Second-degree stochastic dominance decisions and random initial wealth with applications to the economics of insurance

It is known that if random prospect Y stochastically dominates prospect X by the second degree, then all risk-averse agents prefer to hold Y and some random initial wealth Z rather than X and the same initial wealth Z, if Z is statistically independent of both X and Y. We give more general conditions for the invariance of the stochastic dominance ordering to initial wealth to hold: that X be more positively dependent on Z than Y is, and that either X and Z or Y and Z be positively dependent. Applications to the choice of an insurance deductible and of insurance coverage are given.