We analyze individuals’ demand for retirement plans under cumulative prospect theory (CPT), considering traditional and unit-linked annuities as well as innovative, unit-linked tontines, in which benefits depend on mortality and financial market risks. We find that the main parameters of CPT, subjective probabilities and loss aversion heavily affect individuals’ retirement income preferences, explaining why not sufficiently many individuals purchase traditional annuities. Subjective probabilities increase the attractiveness of risk-carrying retirement plans (like unit-linked annuities and tontines) and lead individuals to prefer such to traditional annuities, whereas loss aversion lowers the attractiveness of all retirement products and can lead individuals not to purchase any retirement plan.