Asymptotic fractional-order stochastic dominance with bounded relative risk aversion

2026-07-15

AI Summary

This study addresses limitations in existing asymptotic fractional stochastic dominance criteria, which rely on restrictive assumptions such as non-negative mean log returns and ineffective fractional-order parameters, thereby failing to adequately represent preferences of investors with bounded relative risk aversion. The paper proposes a novel asymptotic fractional stochastic dominance rule tailored for long-horizon investment decisions, allowing for negative mean log returns and establishing distributional equivalence conditions under lognormal returns without requiring the non-negativity constraint. By incorporating a lower bound on relative risk aversion and an additional condition on marginal utility, the proposed rule overcomes the ineffectiveness of fractional-order parameters in conventional approaches while enhancing both economic interpretability and practical applicability. Theoretical analysis and empirical evidence demonstrate that the new criterion significantly improves the accuracy and relevance of long-term asset rankings.

Abstract

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.

Problem

• asymptotic fractional-order stochastic dominance
• bounded relative risk aversion
• lognormal returns
• long-term investment
• distributional characterization

Innovation

• asymptotic fractional-order stochastic dominance
• bounded relative risk aversion
• lognormal returns
• distributional characterization
• long-term investment