Risk aversion for losses and the Nash bargaining solution

We call a decision maker risk averse for losses if that decision maker is risk averse
with respect to lotteries having alternatives below a given reference alternative in
their support. A two-person bargaining solution is called invariant under risk
aversion for losses if the assigned outcome does not change after correcting for risk
aversion for losses with this outcome as pair of reference levels, provided that the
disagreement point only changes proportionally. We present an axiomatic characterization of the Nash bargaining solution based on this condition, and we also
provide a decision-theoretic characterization of the concept of risk aversion for
losses.