Asymptotic fractional-order stochastic dominance with bounded relative risk aversion

In this paper, we propose a novel asymptotic fractional-order stochastic dominance rule for ranking prospects over a sufficiently long investment horizon. The new rule formulates the consensus of decision makers whose relative risk aversion has a negative lower bound. Under the assumption that returns are lognormally distributed, we establish equivalent conditions for the proposed rule without imposing the non-negativity constraint on the mean of log-return, a restriction usually required by the existing asymptotic stochastic dominance rules. Furthermore, to enhance the tractability of this asymptotic fractional-order stochastic dominance, we propose a variant of asymptotic fractional-order stochastic dominance with bounded relative risk aversion, referred to as general asymptotic fractional-order stochastic dominance, under an additional condition on decision makers' marginal utilities. We derive its corresponding equivalent distributional characterizations. The (general) asymptotic fractional-order stochastic dominance with bounded relative risk aversion overcomes the shortcomings of the existing asymptotic fractional-order criterion that the fractional-order parameter has no influence on the equivalent distributional conditions. Empirical examples further show the advantages of the newly proposed rules for asset selection in long-term investment decisions.