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1. Leveraged Exchange-Traded Funds with Market Closure and Frictions

   https://doi.org/10.1287/mnsc.2022.4407  

   Dai, Min; Kou, Steven; Soner, H Mete; Yang, Chen (April 2023, Management Science)

   Although leveraged exchange-traded funds (ETFs) are popular products for retail investors, how to hedge them poses a great challenge to financial institutions. We develop an optimal rebalancing (hedging) model for leveraged ETFs in a comprehensive setting, including overnight market closure and market frictions. The model allows for an analytical optimal rebalancing strategy. The result extends the principle of “aiming in front of target” introduced by Gârleanu and Pedersen (2013) from a constant weight between current and future positions to a time-varying weight because the rebalancing performance is monitored only at discrete time points, but the rebalancing takes place continuously. Empirical findings and implications for the weekend effect and the intraday trading volume are also presented. This paper was accepted by Agostino Capponi, finance. Funding: M. Dai acknowledges support from the National Natural Science Foundation of China [Grant 12071333], the Hong Kong Polytechnic University [Grant P0039114], and the Singapore Ministry of Education [Grants R-146-000-243/306/311-114 and R-703-000-032-112]. H. M. Soner acknowledges partial support from the National Science Foundation [Grant DMS 2106462]. C. Yang acknowledges support from the Chinese University of Hong Kong [Grant 4055132 and a University Startup Grant]. Supplemental Material: Data and the online supplement are available at https://doi.org/10.1287/mnsc.2022.4407 . 

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2. A Riemannian Smoothing Steepest Descent Method for Non-Lipschitz Optimization on Embedded Submanifolds of Rn

   https://doi.org/10.1287/moor.2022.0286  

   Zhang, Chao; Chen, Xiaojun; Ma, Shiqian (August 2023, Mathematics of Operations Research)

   In this paper, we study the generalized subdifferentials and the Riemannian gradient subconsistency that are the basis for non-Lipschitz optimization on embedded submanifolds of [Formula: see text]. We then propose a Riemannian smoothing steepest descent method for non-Lipschitz optimization on complete embedded submanifolds of [Formula: see text]. We prove that any accumulation point of the sequence generated by the Riemannian smoothing steepest descent method is a stationary point associated with the smoothing function employed in the method, which is necessary for the local optimality of the original non-Lipschitz problem. We also prove that any accumulation point of the sequence generated by our method that satisfies the Riemannian gradient subconsistency is a limiting stationary point of the original non-Lipschitz problem. Numerical experiments are conducted to demonstrate the advantages of Riemannian [Formula: see text] [Formula: see text] optimization over Riemannian [Formula: see text] optimization for finding sparse solutions and the effectiveness of the proposed method. Funding: C. Zhang was supported in part by the National Natural Science Foundation of China [Grant 12171027] and the Natural Science Foundation of Beijing [Grant 1202021]. X. Chen was supported in part by the Hong Kong Research Council [Grant PolyU15300219]. S. Ma was supported in part by the National Science Foundation [Grants DMS-2243650 and CCF-2308597], the UC Davis Center for Data Science and Artificial Intelligence Research Innovative Data Science Seed Funding Program, and a startup fund from Rice University. 

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3. A Primal-Dual Approach to Constrained Markov Decision Processes with Applications to Queue Scheduling and Inventory Management

   https://doi.org/10.1287/mnsc.2022.03736  

   Chen, Yi; Dong, Jing; Wang, Zhaoran; Zhang, Chuheng (May 2025, Management Science)

   In many operations management problems, we need to make decisions sequentially to minimize the cost, satisfying certain constraints. One modeling approach to such problems is the constrained Markov decision process (CMDP). In this work, we develop a data-driven primal-dual algorithm to solve CMDPs. Our approach alternatively applies regularized policy iteration to improve the policy and subgradient ascent to maintain the constraints. Under mild regularity conditions, we show that the algorithm converges at rate [Formula: see text], where T is the number of iterations, for both the discounted and long-run average cost formulations. Our algorithm can be easily combined with advanced deep learning techniques to deal with complex large-scale problems with the additional benefit of straightforward convergence analysis. When the CMDP has a weakly coupled structure, our approach can further reduce the computational complexity through an embedded decomposition. We apply the algorithm to two operations management problems: multiclass queue scheduling and multiproduct inventory management. Numerical experiments demonstrate that our algorithm, when combined with appropriate value function approximations, generates policies that achieve superior performance compared with state-of-the-art heuristics. This paper was accepted by Baris Ata, stochastic models and simulation. Funding: Y. Chen was supported by the Hong Kong Research Grants Council, Early Career Scheme Fund [Grant 26508924], and partially supported by a grant from the National Natural Science Foundation of China [Grant 72495125]. J. Dong was supported by the National Science Foundation [Grant 1944209]. Supplemental Material: The data files are available at https://doi.org/10.1287/mnsc.2022.03736 . 

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4. Corrigendum to New Phytologist 230 (2021), 2261–2274, doi: 10.1111/nph. 17152.

   https://doi.org/10.1111nph.17597  

   Wang, J.; Guo, X.; Xiao, Q.; Zhu, J.; Cheung, A.Y.; Yuan, L.; Vierling, E.; Xu. S. (August 2021, New phytologist)

   Since its publication, the authors of Wang et al. (2021) have brought to our attention an error in their article. A grant awarded by the National Science Foundation (grant no. MCB 1817985) to author Elizabeth Vierling was omitted from the Acknowledgements section. The correct Acknowledgements section is shown below. Acknowledgements We thank Suiwen Hou (Lanzhou University) and Zhaojun Ding (Shandong University) for providing the seeds used in this study. We thank Xiaoping Gou (Lanzhou University) and Ravishankar Palanivelu (University of Arizona) for critically reading the manuscript and for suggestions regarding the article. This work was supported by grants from National Natural Science Foundation of China (31870298) to SX, the US Department of Agriculture (USDA-CSREES-NRI-001030) and the National Science Foundation (MCB 1817985) to EV, and the Youth 1000-Talent Program of China (A279021801) to LY. 

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5. Polynomial Voting Rules

   https://doi.org/10.1287/moor.2023.0080  

   Tang, Wenpin; Yao, David D. (February 2024, Mathematics of Operations Research)

   We propose and study a new class of polynomial voting rules for a general decentralized decision/consensus system, and more specifically for the proof-of-stake protocol. The main idea, inspired by the Penrose square-root law and the more recent quadratic voting rule, is to differentiate a voter’s voting power and the voter’s share (fraction of the total in the system). We show that, whereas voter shares form a martingale process that converges to a Dirichlet distribution, their voting powers follow a supermartingale process that decays to zero over time. This prevents any voter from controlling the voting process and, thus, enhances security. For both limiting results, we also provide explicit rates of convergence. When the initial total volume of votes (or stakes) is large, we show a phase transition in share stability (or the lack thereof), corresponding to the voter’s initial share relative to the total. We also study the scenario in which trading (of votes/stakes) among the voters is allowed and quantify the level of risk sensitivity (or risk aversion) in three categories, corresponding to the voter’s utility being a supermartingale, a submartingale, and a martingale. For each category, we identify the voter’s best strategy in terms of participation and trading. Funding: W. Tang gratefully acknowledges financial support through the National Science Foundation [Grants DMS-2113779 and DMS-2206038] and through a start-up grant at Columbia University. D. D. Yao’s work is part of a Columbia–City University/Hong Kong collaborative project that is supported by InnoHK Initiative, the Government of Hong Kong Special Administrative Region, and the Laboratory for AI-Powered Financial Technologies. 

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