Welcome to Ruodu Wang's Homepage

Banff, Canada, 2013

Publications and Manuscripts

Pre-publication Manuscripts

Latest papers posted online

     Please, critical comments on these papers are very much appreciated.
(2020) The directional optimal transport (with Marcel Nutz).
(2019) True and false discoveries with e-values (with Vladimir Vovk).
(2019) Distortion riskmetrics on general spaces (with Qiuqi Wang and Yunran Wei).
(2019) Self-consistency, subjective pricing, and a theory of credit rating (with Nan Guo, Steven Kou and Bin Wang).
(2019) Combining e-values and p-values (with Vladimir Vovk).
(2019) PELVE: Probability equivalent level of VaR and ES (with Hengxin Li).
(2019) Inf-convolution and optimal allocations for tail risk measures (with Fangda Liu and Linxiao Wei).
(2019) Distributional transforms, probability distortions, and their applications (with Peng Liu and Alexander Schied).
(2018) Risk functionals with convex level sets (with Yunran Wei).
(2018) Robustness in the optimization of risk measures (with Paul Embrechts and Alexander Schied).
(2018) Scenario-based risk evaluation (with Johanna Ziegel).
(2018) Characterizing optimal allocations in quantile-based risk sharing (with Yunran Wei).
(2017) Competitive equilibria in a comonotone market (with Tim Boonen and Fangda Liu).
(2017) A model-free continuum of degrees of risk aversion (with Tiantian Mao).

Refereed Journal Articles


[57] (2020) A theory for measures of tail risk. Mathematics of Operations Research, forthcoming (with Fangda Liu).
[56] (2020) An axiomatic foundation for the Expected Shortfall. Management Science, forthcoming (with Ricardas Zitikis).
[55] (2020) Risk aversion in regulatory capital principles. SIAM Journal on Financial Mathematics, forthcoming (with Tiantian Mao).
[54] (2020) Combining p-values via averaging. Biometrika, forthcoming (with Vladimir Vovk).
[53] (2020) Characterization, robustness and aggregation of signed Choquet integrals. Mathematics of Operations Research, forthcoming (with Yunran Wei and Gordon Willmot).
[52] (2020) Quantile-based risk sharing with heterogeneous beliefs. Mathematical Programming, forthcoming (with Paul Embrechts, Haiyan Liu and Tiantian Mao).
[51] (2020) Negative dependence in matrix arrangement problems. Annals of Operations Research, forthcoming (with Edgars Jakobsons).


[50] (2020) Is the inf-convolution of law-invariant preferences law-invariant? Insurance: Mathematics and Economics, 91, 144-154 (with Peng Liu and Linxiao Wei).
[49] (2020) Weak comonotonicity. European Journal of Operational Research, 282, 386-397 (with Ricardas Zitikis).
[48] (2020) Convex risk functionals: representation and applications. Insurance: Mathematics and Economics, 90, 66-79 (with Jun Cai, Christiane Lemieux and Fangda Liu).


[47] (2019) Sums of standard uniform random variables. Journal of Applied Probability, 56(3), 918-936 (with Tiantian Mao and Bin Wang).
[46] (2019) Dual utilities on risk aggregation under dependence uncertainty. Finance and Stochastics, 23(4), 1025-1048 (with Zuoquan Xu and Xunyu Zhou).
[45] (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).
[44] (2019) Centers of probability measures without the mean. Journal of Theoretical Probability, 32(3), 1482-1501 (with Giovanni Puccetti, Pietro Rigo and Bin Wang).
[43] (2019) Distributional compatibility for change of measures. Finance and Stochastics, 23(3), 761-794 (with Jie Shen, Yi Shen and Bin Wang).
[42] (2019) Compatible matrices of Spearman's rank correlation. Statistics and Probability Letters, 151, 67-72 (with Bin Wang and Yuming Wang).
[41] (2019) Random locations of periodic stationary processes. Stochastic Processes and their Applications, 129(3), 878-901 (with Jie Shen and Yi Shen).


[40] (2018) Quantile-based risk sharing. Operations Research, 66(4), 936-949 (with Paul Embrechts and Haiyan Liu).
[39] (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).
[38] (2018) Asymptotic equivalence of risk measures under dependence uncertainty. Mathematical Finance, 28(1), 29-49 (with Jun Cai and Haiyan Liu).


[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

Conference proceedings

(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.