Researchers release paper on convex variational theory for worst-case risk
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Jianjun Gao, Jonathan Li, Zhen Wang, and Yang Zhang published a paper in the arXiv q-fin section on October 22, 2026, proposing a convex variational theory for worst-case risk assessment based on spectral risk measures. This theory unifies fragmented existing analytical conclusions on worst-case risk assessment and extends them to richer ambiguity models, providing closed-form or semi-closed-form solutions for multiple practical models including Wasserstein ambiguity with tail stress and two-sided expected shortfall intervals, and generating projection algorithms with fixed-grid convergence. In high-dimensional portfolio applications, this theory can transform robust portfolio selection into an exact second-order cone programming problem.
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- arXiv q-finDistribution or Quantile? Convex Variational Theory for Worst-Case Risk
This study constructs a convex variational theory based on spectral risk measures, unifying the fragmented analytical conclusions of existing worst-case risk assessment and extending them to richer ambiguity models. The theory can provide closed-form or semi-closed-form solutions for multiple practical models including Wasserstein ambiguity with tail pressure and two-sided expected shortfall intervals, and can also generate projection algorithms with fixed-grid convergence. In high-dimensional portfolio applications, this theory can transform robust portfolio selection into an exact second-order cone programming problem.
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