Robust Markowitz mean‐variance portfolio selection under ambiguous covariance matrix

This paper studies a robust continuous‐time Markowitz portfolio selection problem where the model uncertainty affects the covariance matrix of multiple risky assets. This problem is formulated into a min–max mean‐variance problem over a set of nondominated probability measures that is solved by a McKean–Vlasov dynamic programming approach, which allows us to characterize the solution in terms of a Bellman–Isaacs equation in the Wasserstein space of probability measures. We provide explicit solutions for the optimal robust portfolio strategies and illustrate our results in the case of uncertain volatilities and ambiguous correlation between two risky assets. We then derive the robust efficient frontier in closed form, and obtain a lower bound for the Sharpe ratio of any robust efficient portfolio strategy. Finally, we compare the performance of Sharpe ratios for a robust investor and for an investor with a misspecified model.     

基于改进Dijkstra算法的最短路算法

Dijkstra算法是求解最短路径问题的经典算法。在现如今的城市交通网络中,经常需要寻求两个地点之间的最短距离,减少运输时间。本文将Dijkstra算法与C语言相结合,对Dijkstra算法进行改进,根据实际网络图的情况,建立了相应的数学模型,运用C语言编程,在给定的网络图中,实现了只需确定起始点和终点,就可以直接输出最短路径和最短距离的功能。在有多个相同最短路径的情况下,会将多个最短路径一起输出,在搜索到终点时,立即跳出,结束循环。在一般情况下,无需对所有点进行迭代,提高了效率。这种方法可以应用到现在的物流运输中,以此来节约时间,降低成本。     

关于节水型园林设计规划的思路构架和分析

随着我国社会主义现代化建设和城市化建设进程不断加快,人们对自然资源的过渡开发与利用,带来了诸多环境问题。为提高我国园林生态水平,相关部门应认识到我国园林用水的现状,并积极开发和设计节水型园林,大力推广节水灌溉,优化各类植物配置,加强园林人力资源管理,提高人们的节水意识,从而为建设节水型园林奠定坚实的基础。     

Integrated planning for product selection,shelf-space allocation,and replenishment decision with elasticity and positioning effects

As the retail industry is growing larger and more diversified, retailers' decisions about product selection, shelf-space-allocation, and replenishment become more important and challenging. This paper is to present a model for shelf-space allocation with product selection and replenishment decisions to maximize the retailer's profit. The model is based on a two-dimensional display space in which all shelves and products have widths and heights and includes factors that influence demand for each product, such as space and cross-space elasticities and positioning effects. The integrated model presented is mixed-integer non-linear programming (MINLP) because the demand function is non-convex. This research proposes two heuristic algorithms (tabu search and genetic) to solve the MINLP problem. The results show the effectiveness and efficiency of these algorithms by comparing the outputs to the MINLP optimal solution for small data sets and comparing the algorithm performances for large data sets. The solution methodologies expect to support a simultaneous decision-making process for retailers to maximize their revenue.     

Internal habits formation and optimality

In a very influential model with internal habits, Carroll et al., (2017, 2000), establish that an increase in economic growth may cause a positive change in savings. The optimality of this result, and of many other contributions using a similar framework, has been questioned by some authors who have observed that the parametrization used in these models always implies a utility function not jointly concave in consumption and habits. In this paper, we revisit the optimality issue and, using advanced techniques in Dynamic Programming, we answer the following long-standing open questions: (i) Is the solution found in Carroll et al., (2017, 2000) optimal? (ii) Is it also unique or do other optimal solutions exist?     

基于粒子群算法下的交叉口信号配时优化

为了合理地优化交叉口信号配时,通过分析交叉口的评价指标,建立了以车辆的平均延误、停车次数最小、交叉口整体通行能力最大、各相位有效绿灯时间和交叉口周期时长作为约束条件的数学模型。并通过改进前人研究基础上的动态加权系数,将多目标的非线性优化问题转化为单一目标的非线性规划问题,为了得出更科学稳定的解,提出了改善粒子群算法系统稳定性的2种方法,并将其与粒子群算法结合起来。然后以Matlab为求解工具,结合临邑市某一交叉口实例进行求解分析。最后的结果表明,在使用改进后的粒子群算法进行优化后交叉口通行能力较之现状提升了9%,延误下降了28%,停车次数下降了9%,且各项优化结果均优于Webster,改进后的算法在程序中运行300代,到216代才开始收敛,而未改进的算法稳定性较差,优化结果和收敛曲线则随着实验次数的变化而变化,最后的结论证明了该算法和模型的可靠性。     

A simple characterisation for sustained growth

This article considers an inter-temporal optimisation problem in a general form and gives conditions ensuring the convergence to infinity of the economy. These conditions can be easily verified and applied for a large class of problems in the literature. Some applications for different economies are given as illustrative examples.     

Inference for large financial systems

We treat the parameter estimation problem for mean‐field models of large interacting financial systems such as the banking system and a pool of assets held by an institution or backing a security. We develop an asymptotic inference approach that addresses the scale and complexity of such systems. Harnessing the weak convergence results developed for mean‐field financial systems in the literature, we construct an approximate likelihood for large systems. The approximate likelihood has a conditionally Gaussian structure, enabling us to design an efficient numerical method for its evaluation. We provide a representation of the corresponding approximate estimator in terms of a weighted least‐squares estimator, and use it to analyze the large‐system and large‐sample behavior of the estimator. Numerical results for a mean‐field model of systemic financial risk highlight the efficiency and accuracy of our estimator.     

Heterogeneity and netting efficiency under central clearing: A stochastic network analysis

This paper examines the effect of heterogeneity in clearing members’ exposure management practices under central clearing. Our network model specifies the dynamics of prenetted interbank exposures to shape interdependent exposure distributions beyond normality. Employing over-the-counter derivatives market data from the U.S. Office of the Comptroller of the Currency, our simulation results indicate that heterogeneity in bank-to-bank exposure dynamics is systemically desirable, while the entire system benefits more from the central clearing in more homogeneous environments. Policymakers should incentivize individual clearing members to enhance resiliency and stability in counterparty exposure management to maximize netting efficiency under central clearing.     

Robust consumption‐investment problem under CRRA and CARA utilities with time‐varying confidence sets

We consider a robust consumption‐investment problem under constant relative risk aversion and constant absolute risk aversion utilities. The time‐varying confidence sets are specified by Θ, a correspondence from [0, T] to the space of the Lévy triplets, and describe a priori drift, volatility, and jump information. For each possible measure, the log‐price processes of stocks are semimartingales, and the triplet of their differential characteristics is almost surely a measurable selector from the correspondence Θ. By proposing and investigating the global kernel, an optimal policy and a worst‐case measure are generated from a saddle point of the global kernel, and they constitute a saddle point of the objective function.