility of choice and choice bracketing. We derive 2 measures of regret aversion and show our theory can account for why individuals may display risk averse behaviour in one situation whilst displaying risk-loving behaviour in another. In chapter 2 we present a model in which a risk-neutral monopolist designs a lottery and sells a ticket to a regret averse consumer. We show that, because he pays disproportionate attention to states in which there are large outcome differences across acts, the regret averse consumer may display a preference for a long shot bet that has a negative expected value. For a general preference specification we determine the lottery contract that maximises expected revenue for the monopolist and we derive conditions under which the lottery is neither trivial nor unrealistic. In chapter 3 we use data from the popular television game-show “Deal or No Deal?” to analyse the way individuals make choices under risk. We present a formal game-theoretical model of the show in which both contestant and banker are modelled as strategic players. We investigate the properties of the equilibrium solution to form hypotheses of how rational expected utility-maximisers would behave as players in the game and test these hypotheses with the relevant choice data. The main result is that an increasing offer function is the result of optimal behaviour when the banker is uncertain about the contestant’s risk attitudes.

This thesis addresses household saving behaviour, characterising the extent of self-insurance and public insurance over the life-cycle. Understanding how household saving varies in response to different forms of uncertainty is vitally important. Some risks are not fully insurable when markets are incomplete: for example, it is difficult for private insurers to cover layoff and productivity risk because of moral hazard issues. In these situations saving decisions determine households’ ability to avoid adversity, or to self-insure against such outcomes. While there has been substantial research into the broad questions concerning saving and expenditure choices, issues such as household asset allocation, the adequacy of self-insurance, and the interplay between these decisions and public insurance are less well understood. This thesis investigates these questions, combining theory and empirics in order to further our understanding of the underlying mechanisms of household saving choices. I begin with theory, presenting two structural papers that enrich the basic life-cycle model by increasing the realism of the modelling structure. In the first chapter I formulate a number of extensions to the standard framework, and detail how these permit simultaneous matching of key wealth and asset allocation statistics. In the second, I propose a novel identification strategy that enables us to elicit households’ beliefs about the risk and return of investing in stocks, and allows us to estimate intertemporal allocation parameters harmonising both consumption and financial wealth data. In the third chapter I undertake a reduced form approach to estimate the consumption loss associated with serious health shocks, using the life-cycle model as an organising framework. I develop a systemic analysis of household saving choices in order to better analyse questions about the effectiveness of self-insurance, the degree of preparedness for retirement, and how these respond to different levels of public insurance.

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In finance dynamic stochastic programming traditionally has been applied to institutional pension fund problems and more recently has become usable for more difficult individual wealth management problems. We develop several models to handle specific wealth management issues. We develop a US investment model with an exact tax basis and a rudimentary tax qualified portfolio. We show the ability to solve this model with up to 48 stages in 10 asset classes using an exact tax basis by approximating the solution employing information constraints. For fewer stages we show tractability of solving the full model with at least binary branching at every node of the scenario tree. We also introduce a mortgage model to investigate the effects of interest-only mortgages and their maturity. Modelling maturity selection as a binary decision variable, we find that the interest-only components of a mortgage are of interest when a borrower has a low income initially but expects it to grow. We do not consider the case of investors taking such mortgages to increase their leverage. It is noted that solutions may not be representative of all possibilities because the models reach an upper limit in terms of solvable problem sizes with currently available computing power. Expected value of perfect information (EVPI) calculation capabilities have been added to a modern solver. Given that aggregation is used to decrease solution times of such models we implement for the first time a disaggregator to allow calculation of EVPI subproblems without rereading the problem considered from disk. Aggregation is also found to increase solver speed applied to EVPI subproblems, especially after we reorder nodes. Sequential EVPI importance sampling is shown to be effective for the models introduced here and results improve drastically when mean matching of sampled scenarios is added. We successfully attempt to automate tuning for these algorithms by introducing percentile-based zero thresholds and adjusting these automatically when their current values are found to cause EVPI to fall.

This thesis will look at three problems in financial mathematics. In the first, we seek to model the heterogeneous beliefs of agents in a dynamic economy. We study the class of models in which all agents receive the same stream of information. Their different beliefs about the system cause them to behave differently, yet still rationally. We explain how to determine the equilibrium and deduce the state price density for the agents; this enables us to (theoretically) calculate the price of any contingent claim. We look at three setups. The first is that in which all agents have logarithmic utility. We show how the model can explain observed phenomena such as rational overconfidence, speculation and volume of trade effects. The second setup introduces a continuum of finite-lived agents who learn about an unknown parameter of the output process of the single productive asset. Since the agents are finite-lived, they never discover the true value of the parameter and we can therefore determine a stationary solution. We also consider a third setup, in which the behaviour of the output process depends on a stochastic process that is not fully observed. The second problem is insurance pricing. We consider how prices behave when insurers do not know about the arrival rate and size of claims, as they have very little past data. We examine the amount of business received by each insurance company when they each charge different prices. We use this to determine the optimal price for each insurers to charge, given their perceived cost of providing insurance. Insurers are assumed to be Bayesian and so update their beliefs about the arrival rate and size of claims as they observe more data. This results in the perceiving cost of the insurance changing and the insurers adjusting their prices. The final topic looked at is the effect of market clearing on financial markets. We introduce a model with many CARA agents and many risky assets. We show that the market clearing condition can introduce correlation between assets whose dividend processes are independent.

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