Optimization, Financial Engineering, Risk and Operations Management are fast evolving areas in Operations Research. Recent theoretical developments and newly found applications in those areas are vital to the future of our field and the Operations Research Society in general.

This special issue consists of ten articles, which can be loosely grouped into three broad subject areas that are also central to late Professor Duan Li’s lifelong research.

1 Optimization

  • In On Convexification for a Class of Global Optimization Problems, Qian Yan, Xin-Min Yang and Zhi-You Wu investigated the intrinsic relations between monotone functions and those that can be transformed into convex functions. Such links, aka hidden convexity, are crucial in designing efficient algorithms for global optimization, as Duan’s early works on the topic demonstrated.

  • In Newton-Type Optimal Thresholding Algorithms for Sparse Optimization Problems, Nan Meng and Yun-Bin Zhao studied Lasso-type sparse optimization models, where they established the convergence of Newton style methods under certain assumptions on the restricted isometry constant. One of the co-authors previously worked with Duan along this line of research.

  • In Cubic Regularization Methods with Second-Order Complexity Guarantee Based On a New Subproblem Reformulation, Ru-Jun Jiang, Zhi-Shuo Zhou and Zi-Rui Zhou elaborated on how the subproblem resulting from the cubic regularized Newton method can be solved, to the extent best possible.

  • In Binary Random Projections with Controllable Sparsity Patterns, Wen-Ye Li and Shu-Zhong Zhang showed that the classic Johnson–Lindenstrauss style bounds hold true even if the random projection matrices are restricted to be binary and sparse, instead of i.i.d. Gaussian. This approach has potentials for ample new applications in data processing, learning, and knowledge discovery.

2 Financial Engineering and Risk Modeling

  • In Risk and Potential: An Asset Allocation Framework with Applications to Robo-Advising, Xiang-Yu Cui, Duan Li, Xiao Qiao and Moris Strub (notably, Duan is a co-author) proposed a dynamic asset allocation system under a family of utility functions. These utilities are motivated by efforts to overcome issues and challenges that stem from the traditional mean-variance model.

  • In Time-Consistent Investment Strategies for a DC Pension Member with Stochastic Interest Rate and Stochastic Income, Li-hua Bian, Xing-Yi Li and Zhong-Fei Li developed two multi-period mean-variance model to study investment decisions for a defined contribution pension fund. Applying game theory and the extended Bellman equation, the authors derived explicit solutions to the time-consistent investment strategies and the efficient frontier and demonstrated the impact of stochastic interest rate and stochastic income on investment strategies.

  • In How is Systemic Risk Amplified by Three Typical Financial Networks, Jia-Li Ma, Shu-Shang Zhu and Xiao-Chuan Pang developed a model to study the systemic risk of a network of financial institutions tied together via inter-liability, portfolio overlapping and share cross-holding. The contagion dynamics over these channels due to external shocks are quantified analytically and also compared against simulation results.

  • In Survey on Multi-period Mean-Variance Portfolio Selection Model, Xiang-Yu Cui, Jian-Jun Gao, Xun Li and Yun Shi provided a tutorial-style overview on the dynamic mean-variance portfolio optimization model, focusing on some of the key issues, such as non-separation of mean and variance, and time inconsistency, touched upon earlier in this Preface.

3 Operations Management

  • In Price Competition in the Random Coefficient Attraction Choice Models with Linear Cost, Xiao-Yi Feng, Yang-Yang Xie and Hou-Min Yan studied the pricing game among competing retailers, focusing on how the randomness in cost will affect both price and profit in equilibrium. The study and analysis were carried out based on several consumer choice models.

  • In Inventory Policy and Heuristic for Long-Term Multi-product Perishable Inventory Routing Problem with Static Demand, Xi-Yi Chen, Jian-Bo Yang and Dong-Ling Xu studied an inventory routing problem, with the inventory being perishable, multi-product, and operating under a vendor-managed scheme. Based on insights to the problem structure garnered from numerical studies, the authors proposed a heuristic solution that appears to be near optimal.