Existing portfolio choice models in continuous time typically reduce to finding optimal terminal cash flows which are random variables. While it works for expected utility maximisation, it generally fails to work for models with non expected utility criteria, such as the goal-achieving model, Yaari’s dual model, Lopes’ SP/A model, behavioural model under prospect theory, models with coherent risk measures, as well as optimal stopping with probability distortions. This talk reviews the latest development in solving these non-classical models by changing decision variables - from random variables to their quantile functions.