Optimal lockdown in altruistic economies

The recent COVID-19 crisis has revealed the urgent need to study the impact of an infectious disease on market economies and provide adequate policy recommendations. The present paper studies the optimal lockdown policy in a dynamic general equilibrium model where households are altruistic and they care about the share of infected individuals. The spread of the disease is modeled here using SIS dynamics, which implies that recovery does not confer immunity. To avoid non-convexity issues, we assume that the lockdown is constant in time. This strong assumption allows us to provide analytical solutions. We find that the zero lockdown is efficient when agents do not care about the share of infected, while a positive lockdown is recommended beyond a critical level of altruism. Moreover, the lockdown intensity increases in the degree of altruism. Our robust analytical results are illustrated by numerical simulations, which show, in particular, that the optimal lockdown never trespasses 60% and that eradication is not always optimal.     

绍兴市土地利用时空变化研究

[目的]探讨经济发达地区土地利用变化时空规律,为城市发展提供合理土地利用政策,同时优化土地利用结构以支持经济可持续发展。[方法]通过遥感影像获取长时间序列的土地利用数据,探讨近30多年来绍兴市的土地利用变化,进一步利用土地利用动态变化模型,对绍兴市土地利用变化过程、趋势、变化轨迹进行了深入分析。[结果](1)绍兴市土地利用在1980~2000年相对稳定,在2000年后变化强度逐年增强,2005~2015年土地利用转化量增多和类型多样。绍兴市东北部平原和县区核心区域是经济发达地区土地利用变化的活跃区域,主要是其他类型土地向建设用地转移;(2)1980~2015年绍兴市土地利用变化轨迹主要受到人口增长和GDP增长的影响。[结论]城市化的发展和人口的迅速增长,使城市人口和土地面积迅速增加,造成城市边缘的农业用地转化成了建设用地。经济的发展、科技的进步及政府政策的制定,改变了人们的生活和工作方式,进而影响土地利用类型。     

Integer programming on domains containing inseparable ordered pairs

Using the integer programming approach introduced by Sethuraman et al. (2003), we extend the analysis of the preference domains containing an inseparable ordered pair, initiated by Kalai and Ritz (1978). We show that these domains admit not only Arrovian social welfare functions “without ties,” but also Arrovian social welfare functions “with ties,” since they satisfy the strictly decomposability condition introduced by Busetto et al. (2015). Moreover, we go further in the comparison between Kalai and Ritz (1978)’s inseparability and Arrow (1963)’s single-peak restrictions, showing that the former condition is more “respectable,” in the sense of Muller and Satterthwaite (1985).     

Collective mental accounting: an integrated behavioural portfolio selection model for multiple mental accounts

We propose a behavioural portfolio selection model called collective mental accounting (CMA), which integrates all mental sub-portfolios (mental accounts) in one mathematical model. Moreover, this study contributes to the literature of behavioural portfolio selection in three further ways: first, the CMA model can determine the proportions of wealth allocated to each mental sub-portfolio with and without input from the investor. Second, unlike other mental accounting models (MA), in CMA it is possible to define constraints on total asset holdings such as short-selling, and cardinality constraints. Third, in order to make CMA more tractable and mathematically elegant, we obtain a semi-definite programming representation of the model. We also present a numerical example to investigate the effects of short-selling constraints as well as to compare the portfolio recommendations, utility functions, feasibility, and optimality of the CMA and MA models. The results reveal that although both models’ solutions are mean-variance efficient, CMA outperforms MA in terms of behavioural efficient frontier and utility functions.     

采用航迹特征的智能机型识别

针对空战目标识别中机型自动识别比较困难的问题，提出了采用航迹特征的智能目标识别方法。利用卷积神经网络（Convolutional Neural Network，CNN）分层学习特征的能力，训练CNN算法模型自动地从航迹数据中学习有用的特征并分类。利用沿海实地采集的15个类别的飞机航迹数据，经一系列数据预处理后作为智能识别算法的训练和测试数据，在验证实验中描述了算法网络的相关配置,对比了CNN与其他分类器的识别结果。实验结果表明，CNN具有很好的识别性能。     

Economic interpretations of DEA

Research on productive efficiency at the firm level has developed as an important and active strand of research the last decades, both within operations research, management science and economics. Two apparently different definitions of efficiency are examined, but it is shown that when both estimation methods are based on solving linear programming problems the definitions of efficiency are identical. The purpose of the paper is to give the basic ideas of efficiency analyses using DEA as a tool for researchers not so familiar with efficiency analysis and DEA. The concept of shadow prices is given special attention.     

基于效应的随机灰规划模型和应用

为了解决同时含有随机因素和灰色因素的不确定规划问题,通过结合区间灰数所属区间两个端点的随机性,给出随机区间灰数和随机区间灰函数的定义,提出了随机灰规划模型。通过综合效应函数理论用随机变量期望值和方差综合量化表示灰数所属区间的两个端点值。应用该理论对综合量化后的两个端点值继续进行综合量化,从而将随机灰规划转化为确定型规划问题。应用遗传算法进行求解。通过综合效应函数的理念,综合随机变量的期望和方差,同时综合区间灰数的区间因素,将随机灰规划数学模型转化为确定型规划模型即基于效应的随机灰规划模型。通过选取不同的综合效应函数,得到了关于不同决策意识下的随机灰规划的最优解。这个方法可为决策者进行不确定决策提供参考。     

Optimal investment with vintage capital: Equilibrium distributions

The paper concerns the study of equilibrium points, or steady states, of economic systems arising in modeling optimal investment with vintage capital, namely, systems where all key variables (capitals, investments, prices) are indexed not only by time but also by age. Capital accumulation is hence described as a partial differential equation (briefly, PDE), and equilibrium points are in fact equilibrium distributions in the variable of ages. A general method is developed to compute and study equilibrium points of a wide range of infinite dimensional, infinite horizon, optimal control problems. We apply the method to optimal investment with vintage capital, for a variety of data, deriving existence and uniqueness of equilibrium distribution, as well as analytic formulas for optimal controls and trajectories in the long run. The examples suggest that the same method can be applied to other economic problems displaying heterogeneity. This shows how effective the theoretical machinery of optimal control in infinite dimension is in computing explicitly equilibrium distributions. To this extent, the results of this work constitute a first crucial step towards a thorough understanding of the behavior of optimal paths in the long run.