具有内生人口规模的城市经济增长模型

本文研究了城市经济增长与人口规模的相互关系.通过引入含消费与舒适度的双变量效用函数,提出了城市居民效用最大化问题.利用动态优化与动力系统,得出描述模型的二维动力系统,具有唯一双曲型平衡点和优化问题存在唯一最优增长路径.因而,对城市经济增长存在最优的人口规模.     

公共资本投资的随机内生增长模型

本文假设公共资本是宏观经济的一部分,由此建立一个随机内生增长模型,把公共资本作为宏观经济变量并进入个人效用.分析了经济达均衡时税收,政府投资,个人投资对经济增长率和社会福利的影响.同时还求出子最优的增长率和个人资本与财富比,消费和财富比.     

储备率、铸币收益与经济增长

本文考察了储备需求所增加的铸币收益在货币内生增长模型中的增长效应 .假设政府把铸币收益用在教育和公共生产性开支且对私人厂商有正的外部性 .用两部门内生增长模型分析因储备需求带来的增长效用 ,该经济有唯一的均衡增长路径 ,政府开支存在最优配置 ,且通过数据模拟存在最优储备率 .同样也得了与 [1 ]相类似的结论 :储备率与经济增长率的Laffer曲线关系 .     

偏序偏度量空间中有理分式型广义弱压缩的公共不动点结果北大核心CSCD

在偏序完备偏度量空间中研究了四个映射的公共不动点问题,对满足某种带有理分式项的广义弱压缩条件的四个映射得到了一些公共不动点结果.证明了公共不动点唯一的一个充分条件,并给出一个例子予以说明.最后讨论了在同伦问题中的一个应用.     

度量空间中反交换映射的公共不动点

本文讨论了度量空间中映射在反交换条件下的公共不动点的存在性问题,给出了映射对在满足一定条件时公共不动点的存在性与唯一性结论.并指出了文献[5]中的几处错误.     

度量凸空间上拟收缩型映射族的唯一公共不动点

给出了完备度量凸度量空间上具有拟收缩条件的非自映射族的公共不动点的存在和唯一性定理,并根据该结果得到更一般形式的唯一公共不动点定理.该文的主要结果对文献中的许多同类型的不动点定理进行了改进和一般化.     

度量空间上具有变系数的收缩条件的两个集值映射的公共不动点

在完备的度量空间上利用满足具有某种变系数的收缩条件或φ-收缩条件的两个集值映射构造了一个收敛序列,然后证明了该序列的唯一极限就是两个映射的公共不动点并给出了映射族存在唯一公共不动点的充分条件,同时给出了几个特殊结果.所得结果推广和改进了一些已有的结论.     

Ho-Lee利率模型下多种风险资产的动态投资组合

假设无风险利率可由Ho-Lee利率模型描述,且与股票动态存在一般线性相关系数,应用最优性原理和HJB方程研究了市场存在多种风险资产情形的动态资产分配问题,通过变量替换方法得到了幂效用和指数效用下最优投资策略的显示解,数值算例分析了利率参数和市场参数对最优投资策略的影响趋势。研究结果发现:两种效用下的最优策略均由两部分所构成,一部分由市场参数所确定,另一部分由利率参数所确定。而且,幂效用下的最优投资策略与瞬时利率无关,而指数效用下的最优投资策略与瞬时利率相关。     

基于联合作战兵力配置的非合作博弈研究

基于联合作战实体定量分析的作战能力指数组合期望效用,研究了联合作战任务兵力配置问题,建立了二人零和参数博弈模型,并讨论了模型构建的理论依据与算法.     

拟度量空间上满足收缩条件的映射(族)的不动点和公共不动点

通过构造拟度量空间上的收敛序列,得到满足Lipschitz收缩条件的映射存在唯一不动点的定理和满足由收缩函数决定的收缩条件的映射族的重合点和公共不动点的存在定理以及一个映射的唯一不动点存在定理.     

Stochastic Differential Games with Multiple Modes and Applications to Portfolio Optimization

Abstract

We study a zero-sum stochastic differential game with multiple modes. The state of the system is governed by “controlled switching” diffusion processes. Under certain conditions, we show that the value functions of this game are unique viscosity solutions of the appropriate Hamilton–Jacobi–Isaac' system of equations. We apply our results to the analysis of a portfolio optimization problem where the investor is playing against the market and wishes to maximize his terminal utility. We show that the maximum terminal utility functions are unique viscosity solutions of the corresponding Hamilton–Jacobi–Isaac' system of equations.     

灰色聚类法在城市公共交通发展水平评价中的应用

针对城市公共交通发展水平的评价难以做到客观、全面、准确的问题,构建了城市公共交通发展水平评价的指标体系及其递阶层次结构;运用灰色聚类分析法建立了数学模型对城市公共交通发展水平进行综合评价.利用该评价模型,对青岛市公共交通发展水平进行了实例分析,运行表明,评价结果与青岛市就公交现状所进行的民意调查结果基本吻合,提高了评价效率,从而提供了一条对城市公共交通发展水平进行定量分析的途径.     

多周期公用工程系统运行的模型,优化方法与应用

针对多周期公用工程系统的运行优化问题，考虑了设备的启停费用的情况下。建立了混合整数非线性规划模型并证明了最优解的存在性。针对该运行优化问题本将其分解成若干子问题，然后利用改进的Hooke-Jeeves优化算法求解每个子问题。应用于具体实例，其数值结果与其它方法得到的相比。运行时间短，且更适合多周期公用工程问题的求解。     

Portfolio Optimization in a Semi-Markov Modulated Market

We address a portfolio optimization problem in a semi-Markov modulated market. We study both the terminal expected utility optimization on finite time horizon and the risk-sensitive portfolio optimization on finite and infinite time horizon. We obtain optimal portfolios in relevant cases. A numerical procedure is also developed to compute the optimal expected terminal utility for finite horizon problem. This work was supported in part by a DST project: SR/S4/MS: 379/06; also supported in part by a grant from UGC via DSA-SAP Phase IV, and in part by a CSIR Fellowship.     

具有内生基础设施分配的城市经济增长模型

In this paper, an urban economic growth model with endogenous infrastructure allocation is given by introducing the two-variable utility function for city＇s inhabitant. A twodimensional dynamical system is obtained by solving the utility maximization problem and it is proved that this system has the unique non-zero equilibrium which is a saddle. The model has the unique optimal growth and an optimal rate of infrastructure allocation.     

Optimization of functionality development

The problem of regulation of logistic growth trends is examined in the framework of control theory for problems with infinite horizon. The problem statement is related to microeconomic models of dynamic optimization of a company’s indicator of functionality development. Various control regimes of functionality development are studied for identification of plausible production trends. Optimal control problem is posed to optimize the utility function of logarithmic consumption index of the system entropy type. Solution of the problem is constructed in analysis of the Hamiltonian system and its algebraic properties. Based on this analysis nonlinear stabilizers are elaborated which lead the system to the steady state with the same growth rates as the optimal control regime. The model is tested on the real time series of dynamic trends of functionality development for two generations of mobile phones in Japan.     

公务员招聘的优化模型

对“公务员招聘”问题进行了深入探讨,运用模糊数学和运筹学理论,先建立了招聘人员的模糊多属性综合评价模型,解决了用人单位择优录取公务员的问题;然后建立了0-1整数规划模型解决了人力资源的优化配置问题,从而给出了一种科学有效的公务员招聘的方法.     

Metaheuristics approach for solving personalized crew rostering problem in public bus transit

The crew rostering problem in public bus transit aims at constructing personalized monthly schedules for all drivers. This problem is often formulated as a multi-objective optimization problem, since it considers the interests of both the management of bus companies and the drivers. Therefore, this paper attempts to solve the multi-objective crew rostering problem with the weighted sum of all objectives using ant colony optimization, simulated annealing, and tabu search methods. To the best of our knowledge, this is the first paper that attempts to solve the personalized crew rostering problem in public transit using different metaheuristics, especially the ant colony optimization. The developed algorithms are tested on numerical real-world instances, and the results are compared with ones solved by commercial solvers.     

一类可再生资源系统的最优动态平衡收获

研究一类可再生资源系统的最优利用问题．首先,引进一个新的效用函数, 它依赖于收获努力度和资源量,由此导出最优控制问题．其次证明该控制问题最优解的存在性．然后,利用无穷区间上控制问题的最大值原理,得到一个非线性的四维最优系统．通过对上述系统正平衡解的详细分析,借助 Hopf 分支定理证明了极限环的存在性．之后考虑中心流形上的简化系统, 分析极限环的稳定性．最后,解释所得结果的生物经济学意义．