宏观经济分布参数系统的临界值问题

本文把经济系统作为一类生灭过程来考虑 .应用人口控制论和森林系统的成功经验 ,研究经济系统的临界值问题 .首先 ,基于实际的经济分析、预测模型 ,在宏观层次上建立经济系统的控制模型 .连续模型便于理论研究 ,离散模型便于计算机仿真 .然后在这个控制模型的基础上 ,寻找使国民经济持续发展所需要的最小资产积累率表达形式 .本文得到的理论值将帮助我们更深刻地理解经济系统     

固定资产投资系统的稳定性分析及最优控制问题

给出带有时滞的一类固定资产模型，此模型为含有非局部和时滞边界条件的分布参数系统。通过Lyapunov函数，对系统的稳定性进行了分析，给出系统稳定的充分条件，然后，讨论了积累率的最优控制问题。根据Banach空间的一些理论，证明了其最优解的存在唯一性。     

具有食饵避难的Leslie-Gower最优税收模型分析

建立了发生食饵避难的Leslie-Gower捕食与被捕食系统模型,考虑对捕食种群进行有选择捕获.通过控制税收量加以管理来保护渔业资源不被过渡开发,且讨论了系统平衡点的存在性和稳定性,运用Pontryagin最大值原理得到了达到最优税收量的最优平衡解.     

带有时滞中性技术进步资产投资系统的最优控制分析

对一类带有时滞的非线性中性技术进步的资产投资系统的资产积累率的最优控制问题进行了讨论,运用积分方程和Banach理论,得到了最优解的存在唯一性.     

国民经济中的最优积累率

本文建立数学模型研究国民经济中的最优积累率的问题 ,否定了劳动力按指数增长的假设 ,得到了更加符合实际情况的结论 ,推广了现有文献中的结果 .     

不完全信息的非平稳MDP平均模型

本文考虑的是可数状态空间不完全信息的非平衡ＭＤＰ平均模型，借助于模型的转化，建立了不完全信息的非平衡ＭＤＰ平均模型的最优方程，并进一步给出了最优方程的解及ε（〉，０）－最优策略存在的充分条件。     

两大部类持续扩大再生产的优化

基于经典的马克思两大部类社会再生产公式,建立了离散确定型的持续扩大再生产的优化问题的动态规划模型.在生产资料部类的不变资本产出率高于另一部类的条件下,动态规划的指标函数是作为决策变量的生产资料部类积累率的单调函数,因而可以使用逆序解法或者顺序解法,获得唯一的最优策略和最优指标函数.借助《资本论》中的一个举例,计算验证了最优解.     

几类最优性问题的充分性条件及其在我国最优积累率问题中的应用

对于最优控制问题的无穷限积分性能泛函、末端极限性能泛函和性能泛函中显含控制函数的情形,本文给出韭证明它们最优性问题的充分性条件。文末还给出一个它们在我国的最优积累率问题中的应用例子。     

融合空间扩散与等级结构的种群系统的最优收获控制

分析一类基于个体等级差异和空间扩散的种群模型的最优收获控制问题,系统演化模型由二阶偏微分积分方程表征.运用Aubin引理和极值化序列方法建立了最优解的存在性,借助法锥理论和共轭系统技巧给出了最优控制器的特征刻画.所获成果为实际应用奠定基础.     

两大部类再生产最优平衡增长的形成路径

两大部类再生产最优平衡增长的形成路径,是社会再生产从非平衡的一般增长状态转换到最优平衡增长状态的特殊增长轨迹.基于马克思社会再生产公式,利用当年生产生产资料的部类积累率决定下一年两大部类比例的单调函数关系,推导并证明了生产生产资料的部类优先积累能够导致两大部类比例收敛,从而两大部类再生产形成最优平衡增长.由此阐明了生产生产资料的部类优先积累是两大部类再生产最优平衡增长的形成路径.借助《资本论》中的一个举例,计算验证了这样的形成路径.     

不确定环境下具有减排配额的PM2.5治理博弈与税收决策

由于雾霾治理遵循浓度控制原则,且跨界传输因子存在异质性,因此,要使各地区在追求减排成本最小化时又达到减排指标,中央政府仅实施税收政策并不能满足其收支平衡条件。基于此,本文将税收与减排配额相结合,以期实现中央政府收支平衡与优化各地区治理成本的双重目标。同时,本文以京津冀地区雾霾治理为实证分析对象,验证了具有减排配额的税收决策具有可实施性。     

汇率变动对进出口影响的实证分析

本文研究了汇率变动对中国进出口的影响,在间接标价法下对论文中所用到的汇率贬值改善国际收支的三个必要条件给出了结论和证明(弹性法);在经济理论及经验研究的基础上,建立了论文中所需要的所有模型并且根据模型对相关经济问题利用现代计量经济学方法进行了实证研究.通过实证研究我们得到的结论是:我国满足汇率贬值改善国际收支的必要条件;出口增加有助于GDP的增长,进口增加对GDP的影响是反向的且随着进口增加这种影响逐渐减弱最终趋于零.     

Differential games results for military expenditures of unequal antagonists in the third world

In developing countries, resources are scarce and military expenditure can hinder development. Thus, allocation of resources between defense and civilian sectors is an important decision. Also, in developing countries, most defense spending is related to regional conflicts where one frequently encounters unequal participants (e.g., India—Pakistan, Iran—Iraq, China—Vietnam). In such situations, the bigger power aspires to be the regional leader, and allocates resources to the defense sector accordingly.

A model incorporating the two above mentioned stylized facts has been examined by Deger and Sen [1] in two different ways. They first look at the problem from a single country's point of view, which takes the other's reaction function as given, and show that in the long run, military expenditures and armament stock levels will exhibit stability. Next, they formulate the problem as a noncooperative differential game in which each country assumes knowledge of the other country's welfare function, and conjecture that stability will once again be exhibited. The present paper attempts to verify that conjecture using a simplifying assumption which is necessary to be able to qualitatively solve the problem. This simplifying assumption does not change the results for the optimal control models, however, the conjecture is not valid for the simplified differential game model.     

Optimal control of harvesting coupled with boundary control in a predator—prey system

We consider boundary control and control via harvesting in a parabolic predator—prey system for a bounded region. The boundary control depicts the relationship between the boundary environment and the possibly harmful species. In addition, a proportion of the predator is harvested for profit. We choose to maximize the objective functional which incorporates the amount of the prey and the revenue of harvesting of the predator less the economic cost of sustaining a satisfactory boundary habitat and the cost due to the harvesting component. Moreover, we characterize the unique optimal control in terms of the solution to the optimality system, which is the state system coupled with the adjoint system.     

中国农民消费行为及影响因素分析

本文运用适用预期的消费函数模型,对中国农民的消费行为影响因素进行实证分析。研究表明:农村居民消费的变动呈现出对收入变动的过度敏感,并且农民存在消费习惯,收入的不确定性进一步抑制了农民的消费。本文又做了进一步研究,发现受灾面积,农业支出对收入的影响不大,而农产品生产价格指数是造成收入不确定性的主要因素。     

Stochastic control of helicopter suspended load position

Modelling of the motion of a helicopter with a suspended load is described. The mathematical model takes into account stochastic disturbances acting on the load suspension point. The proposed approach allows solution of the problem of optimal control with minimization of oscillation and control power expenditure. The evolution of the system solution with time is investigated for various disturbance intensities. Computer calculation results are presented as a function of the suspension length and the intensity of stochastic disturbances.     

Platform exploitation in the sharing economy

We model a revenue sharing contract between a sharing economy platform and a freelance service provider, where the latter hides revenue from the former by canceling some assignments and performing them for cash (“platform exploitation”). The platform counters this via costly, imperfect audits with endogenous success probability, and a variable payment. We show that at equilibrium, all agent types except the highest, indulge in revenue falsification. This problem is exacerbated by the principal's ability to extract restitution from the agent.     

Optimal normative policies for marketing of products with limited availability

We develop optimal normative policies for pricing and advertising of products with limited availability by including the traditional product diffusion parameters (Bass, 1969)–innovation and imitation, and the scarcity effects generated due to limited product availability (Swami and Khairnar, 2003). Using optimal control methodology, our pricing policy results suggest that a profit-maximizing firm gradually increases the price as the sales approach the product availability. The optimal normative advertising policy recommends gradually decreasing the expenditure on the awareness advertising and increasing the expenditure on the availability advertising as the product diffusion progresses. These results are illustrated with suitable numerical examples.     

Optimal dynamic pricing of inventories with stochastic demand and discounted criterion

We consider a continuous time dynamic pricing problem for selling a given number of items over a finite or infinite time horizon. The demand is price sensitive and follows a non-homogeneous Poisson process. We formulate this problem as to maximize the expected discounted revenue and obtain the structural properties of the optimal revenue function and optimal price policy by the Hamilton-Jacobi-Bellman (HJB) equation. Moreover, we study the impact of the discount rate on the optimal revenue function and the optimal price. Further, we extend the problem to the case with discounting and time-varying demand, the infinite time horizon problem. Numerical examples are used to illustrate our analytical results.