Table of Content

30 September 2022, Volume 10 Issue 3

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Preface:Special Issue on Optimization,Financial Engineering,Risk and Operations Management

David Yao, Shu-Zhong Zhang, Xun-Yu Zhou

2022, 10(3):  423-425.  doi:10.1007/s40305-022-00426-4

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On Convexification for a Class of Global Optimization Problems

Qian Yan, Xin-Min Yang, Zhi-You Wu

2022, 10(3):  427-446.  doi:10.1007/s40305-021-00379-0

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In this paper,firstly,we give a counterexample to point out there exist deficiencies in our previous works (Wu et al.in J Glob Optim 31:45-60,2005).In addition,we improve the corresponding results.Finally,an example is presented to illustrate how a monotone non-convex optimization problem can be transformed into an equivalent convex minimization problem.

Newton-Type Optimal Thresholding Algorithms for Sparse Optimization Problems

Nan Meng, Yun-Bin Zhao

2022, 10(3):  447-469.  doi:10.1007/s40305-021-00370-9

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Sparse signals can be possibly reconstructed by an algorithm which merges a traditional nonlinear optimization method and a certain thresholding technique.Different from existing thresholding methods,a novel thresholding technique referred to as the optimal k-thresholding was recently proposed by Zhao (SIAM J Optim 30(1):31-55,2020).This technique simultaneously performs the minimization of an error metric for the problem and thresholding of the iterates generated by the classic gradient method.In this paper,we propose the so-called Newton-type optimal k-thresholding (NTOT) algorithm which is motivated by the appreciable performance of both Newton-type methods and the optimal k-thresholding technique for signal recovery.The guaranteed performance (including convergence) of the proposed algorithms is shown in terms of suitable choices of the algorithmic parameters and the restricted isometry property (RIP) of the sensing matrix which has been widely used in the analysis of compressive sensing algorithms.The simulation results based on synthetic signals indicate that the proposed algorithms are stable and efficient for signal recovery.

Cubic Regularization Methods with Second-Order Complexity Guarantee Based on a New Subproblem Reformulation

Ru-Jun Jiang, Zhi-Shuo Zhou, Zi-Rui Zhou

2022, 10(3):  471-506.  doi:10.1007/s40305-022-00398-5

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Thecubicregularization (CR) algorithmhasattractedalotofattentionsintheliterature in recent years.We propose a new reformulation of the cubic regularization subproblem.The reformulation is an unconstrained convex problem that requires computing the minimum eigenvalue of the Hessian.Then,based on this reformulation,we derive a variant of the (non-adaptive) CR provided a known Lipschitz constant for the Hessian and a variant of adaptive regularization with cubics (ARC).We show that the iteration complexity of our variants matches the best-known bounds for unconstrained minimization algorithms using first-and second-order information.Moreover,we show that the operation complexity of both of our variants also matches the state-of-the-art bounds in the literature.Numerical experiments on test problems from CUTEst collection show that the ARC based on our new subproblem reformulation is comparable to the existing algorithms.

Binary Random Projections with Controllable Sparsity Patterns

Wen-Ye Li, Shu-Zhong Zhang

2022, 10(3):  507-528.  doi:10.1007/s40305-021-00387-0

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Random projection is often used to project higher-dimensional vectors onto a lowerdimensional space,while approximately preserving their pairwise distances.It has emerged as a powerful tool in various data processing tasks and has attracted considerable research interest.Partly motivated by the recent discoveries in neuroscience,in this paper we study the problem of random projection using binary matrices with controllable sparsity patterns.Specifically,we proposed two sparse binary projection models that work on general data vectors.Compared with the conventional random projection models with dense projection matrices,our proposed models enjoy significant computational advantages due to their sparsity structure,as well as improved accuracies in empirical evaluations.

Risk and Potential:An Asset Allocation Framework with Applications to Robo-Advising

Xiang-Yu Cui, Duan Li, Xiao Qiao, Moris S. Strub

2022, 10(3):  529-558.  doi:10.1007/s40305-022-00400-0

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We propose a novel dynamic asset allocation framework based on a family of mean-variance-induced utility functions that alleviate the non-monotonicity and timeinconsistency problems of mean-variance optimization.The utility functions are motivated by the equivalence between the mean-variance objective and a quadratic utility function.Crucially,our framework differs from mean-variance analysis in that we allow different treatment of upside and downside deviations from a target wealth level.This naturally leads to a different characterization of possible investment outcomes below and above a target wealth as risk and potential.Our proposed asset allocation framework retains two attractive features of mean-variance optimization:an intuitive explanation of the investment objective and an easily computed optimal strategy.We establish a semi-analytical solution for the optimal trading strategy in our framework and provide numerical examples to illustrate its behavior.Finally,we discuss applications of this framework to robo-advisors.

Time-Consistent Investment Strategies for a DC Pension Member with Stochastic Interest Rate and Stochastic Income

Li-Hua Bian, Xing-Yi Li, Zhong-Fei Li

2022, 10(3):  559-577.  doi:10.1007/s40305-021-00386-1

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This paper studies two multi-period mean-variance investment problems for a DC pension member before and after retirement.At any time,the pension manager can invest in a risk-free asset and multi-risky assets.Before retirement,the manager tries to optimize the mean-variance utility of the wealth in the member's pension account at retirement.At retirement,the pension account wealth (or part of it) is used to purchase a paid-up annuity.After retirement,the manager has to pay the guaranteed annuity,continues to invest,and aims to optimize the mean-variance utility of the terminal wealth at a fix future time,to satisfy the pension member's heritage and life needs in the next stage.Interest rate risk and income risk are introduced.Applying the game theory and the extended Bellman equation,the time-consistent investment strategies and the efficient frontiers before and after retirement are obtained explicitly.Obtained results indicate that the stochastic interest rate and the stochastic income have essential effects on the investment strategies.

How is Systemic Risk Amplified by Three Typical Financial Networks

Jia-Li Ma, Shu-Shang Zhu, Xiao-Chuan Pang

2022, 10(3):  579-598.  doi:10.1007/s40305-021-00389-y

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Financial institutions are typically tied together via inter-liability,portfolio overlapping and share cross-holding.These connections among financial institutions constitute the three most common financial networks,which may lead to financial risk contagion and even systemic risk when some institutions suffer shock.In this paper,firstly,for a given shock,we prove the existence of the equilibrium clearing vector of the financial system characterized by these three typical financial networks.Then,we mathematically derive an analytical form to show how these three contagion channels jointly affect and amplify the loss of the non-default institutions,and explain how the lack of liquidity of external investment assets exacerbates the loss caused by portfolio overlapping.Finally,the influence of the characteristics of financial network on risk contagion is verified by numerical simulation.These results provide basis for understanding the financial systemic risk contagion in the real world.

Survey on Multi-period Mean-Variance Portfolio Selection Model

Xiang-Yu Cui, Jian-Jun Gao, Xun Li, Yun Shi

2022, 10(3):  599-622.  doi:10.1007/s40305-022-00397-6

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Due to the non-separability of the variance term,the dynamic mean-variance (MV) portfolio optimization problem is inherently difficult to solve by dynamic programming.Li and Ng (Math Finance 10(3):387-406,2000) and Zhou and Li (Appl Math Optim 42(1):19-33,2000) develop the pre-committed optimal policy for such a problem using the embedding method.Following this line of research,researchers have extensively studied the MV portfolio selection model through the inclusion of more practical investment constraints,realistic market assumptions and various financial applications.As the principle of optimality no longer holds,the pre-committed policy suffers from the time-inconsistent issue,i.e.,the optimal policy computed at the intermediate time t is not consistent with the optimal policy calculated at any time before time t.The time inconsistency of the dynamic MV model has become an important yet challenging research topic.This paper mainly focuses on the multi-period mean-variance (MMV) portfolio optimization problem,reviews the essential extensions and highlights the critical development of time-consistent policies.

Price Competition in the Random Coefficient Attraction Choice Models with Linear Cost

Xiao-Yi Feng, Yang-Yang Xie, Hou-Min Yan

2022, 10(3):  623-658.  doi:10.1007/s40305-021-00366-5

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We study the pricing game between competing retailers under various random coefficient attraction choice models.We characterize existence conditions and structure properties of the equilibrium.Moreover,we explore how the randomness and cost parameters affect the equilibrium prices and profits under multinomial logit (MNL),multiplicative competitive interaction (MCI) and linear attraction choice models.Specifically,with bounded randomness,for the MCI and linear attraction models,the randomness always reduces the retailer's profit.However,for the MNL model,the effect of randomness depends on the product's value gap.For high-end products (i.e.,whose value gap is higher than a threshold),the randomness reduces the equilibrium profit,and vice versa.The results suggest high-end retailers in MNL markets exert more effort in disclosing their exact product performance to consumers.We also reveal the effects of randomness on retailers'pricing decisions.These results help retailers in making product performance disclosure and pricing decisions.

Inventory Policy and Heuristic for Long-Term Multi-product Perishable Inventory Routing Problem with Static Demand

Xi-Yi Chen, Jian-Bo Yang, Dong-Ling Xu

2022, 10(3):  659-683.  doi:10.1007/s40305-021-00390-5

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This work considers a long-term Perishable Inventory Routing Problem with multiple products,static demand,and single vehicle,in the setting of Vendor Managed Inventory.By analyzing the optimal solutions of long-term cases that can be solved in Python+Gurobi within 2 h,we capture some patterns of optimal solutions.Utilizing these patterns,experiments show that under certain conditions,the mathematical models of multi-product problems could be simplified to single-product problems,which have the same optimal solutions while taking less time to solve.Managerial insights were generated that for products with static demand in the long term,delivery should be arranged at the store level rather than at the product level.Products in the same store should have the same delivery pattern,no matter how different the unit holding costs are.By further analyzing the optimal solutions of the simplified models,we find that optimal value will stabilize in the long term,and the optimal solution is very close to the solution point where total inventory holding cost and transportation cost are close.Based on these findings,we have developed a heuristic that always provides optimal or close-to-optimal solutions with far less computational time,compared with Python+Gurobi.