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stat.ME2026

E-Backtesting Expected Shortfall without Value-at-Risk Forecasts under Time-series Models

Ruodu Wang, Jingcheng Yu

Expected Shortfall (ES) measures the average size of tail losses. Its sequential backtests typically also require a Value-at-Risk (VaR) forecast. We develop two e-backtesting metho…

q-fin.TR2026

Equilibrium in closed constant-function market maker economies

Muqiao Huang, Ruodu Wang, Yiyun Wang

We study equilibria in a closed, fee-free constant-function market maker (CFMM) economy with two assets and two agents. An interior state is a unilateral no-trade equilibrium exact…

math.ST2026

Confidence intervals for causal effects in sequential decision making

Vladimir Vovk, Ruodu Wang

We derive confidence intervals and confidence sequences for causal effects in situations where the back-door criterion is applicable. Our tightest confidence intervals hold in the…

q-fin.RM2026

Submodular risk measures

Ruodu Wang, Jingcheng Yu

We study submodularity for law-invariant functionals, with particular attention to convex risk measures. Expected losses are modular, and certainty equivalents are submodular exact…

q-fin.RM2026

Adaptive Window Selection for Financial Risk Forecasting

Yinhuan Li, Chenxin Lyu, Ruodu Wang

Risk forecasts in financial regulation and internal management are calculated through historical data. The unknown structural changes of financial data pose a substantial challenge…

q-fin.MF2026

Lambda Expected Shortfall

Fabio Bellini, Muqiao Huang, Qiuqi Wang +1

The Lambda Value-at-Risk (Lambda-VaR) is a generalization of the Value-at-Risk (VaR), which has been actively studied in quantitative finance. Over the past two decades, the Expect…