Empirical evidence has shown that people are unwilling to insure rare losses at subsidized premiums and at the same time take-up insurance for moderate risks at highly loaded premiums. This paper explores whether prospect theory, in particular diminishing sensitivity and loss aversion, can accommodate this evidence. A crucial factor for applying prospect theory to insurance problems is the choice of the reference point. We motivate and explore two possible reference points, state-dependent initial wealth and final wealth after buying full insurance. It turns out that particularly the latter reference point seems to provide a realistic explanation of the empirical evidence.