Loss aversion and perceptual risk aversion

We prove that, in cumulative prospect theory, the weak loss aversion for S-shaped value functions is equivalent to a notion of risk aversion that we define from the perceptual point of view. No additional assumption or condition on the probability distortion is needed. It is demonstrated that a power S-shaped value function does not satisfy weak loss aversion, i.e., a decision maker is risk seeking with respect to some mixed sign lotteries.