Complementary symmetry in Cumulative Prospect Theory with random reference

It is shown that complementary symmetry holds in Cumulative Prospect Theory with random reference if the utility function for gains and losses is strictly increasing and continuous. Previous results imposed more restrictions involving preference homogeneity, reflection, and loss aversion. The result holds true in the general version of the Third-Generation Prospect Theory provided that the relative value function v takes the same form as in Cumulative Prospect Theory.