Welcome to Ruodu Wang's Homepage

Banff, Canada, 2013

Publications and Manuscripts

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Pre-publication Manuscripts

Latest working papers posted online

     Please, critical comments on these papers are very much appreciated.
(2022) Quasi-convexity in mixtures for generalized rank-dependent functions (with Qinyu Wu).
(2022) E-backtesting (with Qiuqi Wang and Johanna Ziegel).
(2022) Efficiency of nonparametric e-tests (with Vladimir Vovk).
(2022) Choquet regularization for reinforcement learning (with Xia Han and Xunyu Zhou).
(2022) An unexpected stochastic dominance: Pareto distributions, catastrophes, and risk exchange (with Yuyu Chen and Paul Embrechts).
(2022) An axiomatic theory to anonymized risk sharing (with Zhanyi Jiao and Yang Liu).
(2022) Diversification quotients: Quantifying diversification via risk measures (with Xia Han and Liyuan Lin).
(2022) Merging sequential e-values via martingales (with Vladimir Vovk).
(2022) E-values as unnormalized weights in multiple testing (with Aaditya Ramdas).
(2022) Joint mixability and negative orthant dependence (with Takaaki Koike and Liyuan Lin).
(2022) Calibrating distribution models from PELVE (with Hirbod Assa and Liyuan Lin).
(2022) Post-selection inference for e-value based confidence intervals (with Aaditya Ramdas and Ziyu Xu).
(2022) A reverse Expected Shortfall optimization formula (with Yuanying Guan and Zhanyi Jiao).
(2022) Model aggregation for risk evaluation and robust optimization (with Tiantian Mao and Qinyu Wu).
(2022) Simultaneous optimal transport (with Zhenyuan Zhang).
(2021) A theory of multivariate stress testing (with Pietro Millossovich and Andreas Tsanakas).
(2021) Cash-subadditive risk measures without quasi-convexity (with Xia Han, Qiuqi Wang and Jianming Xia).
(2021) One axiom to rule them all: A minimalist axiomatization of quantiles (with Tolulope Fadina and Peng Liu).
(2021) A framework for measures of risk under uncertainty (with Tolulope Fadina and Yang Liu).
(2021) Risk concentration and the mean-Expected Shortfall criterion (with Xia Han, Bin Wang and Qinyu Wu).
(2020) Optimizing distortion riskmetrics with distributional uncertainty (with Silvana Pesenti and Qiuqi Wang).
(2020) Testing with p*-values: Between p-values, mid p-values, and e-values.
(2020) Dependence and risk attitudes: An equivalence (with Qinyu Wu).
(2020) Convolution bounds on quantile aggregation (with Jose Blanchet, Henry Lam and Yang Liu).
(2020) True and false discoveries with independent e-values (with Vladimir Vovk).
(2019) Confidence and discoveries with e-values (with Vladimir Vovk).
(2019) Self-consistency, subjective pricing, and a theory of credit rating (with Nan Guo, Steven Kou and Bin Wang).
(2017) A model-free continuum of degrees of risk aversion (with Tiantian Mao).

Refereed Articles


[84] (2022) Fractional stochastic dominance in rank-dependent utility and cumulative prospect theory. Journal of Mathematical Economics, forthcoming (with Tiantian Mao).
[83] (2022) An impossibility theorem on capital allocation. Scandinavian Actuarial Journal, forthcoming (with Yuanying Guan and Andreas Tsanakas).
[82] (2022) Star-shaped risk measures. Operations Research, forthcoming (with Erio Castagnoli, Giacomo Cattelan, Fabio Maccheroni and Claudio Tebaldi).
[81] (2021) PELVE: Probability equivalent level of VaR and ES. Journal of Econometrics, forthcoming (with Hengxin Li).
[80] (2021) Trade-off between validity and efficiency of merging p-values under arbitrary dependence. Statistica Sinica, forthcoming (with Yuyu Chen, Peng Liu and Ken Seng Tan).


[79] (2022) Inf-convolution, optimal allocations, and model uncertainty for tail risk measures. Mathematics of Operations Research, 47(3), 2494-2519 (with Fangda Liu, Tiantian Mao and Linxiao Wei).
[78] (2022) False discovery rate control with e-values. Journal of the Royal Statistical Society Series B, 84(3), 822-852 (with Aaditya Ramdas).
[77] (2022) Parametric measures of variability induced by risk measures. Insurance: Mathematics and Economics, 106, 270-284 (with Fabio Bellini, Tolulope Fadina and Yunran Wei).
[76] (2022) The directional optimal transport. Annals of Applied Probability, 32(2), 1400-1420 (with Marcel Nutz).
[75] (2022) Admissible ways of merging p-values under arbitrary dependence. Annals of Statistics, 50(1), 351-375 (with Vladimir Vovk and Bin Wang).
[74] (2022) Optimal insurance to maximize RDEU under a distortion-deviation premium principle. Insurance: Mathematics and Economics, 104, 35-59 (with Xiaoqing Liang and Virginia Young).
[73] (2022) Variance comparison between Infinitesimal Perturbation Analysis and Likelihood Ratio estimators to stochastic gradient. Operations Research Letters, 50(2), 199-204 (with Zhenyu Cui and Yanchu Liu).
[72] (2022) Robustness in the optimization of risk measures. Operations Research, 70(1), 95-110 (with Paul Embrechts and Alexander Schied).
[71] (2022) Risk measures induced by efficient insurance contracts. Insurance: Mathematics and Economics, 103, 56-65 (with Qiuqi Wang and Ricardas Zitikis).
[70] (2022) Ordering and inequalities for mixtures on risk aggregation. Mathematical Finance, 32(1), 421-451 (with Yuyu Chen, Peng Liu and Yang Liu).
[69] (2022) Risk aggregation under dependence uncertainty and an order constraint. Insurance: Mathematics and Economics, 102, 169-187 (with Yuyu Chen and Liyuan Lin).
[68] (2022) Adjusted Expected Shortfall. Journal of Banking and Finance, 134, 106297 (with Matteo Burzoni and Cosimo Munari).


[67] (2021) A unified framework for bandit multiple testing. Advances in Neural Information Processing Systems (NeurIPS 2021), 16833-16845 (with Aaditya Ramdas and Ziyu Xu).
[66] (2021) Distributional transforms, probability distortions, and their applications. Mathematics of Operations Research, 46(4), 1490-1512 (with Peng Liu and Alexander Schied).
[65] (2021) Competitive equilibria in a comonotone market. Economic Theory, 72, 1217-1255 (with Tim Boonen and Fangda Liu).
[64] (2021) Bayes risk, elicitability, and the Expected Shortfall. Mathematical Finance, 31, 1190-1217 (with Paul Embrechts, Tiantian Mao and Qiuqi Wang).
[63] (2021) Scenario-based risk evaluation. Finance and Stochastics, 25, 725-756 (with Johanna Ziegel).
[62] (2021) A theory for measures of tail risk. Mathematics of Operations Research, 46(3), 1109-1128 (with Fangda Liu).
[61] (2021) E-values: Calibration, combination, and applications. Annals of Statistics, 49(3), 1736-1754 (with Vladimir Vovk).
[60] (2021) Stochastic decomposition for p-norm symmetric survival functions on the positive orthant. Journal of Multivariate Analysis, 184, 104760 (with Jan-Frederik Mai).
[59] (2021) An axiomatic foundation for the Expected Shortfall. Management Science, 67(3), 1413-1429 (with Ricardas Zitikis).


[58] (2020) Combining p-values via averaging. Biometrika, 107(4), 791-808 (with Vladimir Vovk).
[57] (2020) Distortion riskmetrics on general spaces. ASTIN Bulletin, 50(4), 827-851 (with Qiuqi Wang and Yunran Wei).
[56] (2020) Risk functionals with convex level sets. Mathematical Finance, 30(4), 1337-1367 (with Yunran Wei).
[55] (2020) Characterization, robustness and aggregation of signed Choquet integrals. Mathematics of Operations Research, 45(3), 993-1015 (with Yunran Wei and Gordon Willmot).
[54] (2020) Characterizing optimal allocations in quantile-based risk sharing. Insurance: Mathematics and Economics, 93, 288-300 (with Yunran Wei).
[53] (2020) Quantile-based risk sharing with heterogeneous beliefs. Mathematical Programming, 181(2), 319-347 (with Paul Embrechts, Haiyan Liu and Tiantian Mao).
[52] (2020) Risk aversion in regulatory capital principles. SIAM Journal on Financial Mathematics, 11(1), 169-200 (with Tiantian Mao).
[51] (2020) Is the inf-convolution of law-invariant preferences law-invariant? Insurance: Mathematics and Economics, 91, 144-154 (with Peng Liu and Linxiao Wei).
[50] (2020) Weak comonotonicity. European Journal of Operational Research, 282, 386-397 (with Ricardas Zitikis).
[49] (2020) Convex risk functionals: Representation and applications. Insurance: Mathematics and Economics, 90, 66-79 (with Jun Cai, Christiane Lemieux and Fangda Liu).


[48] (2019) Sums of standard uniform random variables. Journal of Applied Probability, 56(3), 918-936 (with Tiantian Mao and Bin Wang).
[47] (2019) Dual utilities on risk aggregation under dependence uncertainty. Finance and Stochastics, 23(4), 1025-1048 (with Zuoquan Xu and Xunyu Zhou).
[46] (2019) An efficient approach to quantile capital allocation and sensitivity analysis. Mathematical Finance, 29(4), 1131-1156 (with Vali Asimit, Liang Peng and Alex Yu).
[45] (2019) Centers of probability measures without the mean. Journal of Theoretical Probability, 32(3), 1482-1501 (with Giovanni Puccetti, Pietro Rigo and Bin Wang).
[44] (2019) Distributional compatibility for change of measures. Finance and Stochastics, 23(3), 761-794 (with Jie Shen, Yi Shen and Bin Wang).
[43] (2019) Compatible matrices of Spearman's rank correlation. Statistics and Probability Letters, 151, 67-72 (with Bin Wang and Yuming Wang).
[42] (2019) Random locations of periodic stationary processes. Stochastic Processes and their Applications, 129(3), 878-901 (with Jie Shen and Yi Shen).


[41] (2018) Quantile-based risk sharing. Operations Research, 66(4), 936-949 (with Paul Embrechts and Haiyan Liu).
[40] (2018) Worst-case Range Value-at-Risk with partial information. SIAM Journal on Financial Mathematics, 9(1), 190-218 (with Lujun Li, Hui Shao and Jingping Yang).
[39] (2018) Asymptotic equivalence of risk measures under dependence uncertainty. Mathematical Finance, 28(1), 29-49 (with Jun Cai and Haiyan Liu).


[38] (2017) Negative dependence in matrix arrangement problems. Annals of Operations Research, online publication (with Edgars Jakobsons).
[37] (2017) Pareto-optimal reinsurance arrangements under general model settings. Insurance: Mathematics and Economics, 77, 24-37 (with Jun Cai and Haiyan Liu).
[36] (2017) Gini-type measures of risk and variability: Gini shortfall, capital allocations, and heavy-tailed risks. Journal of Banking and Finance, 83, 70-84 (with Edward Furman and Ricardas Zitikis).
[35] (2017) Risk bounds for factor models. Finance and Stochastics, 21(3), 631-659 (with Carole Bernard, Ludger Rüschendorf and Steven Vanduffel).
[34] (2017) Collective risk models with dependence uncertainty. ASTIN Bulletin, 47(2), 361-389 (with Haiyan Liu).


[33] (2016) Joint mixability. Mathematics of Operations Research, 41(3), 808-826 (with Bin Wang).
[32] (2016) Bernoulli and tail-dependence compatibility. Annals of Applied Probability, 26(3), 1636-1658 (with Paul Embrechts and Marius Hofert).
[31] (2016) Diversification limit of quantiles under dependence uncertainty. Extremes, 19(2), 143-170 (with Valeria Bignozzi, Tiantian Mao and Bin Wang).
[30] (2016) Regulatory arbitrage of risk measures. Quantitative Finance, 16(3), 337-347.
[29] (2016) Computation of credit portfolio loss distribution by a cross entropy method. Journal of Applied Mathematics and Computing, 52(1), 287-304 (with Xiaoying Han).
[28] (2016) General convex order on risk aggregation. Scandinavian Actuarial Journal, 2016(8), 713-740 (with Xiaoying Han and Edgars Jakobsons).


[27] (2015) Extremal dependence concepts. Statistical Science, 30(4), 485-517 (with Giovanni Puccetti).
[26] (2015) Seven proofs for the subadditivity of Expected Shortfall. Dependence Modeling, 3, 126-140 (with Paul Embrechts).
[25] (2015) Aggregation-robustness and model uncertainty of regulatory risk measures. Finance and Stochastics, 19(4), 763-790 (with Paul Embrechts and Bin Wang).
[24] (2015) Current open questions in complete mixability. Probability Surveys, 12, 13-32.
[23] (2015) How superadditive can a risk measure be? SIAM Journal on Financial Mathematics, 6(1), 776-803 (with Valeria Bignozzi and Andreas Tsanakas).
[22] (2015) On aggregation sets and lower-convex sets. Journal of Multivariate Analysis, 138, 170-181 (with Tiantian Mao).
[21] (2015) Elicitable distortion risk measures: A concise proof. Statistics and Probability Letters, 100, 172-175 (with Johanna Ziegel).
[20] (2015) Extreme negative dependence and risk aggregation. Journal of Multivariate Analysis, 136, 12-25 (with Bin Wang).
[19] (2015) Composite Bernstein copulas. ASTIN Bulletin, 45(2), 445-475 (with Zhijin Chen, Fang Wang and Jingping Yang).
[18] (2015) Detecting complete and joint mixability. Journal of Computational and Applied Mathematics, 280, 174-187 (with Giovanni Puccetti).
[17] (2015) CreditRisk+ model with dependent risk factors. North American Actuarial Journal, 19(1), 24-40 (with with Liang Peng and Jingping Yang).


[16] (2014) Interval estimation for bivariate t-copulas via Kendall's tau. Variance, 8(1), 43-54 (with Liang Peng).
[15] (2014) Sum of arbitrarily dependent random variables. Electronic Journal of Probability, 19(84), 1-18.
[14] (2014) An academic response to Basel 3.5. Risks, 2(1), 25-48 (with Antonela Beleraj, Paul Embrechts, Giovanni Puccetti and Ludger Rüschendorf).
[13] (2014) Empirical likelihood test for high-dimensional linear models. Statistics and Probability Letters, 86, 85-90 (with Liang Peng and Yongcheng Qi).
[12] (2014) Asymptotic bounds for the distribution of the sum of dependent random variables. Journal of Applied Probability, 51(3), 780-798.
[11] (2014) Risk aggregation with dependence uncertainty. Insurance: Mathematics and Economics, 54, 93-108 (with Carole Bernard and Xiao Jiang).


[10] (2013) Complete mixability and asymptotic equivalence of worst-possible VaR and ES estimates. Insurance: Mathematics and Economics, 53(3), 821-828 (with Giovanni Puccetti and Bin Wang).
[9] (2013) Tests for covariance matrix with fixed or divergent dimension. Annals of Statistics, 41(4), 2075-2096 (with Liang Peng and Rongmao Zhang).
[8] (2013) Jackknife empirical likelihood test for equality of two high-dimensional means. Statistica Sinica, 23(2), 667-690 (with Liang Peng and Yongcheng Qi).
[7] (2013) Bounds for the sum of dependent risks and worst Value-at-Risk with monotone marginal densities. Finance and Stochastics, 17(2), 395-417 (with Liang Peng and Jingping Yang).
[6] (2013) Jackknife empirical likelihood for parametric copulas. Scandinavian Actuarial Journal, 2013(5), 325-339 (with Liang Peng and Jingping Yang).

2009 - 2012

[5] (2012) Jackknife empirical likelihood method for some risk measures and related quantities. Insurance: Mathematics and Economics, 51(1), 142-150 (with Liang Peng, Yongcheng Qi and Jingping Yang).
[4] (2012) Advances in complete mixability. Journal of Applied Probability, 49(2), 430-440 (with Giovanni Puccetti and Bin Wang).
[3] (2011) Jackknife empirical likelihood intervals for Spearman's rho. North American Actuarial Journal, 15(4), 475-486 (with Liang Peng).
[2] (2011) The complete mixability and convex minimization problems for monotone marginal densities. Journal of Multivariate Analysis, 102(10), 1344-1360 (with Bin Wang).
[1] (2009) A class of multivariate copulas with bivariate Frechet marginal copulas. Insurance: Mathematics and Economics, 45(1), 139-147 (with Yongcheng Qi and Jingping Yang).

Other Publications and Manuscripts

(2021) Discussion of 'Testing by betting: A strategy for statistical and scientific communication' by Glenn Shafer. Journal of the Royal Statistical Society Series A, 184(2), 463-464.
(2015) The most dangerous model: A natural benchmark for assessing model risk. Society of Actuaries Monograph: Enterprise Risk Management Symposium, 2015 (with John Major and Micah Woolstenhulme).



(2011) Sanguosha: the Royal Road (in Chinese). Publishing House of Electronics Industry, China. ISBN-9787121126833.