DC函数优化问题的非精确邻近点算法

本文对DC函数(即两凸函数之差)的最小化问题提出了一个非精确邻近点算法,并证明此算法的下降性和全局收敛性.     

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This paper investigate a stochastic differential games for DC (defined contribution plans) pension under Vasicek stochastic interest rate. The finance market as the hypothetical counterpart, the investor as pension the leader of game. Our goal is through the game between pension plan investor and financial market, obtain optimal strategies to maximizes the expected utility of the terminal wealth. Under power utility function, by using stochastic control theory, we obtain closed-form solutions for the value function as well as the strategies. Finally, explain the research results in the economic sense, and though numerical calculation given the influence of some parameters on the optimal strategies     

基于通货膨胀和最低保障的DC养老金最优投资

主要研究了通货膨胀和最低保障下的DC养老金的最优投资问题。 首先, 应用伊藤公式得到通胀折现后真实股票价格的微分方程。 然后, 在DC养老金终端财富外部保障约束下, 引入欧式看涨期权, 考虑随机通胀环境下的退休时刻终端财富期望效用最大化问题, 应用鞅方法推导退休时刻以及退休前任意时刻DC养老金最优投资策略的显式解。 最后, 应用蒙特卡洛方法对结果进行数值分析, 分析最低保障对DC养老金最优投资策略的影响。     

基于Stein-Stein波动率和动态VaR约束下DC型养老基金的最优投资策略

研究了确定缴费型养老基金在退休前累积阶段的最优资产配置问题.假设养老基金管理者将养老基金投资于由一个无风险资产和一个价格过程满足Stein-Stein随机波动率模型的风险资产所构成的金融市场.利用随机最优控制方法,以最大化退休时刻养老基金账户相对财富的期望效用为目标,分别获得了无约束情形和受动态VaR (Value at Risk)约束情形下该养老基金的最优投资策略,并获得相应最优值函数的解析表达形式.最后通过数值算例对相关理论结果进行数值验证并考察了最优投资策略关于相关参数的敏感性.     

一类DC规划问题的分支定界算法

本文针对一类带有箱子和线性不等式约束的特殊DC规划问题,提出了一种分支定界算法.首先将原问题转化为其等价问题,然后利用目标函数的特点将等价问题松弛为凸规划问题,通过求解一系列凸规划问题得到原问题的最优解,最后给出算法的收敛性证明.数值实验表明该算法是可行有效的.     

Electrohydrodynamic behaviors of droplet under a uniform direct current electric field

The electrohydrodynamic behaviors and evolution processes of silicone oil droplet in castor oil under uniform direct current(DC)electric field are visually observed based on a high-speed microscopic platform.Subsequently,the effects of different working conditions,such as electric field strength,droplet size,etc.,on droplet behaviors are roundly discussed.It can be found that there are four droplet behavior modes,including Taylor deformation,typical oblique rotation,periodic oscillation,and fracture,which change with the increase of electric field strength.It is also demonstrated that the degree of flat ellipse deformation gets larger under a stronger electric field.Moreover,both of the stronger electric field and smaller droplet size lead to an increase in the rotation angle of the droplet.     

基于跳扩散模型的DC型 养老金时间一致最优投资策略的研究

将养老金投资过程分成财富积累阶段和财富给付阶段,建立了DC型养老金在退休前和退休后个人账户积累额变动的连续时间随机模型.该模型考虑了工资的随机风险因素,并用跳-扩散模型刻画风险资产.以均值-方差准则作为优化目标,运用推广的HJB方程分别得到了退休前和退休后的时间一致最优风险资产投资最优解.最后通过算例及敏感性分析研究了各个因素对风险资产投资的影响.在这些因素中缴费比例、死亡力对风险资产投资比例均有负向影响.     

F题“可持续的中国城乡居民养老保险体系的数学模型研究”(综述)

随着经济的结构性放缓以及人口老龄化的迅速到来,中国未来的养老金支付将面临很大的挑战.如何保持社会养老保险体系的可持续健康发展?这是2013年全国研究生数学建模竞赛试题之一(F题).对此作一综述.     

Transient plasma-enhanced remediation of nanoscale particulate matter in restaurant smoke emissions via electrostatic precipitation

It is now recognized that nanoscale particulate matter(PM)represents a substantial health hazard for our society,including PM from restaurant smoke.In this study,we explored the use of a transient pulsed plasma in conjunction with an applied DC bias to treat oil aerosols that closely resemble restaurant(i.e.,charbroiler)smoke emissions.For polyaromatic olefin PAO-4 and soybean oil,we found that a three-order-of-magnitude reduction in particulates(i.e.,99.9%remediation)could be achieved with this system.Here,the plasma discharge was produced in a 4-in.-diameter cylindrical reactor with a 5-10 ns high voltage(30 kV)pulse generator together with applied DC bias voltages up to 10 kV.The distribution of nanoparticle sizes was measured using a scanning mobility particle sizer(SMPS)with diameter centered around 225 nm.Here,the main mechanism of remediation occurs in a two-step process in which the oil nanoparticles are first ionized by the free electrons and free radicals in the plasma and then the charged particles are swept out to the sidewalls of the reactor by the applied DC potential.We believe this general approach opens up new degrees of freedom in the design of electrostatic oil aerosol pollution control devices.     

DC分式规划问题的最优性条件(英文)

本文主要研究约束DC分式规划问题.通过借助共轭函数上图的性质,首先讨论了约束DC分式规划问题的全局最优解和局部最优解的必要条件或充分条件.作为应用,还阐明了许多关于优化问题的结果可以作为本文的特殊情况.