项目投资组合的风险度及其最优决策

本文针对项目组合投资问题引入了风险度概念，并建立其风险度模型．在无零风险度项目的情况下，给出了该模型的最优项目组合投资策略并证明该策略为马氏有效．在有零风险度项目的情况下，讨论了该模型的有效前沿的结构、性质和有效性，同时还论证了该模型的有效前沿与威廉·夏普提出的资本资产定价模型的有效前沿相一致的线性关系．最后作为本模型的应用，构造了”保证还本”模型，给出了其最优项目投资组合的策略．     

最优消费条件下的动态风险投资组合决策模型

本文给出了一个考虑最优消费的动态风险投资组合数学模型 ,通过该模型投资者能合理确定投资、储蓄和消费的最佳比例。同时本文也指出了该模型所隐含的一些政策涵义     

对Treynor-Black投资组合模型的推广

Treynor-Black在1973年给出了一种不考虑交易成本，没有卖空、投资比例限制的基于单指数模型投资组合构建方法[1]，该模型这种方法相比Markowitzl952年的方法更为简单，并且容易推广。本将该模型的限制卖空和具有投资比例限制以及多因子的情形，推广的结果使得该模型在实际投资中更为适用。     

证券投资组合理论的一种新模型及其应用

马科维茨(Markowitz)以证券收益率的方差作为投资风险的测度建立了组合证券投资模型，本基于熵的概念，在研究马科维茨(Markowitz)证券投资组合模型的基础上，分析了该模型用方差度量风险的不足，进而提出一种新的证券投资组合优化模型，并以实例作了说明。     

二层次消费与投资决策优化动态规划模型

在动态多阶段情形,投资者面临的环境不仅只有投资环境,还包括消费环境.投资者关于投资与消费的决策具有层次性.因为消费事关人的生存需要,是优先要考虑的问题,且投资的最终目的还是为了消费,所以使消费最大化应是高一层次的目标,而使投资最大化则应是次一级的目标.因此,试图建立一个二层次消费与投资决策优化动态规划模型,以便更好地模拟现实世界的情况.讨论了该模型的动态决策过程和最优解的性质.     

绿色食品需求函数的一种求解方法

本分析了影响绿色食品消费的因素，建立了消费消费绿色食品及同类一般食品的效用最大化数学规划模型，给出了Kuhn-Tucker条件；引入了绿色食品置信度参数并建立了一个可计算的二次效用函数，导出了该二次效用函数对应的需求函数，并详细地表述了求解过程和方法，讨论了绿色食品需求函数的性质。     

基于进化金融的证券投资策略动态博弈模型研究

本研究构建并证明了一个内生平衡资产价格的证券市场动态博弈进化模型。模型中资产产生的股息分别用于消费和再投资。投资者使用一般的、自适应投资策略以特定的比例在不同资产间进行投资,投资依据是环境的外生状态和观察到的博弈历史记录。本研究的主要目标是探索并定义投资者的生存策略,即在整个有限的时间范围内,该策略需确保投资者拥有积极的、远离零界的市场财富份额。本研究把进化金融的最新理论和非合作市场博弈的经典主题结合在一起,证明了投资策略成为稳定生存策略的条件及生存策略的渐进唯一性。     

最优投资消费策略

投资消费问题是数理金融中的一个主要问题,Merton在假设股票价格过程为扩散过程的情形下,给出了最优投资消费策略的显式解,本在股份价格过程为跳－扩散过程的情形下,讨论了最优投资消费策略问题,得到了最优投资消费策略的偏微分方程。     

国民经济的最优增长模型

本文利用 Cobb-Douglas生产函数建立了一类描述国民经济收入和积累率关系的数学模型 ,并利用该模型求出了国家预定经济增长目标下的计划投资量以及保持国民经济快速增长的合理的投资量和消费目标 .     

顾客满意度模型

本运用层次分析法建立数学模型，对顾客在消费过程中对企业满意程度的问题进行科学的测量，该模型可推广到一般满意度的测量问题中。     

Vasicek利率模型下带有零息票债券的投资-消费模型

应用随机最优控制理论研究Vasicek利率模型下的投资-消费问题,其中假设无风险利率是服从Vasicek利率模型的随机过程,且与股票价格过程存在一般相关性.假设金融市场由一种无风险资产、一种风险资产和一种零息票债券所构成,投资者的目标是最大化中期消费与终端财富的期望贴现效用.应用变量替换方法得到了幂效用下最优投资-消费策略的显示表达式,并分析了最优投资-消费策略对市场参数的灵敏度.     

Optimal consumption and investment problem with random horizon in a BMAP model

In this paper, we consider the consumption and investment problem with random horizon in a Batch Markov Arrival Process (BMAP) model. The investor invests her wealth in a financial market consisting of a risk-free asset and a risky asset. The price processes of the riskless asset and the risky asset are modulated by a continuous-time Markov chain, which is the phase process of a BMAP. The possible consumption or investment are restricted to a sequence of random discrete time points which are determined by the same BMAP. The investor has only consumption opportunities at some of these random time points, has both consumption and investment opportunities at some other random time points, and can do nothing at the remaining random time points. The object of the investor is to select the consumption–investment strategy that maximizes the expected total discounted utility. The purpose of this paper is to analyze the impact of the consumption–investment opportunity and the economic state on the value functions and consumption–investment strategies. The general solution and the exact solution under the assumption that the consumption and the terminal wealth are evaluated by the power utility are obtained. Finally, a numerical example is presented.     

坑口电厂低碳经济发展系统动力学仿真研究

通过分析坑口电厂低碳经济系统的复杂结构特征和动态反馈机制,建立了坑口电厂低碳经济系统动力学模型,描述系统内部各要素之间的相互关系,并以平煤集团坑口电厂为例,对不同发展方案下的坑口电厂低碳经济系统进行仿真模拟.结果表明:科技投资、环保投资、能源利用率、能源消费结构等因素是影响坑口电厂低碳经济发展的关键因素;可以通过优化能源消费结构,提高煤矸石消耗比例;增加科技投资和环保投资,提高能源利用和转换效率,降低污染物和二氧化碳排放量,从而达到高效率、低能耗、低排放的低碳经济发展模式.     

Limited self-control and long-run growth

This paper integrates imperfect self-control into the standard model of endogenous growth. In their long-run savings decisions individuals take into account a cost of self-control, which depends on the consumption temptations of their impatient short-run self. I obtain a closed-form solution for consumption and show that within a certain range of self-control an investment subsidy can be useful in order to reduce consumption and to increase investment, growth, and welfare of the long-run self. A consumption tax, perhaps surprisingly, is found to be counterproductive. It induces individuals with limited self-control to consume even more.     

中国投资与消费不均衡发展的实证研究:基于因子-Copula模型

在现有对投资与消费关系研究缺乏定量研究的基础上,引入Copula函数来探讨投资与消费的变动关系。首先利用因子分析进行投资与消费高维指标的降维处理,这样有效避免了Copula函数在多维变量下的建模复杂性;接着利用半参数建模方法选择了Cumbel函数来描述当前二者的关系;结果显示当前我国投资与消费存在显著不均衡关系,同时二者具有非对称性、非线性等数量特征;最后对上述研究结论进行了经济解释分析。     

个人投资与消费模型的期望效用最大化

研究了具有初始财富的投资者如何最大化终端资产和消费的期望效用,首先通过交易费用函数建立带交易费的连续时间投资与消费模型,然后运用鞅分析和对偶理论证明了：在有效市场中,如果投资者积极交易,则只会降低终端财富的期望值,并得到了最优投资消费组合过程和终端资产.     

Asset allocation,sustainable withdrawal,longevity risk and non-exponential discounting

The present paper studies an optimal withdrawal and investment problem for a retiree who is interested in sustaining her retirement consumption above a pre-specified minimum consumption level. Apparently, the withdrawal and investment policy depends substantially on the retiree’s health condition and her time preferences (subjective discount factor). We assume that the health of the retiree can worsen or improve in an unpredictable way over her lifetime and model the retiree’s mortality intensity by a stochastic process. In order to make the decision about the consumption and investment policy more realistic, we assume that the retiree applies a non-exponential discount factor (an exponential discount factor with a small amount of hyperbolic discounting) to value her future income. In other words, we consider an optimization problem by combining four important aspects: asset allocation, sustainable withdrawal, longevity risk and non-exponential discounting. Due to the non-exponential discount factor, we have to solve a time-inconsistent optimization problem. We derive a non-local HJB equation which characterizes the equilibrium optimal investment and consumption strategy. We establish the first-order expansions of the equilibrium value function and the equilibrium strategies by applying expansion techniques. The expansion is performed on the parameter controlling the degree of discounting in the hyperbolic discounting that is added to the exponential discount factors. The first-order equilibrium investment and consumption strategies can be calculated in a feasible way by solving PDEs.     

带有交易成本和红利的最优消费投资策略研究

本文利用HJB方程粘性解理论,考虑带有红利收益和交易成本后,对现有最优消费投资模型作了推广,研究了投资者在带有红利和交易成本情形下的最优消费投资策略。     

Health shock risk,critical illness insurance,and housing services

This paper studies a consumption–investment problem involving health shock risk, perishable consumption, and consumption of housing services. Additionally to a risk-free asset and a stock index, the agent can invest in real estate. I analyze the impact of health shocks on the optimal consumption and investment decisions in model specifications with and without the possibility to buy critical illness insurance. I discuss the influence of critical illness insurance on the optimal strategy and analyze the drivers of the optimal critical illness insurance demand. The results indicate that health shock risk has potentially devastating consequences, especially for young agents. It turns out that critical illness insurance is an excellent instrument for hedging health shock risk and for consumption smoothing across different health states. Optimal critical illness insurance demand is decreasing in financial wealth and increasing in human wealth. Real estate prices have a minor influence on optimal critical illness insurance demand.     

Optimal consumption and investment strategies with liquidity risk and lifetime uncertainty for Markov regime-switching jump diffusion models

In this paper, we consider the optimal consumption and investment strategies for households throughout their lifetime. Risks such as the illiquidity of assets, abrupt changes of market states, and lifetime uncertainty are considered. Taking the effects of heritage into account, investors are willing to limit their current consumption in exchange for greater wealth at their death, because they can take advantage of the higher expected returns of illiquid assets. Further, we model the liquidity risks in an illiquid market state by introducing frozen periods with uncertain lengths, during which investors cannot continuously rebalance their portfolios between different types of assets. In liquid market, investors can continuously remix their investment portfolios. In addition, a Markov regime-switching process is introduced to describe the changes in the market’s states. Jumps, classified as either moderate or severe, are jointly investigated with liquidity risks. Explicit forms of the optimal consumption and investment strategies are developed using the dynamic programming principle. Markov chain approximation methods are adopted to obtain the value function. Numerical examples demonstrate that the liquidity of assets and market states have significant effects on optimal consumption and investment strategies in various scenarios.