Asymptotic fractional-order stochastic dominance with bounded relative risk aversion

Battle Count: 78

The paper is primarily relevant to long-term strategic asset allocation rather than short-term quantitative trading. It provides a rigorous theoretical framework for ranking assets over sufficiently long investment horizons, which is applicable to pension fund management, retirement portfolio optimization, and institutional long-term investment strategies. The moment-based conditions (mean and variance of log-returns) are straightforward to compute from historical data, making implementation feasible for long-horizon asset selection. However, it does not address short-term trading signals, high-frequency strategies, or dynamic rebalancing.

The core implementation requires: (1) estimating mean and variance of daily log-returns for each asset, (2) computing the fractional-order parameter ℓ using the closed-form estimator (Equation 16), (3) checking the moment conditions μ_F + σ²_F/(2ℓ) ≥ μ_G + σ²_G/(2ℓ) and σ_F ≤ σ_G for pairwise comparisons. The mathematical derivations are complex, but the final decision rules reduce to simple comparisons of estimated moments. The general 1+ℓ-ASD variant further simplifies to comparing μ + σ²/(2ℓ) values. Implementation is moderate complexity for practitioners familiar with basic statistics.

The paper provides complete mathematical proofs in the appendix, explicit formulas for all conditions, and uses publicly available data from investing.com. The estimation procedure for the fractional-order parameter ℓ is clearly defined (Equation 16). However, the theoretical framework requires careful implementation of integral inequalities and distributional comparisons.