Shift-Aware Gaussian-Supremum Validation for Wasserstein-DRO CVaR Portfolios

2025-12-18

AI Summary

This paper addresses portfolio optimization under distributional shift and temporal dependence, subject to Conditional Value-at-Risk (CVaR) constraints. The core challenge lies in selecting the ambiguity set radius in Wasserstein distributionally robust optimization (DRO): excessive radii induce over-conservatism, while insufficient ones fail to mitigate regime-change risk. To resolve this, we propose a two-stage shift-aware validation framework. First, we introduce a Gaussian supremum test—novelly integrating density-ratio weighting, block multiplier bootstrap, and simultaneous confidence band upper bounds for DRO calibration. Second, we employ an efficient solver based on Lp-norm dual reformulation. Theoretically, our approach extends to non-i.i.d. financial time series. Empirically, it significantly improves the risk-return trade-off, achieving higher CVaR constraint satisfaction rates and superior sample robustness versus baselines; moreover, it automatically detects and rejects invalid configurations under data degradation.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Distributed Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

We study portfolio selection with a Conditional Value-at-Risk (CVaR) constraint under distribution shift and serial dependence. While Wasserstein distributionally robust optimization (DRO) offers tractable protection via an ambiguity ball around empirical data, choosing the ball radius is delicate: large radii are conservative, small radii risk violation under regime change. We propose a shift-aware Gaussian-supremum (GS) validation framework for Wasserstein-DRO CVaR portfolios, building on the work by Lam and Qian (2019). Phase I of the framework generates a candidate path by solving the exact reformulation of the robust CVaR constraint over a grid of Wasserstein radii. Phase II of the framework learns a target deployment law $Q$ by density-ratio reweighting of a time-ordered validation fold, computes weighted CVaR estimates, and calibrates a simultaneous upper confidence band via a block multiplier bootstrap to account for dependence. We select the least conservative feasible portfolio (or abstain if the effective sample size collapses). Theoretically, we extend the normalized GS validator to non-i.i.d. financial data: under weak dependence and regularity of the weighted scores, any portfolio passing our validator satisfies the CVaR limit under $Q$ with probability at least $1-β$; the Wasserstein term contributes a deterministic margin $(δ/α)|x|_*$. Empirical results indicate improved return-risk trade-offs versus the naive baseline.

Problem

• Selecting optimal portfolio radius under distribution shifts
• Validating CVaR constraints with serial dependence in data
• Balancing conservatism and risk in Wasserstein-DRO portfolios

Innovation

• Wasserstein DRO CVaR portfolios with shift-aware Gaussian-supremum validation
• Two-phase framework: candidate path generation and target law learning
• Block multiplier bootstrap for dependent data with confidence bands