Thesis submitted by Jinrui Pan for the Degree of Doctor of Philosophy in the University of Manchester, and entitled, "Time and Risk Preferences: Theoretical Models and Applications." Date of submission 2014.This thesis makes contributions to two important areas of behavioural economics, namely individual decision making over time and under risk.Following the Introduction, Chapter 2 presents a new discounting function for analysing intertemporal choice. Liminal discounting, the model developed here, generalises exponential discounting in a parsimonious way. It allows for well-known departures, whilst maintaining its elegance and tractability. It also can be seen as an extension of quasi-hyperbolic discounting to continuous time. A liminal discounter has a constant rate of time preference before and after some threshold time; the liminal point. A preference foundation is provided, showing that the liminal point is derived endogenously from behaviour.Chapter 3 proposes an axiomatic model featuring a differential treatment of attitudes towards risk and time. Such distinction has been strongly suggested by experimental research when studying intertemporal choice, since the future is inherently risky. In the proposed model, non-linear probability distortions are incorporated into a dynamic model with discounted utility. Time is captured by a general discounting function independent of probabilities and outcomes. Utility of outcomes is captured by standard vNM utility independent of time. A two-parameter probability weighting function captures intertemporal probabilistic risk attitudes, with one parameter being constant over time, the other being time-dependent. An index of optimism is derived that depends on both parameters, which allows to model the observed high risk tolerance for delayed lotteries. Further, a preference foundation is provided. Interestingly, the model allows behaviour to be consistent with discounted expected utility, when risk is sufficiently distant from the present.