Comparing Risks by Acceptance and Rejection
Stochastic dominance is a partial order on risky assets ("gambles")
that is based on the uniform preference—of all decision-makers in an
appropriate class—for one gamble over another. We modify this, first,
by taking into account the status quo (given by the current wealth)
and the possibility of rejecting gambles, and second, by comparing
rejections that are substantive (that is, uniform over wealth levels or
utilities). This yields two new stochastic orders: "wealth-uniform
and "utility-uniform dominance". Unlike stochastic dominance,
these two orders are complete: any two gambles can be compared.
Moreover, they are equivalent to the orders induced by, respectively,
the Aumann–Serrano (JPE 2008) index of riskiness and the
(JPE 2009) measure of riskiness.
© Sergiu Hart