Downside risk neutral probabilities

Risk neutral probabilities are adjusted to take into account the asset price effect of risk preferences. This paper introduces downside (respectively outer) risk neutral probabilities, which are adjusted to take into account the asset price effect of preferences for downside (resp. outer) risk and higher degree risks. Using risk preference theory, we interpret these three changes in probability measures in terms of risk substitution. With downside risk neutral probabilities, the pricing kernel is linear in wealth. Outer risk neutral probabilities can be viewed as a reasonable approximation of physical probabilities.