考虑随机方差的最优消费和投资决策问题

研究在证券价格服从一个带有随机方差几何布朗运动情况下的最优消费和投资问题.首先建立了最优消费和投资问题随机最优控制数学模型,运用随机最优控制理论,得到了最优消费和投资随机最优控制问题的值函数所满足的偏微分方程;其次,基于最优控制问题的值函数给出了具有反馈形式的最优消费和投资策略,并与经典Merton问题进行了比较分析;最后,进行了算例分析.     

含期权的最优投资消费决策

当投资对象中含有期权时如何安排自己的投资和消费是当前投资者所面临的实际问题。本文在Black-Scholes模型假设的市场条件下,假定投资者的投资对象中含有一个欧式看涨期权,讨论了在该情形下投资者如何进行投资和消费的问题。建立效用最大化模型,应用最优控制原理得到了关于指数效用函数的最优投资消费策略,另外还得到了投资者的套期保值策略,并对这两种策略进行了对比,得到了它们之间的关系式。最后给出了数值示例验证了最优策略优于套期保值策略。     

基于最差情况的最优消费和投资策略

在假设证券收益存在有界不确定干扰和考虑交易费用的情况下 ,基于微分对策理论 ,研究了最差情况下的最优消费和投资策略问题 .首先 ,建立了最优消费和投资决策的微分对策模型 ;其次 ,证明了该微分对策模型存在唯一的值函数 ,并根据微分对策理论推导出了值函数满足的 IB偏微分方程 ;再次 ,基于微分对策值函数 ,给出了最差情况下的最优消费和投资策略 ;最后 ,给出了 IB偏微分方程解析解的一种求解方法 ,并对解的性质做了初步探讨     

基于过度外推的最优投资与消费策略

本文研究了在Merton最优投资消费问题中[1],行为金融学中的过度外推偏差如何影响投资者的决策和福利.运用随机动态最优控制方法和Kalman滤波技术,得到了CRRA效用函数下投资者的确定性等价财富的半闭式解,以及相应的最优投资和消费策略.通过对模型参数校准,其数值分析发现,过度外推行为会导致投资不足和消费过度,并显著增加投资者的边际消费倾向.数值结果表明,10％的外推性偏差会引致非理性投资者高达30％的福利损失.     

主观死亡评估下的退休后投资-消费-年金化时刻决策

考虑退休者的死亡风险和遗产效用,研究了退休后期最优投资-消费-年金化时刻决策问题.根据退休者在退休时刻对自身死亡概率的主观评估,把退休者分为两大类：第一类退休者自我评估以概率1活不到最大年金化时刻,第二类退休者自我评估以一定概率活得过最大年金化时刻.自退休时刻开始到死亡时刻或年金化时刻为止,退休者要进行投资和消费决策.假设最优的年金化时刻是使得年金化前后的累计消费效用均值以及遗产效用均值之和达到最大.采取幂效用函数形式,得到了最优投资-消费策略的解析解、第一类退休者在生存期内都不购买年金的条件以及第二类退休者选择在最大年金化时刻购买年金的条件.利用数值分析方法,详细分析了性别、生存周期、遗产效用、折现函数、风险厌恶系数、金融投资环境以及年金产品价格对退休者年金行为的影响.     

随机跳跃幅度的最优消费与证券选择策略问题

在最优消费与证券选择问题中,假定投资市场有两种资产可供选择:一种为无风险资产(银行债券),另一种为风险资产(股票).由于受重大信息的影响,风险资产的价格往往会产生跳跃.文章研究了这种带跳跃的投资问题,用泊松过程与布朗运动模拟了投资者的财富过程.为使投资者在整个生命周期的消费效用期望值最大,在跳跃幅度为一随机变量的条件下,利用贝尔曼动态规划原理,导出了最优消费及投资策略所满足的方程组,并且在跳跃幅度的概率分布已知的情况下,针对具体的参数值,给出了最优初始策略的数值解与最大消费效用期望值.     

基于非参数估计框架的期望效用最大化最优投资组合

本文基于期望效用最大化和非参数估计框架研究了最优投资组合选择问题。和以往大多文献假定资产收益率服从某些特定分布不同资产收益率的分布类型无需作任何假设。首先在一般效用函数下,利用组合收益率密度函数的非参数核估计给出了期望效用的基本非参数估计公式,并建立了期望效用最大化投资组合选择问题的基本框架。然后,在投资者具有幂效用函数的假定下,给出了期望效用具体的非参数计算公式,并给出了求解最大期望效用的数值算法。最后,利用中国证券交易所11支股票日收益率的真实数据给出了一个数值算例。本文提出的非参数估计框架具有一般性,还可以进一步用来研究各种现实条件下（如各种现实不等式约束和具有交易成本）的投资组合管理问题。     

不确定终止时间的多阶段最优投资组合

研究了当终止时间不确定时的多阶段最优投资组合问题.假定终止时间是个服从某分布的随机变量,将不确定终止时间的问题转化为确定时间的问题,应用动态规划求解模型,得到最优投资策略以及有效边界的解析形式.实例证明所得的结论是对确定终止时间情形的推广,最优投资策略受终止时间分布的影响.     

复杂不确定环境下考虑代理人通过努力减少项目持续期限的最优代理合同

本文着重研究复杂不确定环境下如何设计最优合同,以激励代理人减少项目持续期限。在代理问题中,以往的数量研究大多使用随机变量刻画项目参数和代理人的努力程度。但是,在某些情况下,项目参数和代理人的努力程度不能被历史数据获得,而必须由专家进行估计。运用不确定变量刻画专家对这些参数的估计,并且证明这样做是合理的。通过应用不确定理论,提出复杂不确定环境下考虑代理人通过努力减少项目持续期限的最优代理合同模型。之后,为了解决这个问题,给出了该模型的确定性形式。此外,对是否考虑代理人不确定努力的最优合同进行了比较。结果显示,当其他条件相同时,委托人在考虑代理人不确定努力程度的合同中得到的期望收益不低于在没有考虑代理人不确定努力程度的合同中到的期望收益。最后,为了更好地展示模型的应用,给出了一个数值例子并进行了相关讨论。     

Optimal Auction with Resale

This paper investigates the design of seller–optimal auctions when winning bidders can attempt to resell the good. In that case, the optimal allocation characterized by Myerson (1981) cannot be achieved without resale. I find a sufficient and necessary condition for sincere bidding given the possibility of resale. In two–bidder cases, I prove that the Myerson allocation can be achieved under standard conditions supplemented with two assumptions. With three or more bidders, achieving the Myerson allocation is more difficult. I prove that it can be implemented in special cases. In those cases, the Myerson allocation is generated through a sequence of resale auctions, each optimally chosen by a reseller.     

存在违约风险时的最优资产组合

本文研究了当存在违约风险时,一个代表性投资者投资于一个可违约债券、股票以及银行存款的最优资产配置问题。利用简约化模型来刻画可违约债券的违约风险,并给出其价格的动态过程。通过随机控制方法给出了此优化问题的解析解。结果表明跳跃(违约)风险的存在,使可违约债券的最优投资策略不再是连续函数。当可违约债券违约时,投资者对可违约债券的持有量为零;当债券未发生违约时,投资者对可违约债券的最优持有量主要受信用利差、违约强度以及投资期限的影响。     

Productivity-based financial net income analysis

This paper develops the analytical framework for a productivity based financial analysis, which has been successfully introduced by the authors as standard reporting in a major corporation. This analysis is designed to broaden and supplement conventional income statement analysis. It partitions expense and revenue items into their respective price and quantity components and establishes the precise relationship between total factor productivity performance and key aspects of financial performance. The underlying theory is reviewed. Subsequently, an actual case study example is analyzed. Some of the major additional insights into factors affecting the economic health of a productive enterprise and their implications for corrective actions are illustrated and discussed.     

Evaluating time streams of income

When a decision maker considers possible returns from a business project or investment, he often faces the problem that these returns are not all received at the same time, and thus he must make some adjustments to take account of his time preference for money. After a review of discounting, a utility theory approach is made by developing a two-attribute utility function u(x, t) which represents the desirability of an income of x at a time t in the future. Assumptions to simplify the assessment of this function are considered. Then u(x, t) is used to form a criterion for evaluating infinite time streams of income.     

Optimal Retail Return Policies with Wardrobing

Many retailers offer refunds to consumers who, after a trial period, return a product that they find does not fit their needs. Some consumers are willing to use this return option opportunistically for short‐term consumption rather than its intended purpose of resolving fit uncertainty. Such behavior has been termed “wardrobing.” Restocking fees (partial refunds) can be used to combat wardrobing. However, there is a trade‐off involved, since partial refunds will be viewed negatively by consumers who return an item due to a true lack of fit. In this study, we consider how the extent of wardrobing (how many consumers consider such behavior) and the benefit of wardrobing (how much value can be extracted during the trial) impact firm pricing decisions and profits in this retail context. Our results imply that an increase in the extent of wardrobing is most detrimental to profits when the current extent of wardrobing is low. On the contrary, if the extent of wardrobing is already very high, and the benefit of wardrobing to consumers is also high, the retailer can set prices and refunds such that additional wardrobing actually increases firm profits. In a model extension, we show how a retailer can effectively screen wardrobers from ordinary consumers by offering a menu of price/refund pairs, and that such an approach can lead to increased profits if the extent of wardrobing is sufficiently high. Overall, our findings provide new insights into how retailers can set prices and refund policies to effectively manage opportunistic behavior by consumers.     

具有技术转让的捆绑采购最优决策研究

为了获取先进的技术,采购方通常采用将产品和技术进行捆绑采购的采购策略.不同的供应商有着不同的技术优势,采购方可以在不同供应商之间分配采购量来获得拥有不同技术优势供应商的技术,并加以组合吸收以提高自身技术水平.基于此,研究了具有技术转让的捆绑采购最优决策问题,通过对采购方利用供应商之间技术的互补性而采取的组合捆绑采购策略的描述,用经典的消费者效用函数构建了采购方进行捆绑采购的效用,并结合随机效用理论建立了离散选择模型研究了技术捆绑采购过程中最优采购量、最优分配比例问题,给出了单变量决策中的最优采购量和最优分配比例,并进一步研究了最优采购量和最优分配比例的双变量决策问题,给出了最优双变量组合决策和条件.最后,给出了一个算例,并进行了敏感性分析.     

A note on arbitrage-free asset prices with and without personal income taxes

We study the implications of the absence of arbitrage possibilities on asset pricing with and without personal income taxes. While no-arbitrage conditions in frictionless markets have sufficiently been investigated, personal income taxation is still beyond of being fully integrated into arbitrage theory. In extending the primary analysis of Ross (J Polit Econ 95:371–393, 1987) to a multiperiod framework allowing for dynamic trading strategies, we take a major step in this direction. The existence of a positive linear pricing functional is proven in a general discrete time and discrete state space model. In order to obtain the linearity of the pricing functional, one has to allow for short sales or, at most, to restrict sales to positions initially given. Hints at far-reaching economic applications are available.

具有网络外部性特征的企业定价策略研究

随着信息技术的发展,传统经济中普遍采用的单一定价策略采用者正在逐渐减少,尤其在具有网络外部性特征的产业中,更多地采用歧视定价策略.针对具有网络外部性的产业中双寡头垄断厂商的定价策略选择行为,将传统Hotelling模型中外生的定价策略作为内生变量,分析了厂商对单一定价和歧视定价的战略选择.模型的子博弈精炼Nash均衡表明:当网络效应不存在时,厂商或者同时采用单一定价,或者同时采用歧视定价;当网络效应存在时,由于网络效应的影响,厂商选择歧视定价的均衡条件放宽,导致厂商采用歧视定价比单一定价更具有成本优势,从而增强了厂商选择歧视定价的趋向.另一方面,若消费者对产品特征的敏感程度加强,也促使厂商选择歧视定价.     

具有差异化选择特征的复杂社会网络扩散研究

人们有时会偏好与他人保持差异,例如搭便车者总是选择与邻居相反的策略.利用反协调博弈刻画了个体的差异化选择特征,分析了复杂社会网络上的扩散过程及其影响因素.结论表明,这类扩散总能成功,当采用策略的风险占优程度越高时,同质性网络中的采用者数量越多,而异质性网络中的采用者数量可能减少,且存在惟一的最优风险占优度.网络结构特征变化能够显著影响采用者数量,则小世界特征的影响效果取决于策略是否风险占优,而平均度和异质性的影响效果还需要考虑策略风险占优度的大小.若个体对邻居信息出现认知偏差,会显著改变最终的采用者个数.因此,通过调整个体采用收益、认知程度和个体间相互联系,可以有效管理和控制具有差异化选择特征的扩散,如度假产品、奢侈品、搭便车行为、流行与时尚等.     

Optimal space coverage with white convex polygons

Assume that we are given a set of points some of which are black and the rest are white. The goal is to find a set of convex polygons with maximum total area that cover all white points and exclude all black points. We study the problem on three different settings (based on overlapping between different convex polygons): (1) In case convex polygons are permitted to have common area, we present a polynomial algorithm. (2) In case convex polygons are not allowed to have common area but are allowed to have common vertices, we prove the NP-hardness of the problem and propose an algorithm whose output is at least \(\left( \frac{OPT}{log(2n/OPT) + 2log(n)}\right) ^{1/4}\). (3) Finally, in case convex polygons are not allowed to have common area or common vertices, also we prove the NP-hardness of the problem and propose an algorithm whose output is at least \(\frac{3\sqrt{3}}{4.\pi }\left( \frac{OPT}{log(2n/OPT) + 2log(n)}\right) ^{1/4}\).