This thesis investigates the choices under risk in the framework of non-expected utility theories. One of the key contributions of this thesis is providing an approach that allows for a complete characterisation of Cumulative Prospect Theory (CPT) preferences without prior knowledge of the reference point. The location of the reference point that separates gains from losses is derived endogenously, thus, without any additional assumptions on the decision makers risk behaviour. This is different to the convention used in the literature, according to which, the reference point is preselected. The problem arising from imposing the location of the reference point is that the underlying preference conditions might not be alligned with the predictions made by the model. Consequently, it is difficult to verify such a model or to test it empirically. The present contribution offers a set of normatively and descriptively appealing preference conditions, which enable the elicitation of the reference point from the decision makers behaviour. Since these conditions are derived using objective probabilities, they can also be applied to settings such as health or insurance, where the continuity of the utility function is not required. As a result, the obtained representation theorem is not only the most general foundation for CPT currently available, but it also provides further support for the use of CPT as a modelling tool in decision theory and fi
nance.Another contribution that this thesis can be credited with is an application of rank-dependent utility theory (RDU) to the problem of insurance demand in the monopoly market affected by adverse selection. The present approach extends the classical model of Stiglitz (1977) by accounting for an additional component of heterogeneity among consumers, the heterogeneity in risk perception. Speci
fically, consumers employ distinctive probability weighting functions to assess the likelihood of risky events. This aspect of consumers' behaviour highlights the importance that the probabilistic risk attitudes within the RDU framework, such as optimism and pessimism, have for the choice of insurance contract. The analysis yields a separating equilibrium, with full insurance for a sufficiently pessimistic decision maker. An important implication of this result is that any low-risk individual who sufficiently overestimates his probability of loss will induce the uninformed insurer to o¤er him full coverage, thereby, affecting the high-risk type adversely. This outcome is consistent with the recent empirical puzzle regarding the correlation between ex-post risk and insurance coverage, according to which, agents with low exposure to risk receive a larger amount of compensation. By providing an explanation of this pattern of individual behaviour, the current work demonstrates that theory and practice of insurance demand can be reconciled to a greater extent. The paper also provides a behavioural rationale for policy intervention in the market with RDU agents, where the initial distortions in contracts due to unobservable risks are aggravated by the non-linear weighting of probability of a risky event.