部分信息下含债务的马氏调制收益率的最优投资组合问题

带有确定性参数的金融模型只能描述较短的时间内的状态演化,不能反映市场条件的变化.在投资过程中,投资者一般仅能够观察到资产的价格,不能直接观察到资产的平均收益率和波动率.考虑一个简化的连续时间的金融市场,这个市场带有无风险资产(债券)和风险资产(股票)两种资产.在债务为线性扩散模型下,利用Wonham滤波理论估计股票的平均收益率,研究了使得指数期望效用最大的最优投资组合选择问题.利用随机线性二次控制方法,得到最优投资组合策略和最大期望指数效用的显示解.     

投资者情绪影响下资本资产定价的区制性研究——基于股票论坛发帖的情感分析

本文首先建立一个考虑投资者情绪的资本资产定价模型,研究发现,投资者情绪是资产定价的系统性因子且对其影响具有区制性(存在三个区制)。在此基础上通过仿真揭示投资者情绪对资产定价影响存在区制性的原因在于当投资者情绪增加时,最优组合超额收益受组合效应与情绪效应的综合影响。最后基于股票论坛发帖的情感分析构建投资者情绪指标,实证检验了本文的理论模型,并发现基于普通的线性回归模型得到的投资者情绪对股指超额收益影响,一方面会在投资者情绪处于第二区制内时将其对股指超额收益影响方向弄反,另一方面会在投资者情绪处于第三区制内时低估其增加导致的股指超额收益平均增加程度。     

跳扩散模型下的非零和随机微分投资组合博弈

现实经济中,当股票价格受到一些重大信息影响而发生突发性的跳跃时,用跳扩散过程来描述股票价格的趋势更符合实际情况。基于这一观察,本文研究跳扩散模型下包含两个投资者的非零和投资组合博弈问题。假设金融市场中包含一种无风险资产和一种风险资产,其中风险资产的价格动态用跳扩散模型来描述。将该非零和博弈问题构造成两个效用最大化问题,每个投资者的目标是最大化终端时刻自身财富与其竞争对手财富差的均值-方差效用。运用随机控制理论,得到了均衡投资策略以及相应值函数的解析表达。最后通过数值仿真算例分析了模型相关参数变动对均衡投资策略的影响。仿真结果显示:当股价发生不连续跳跃,投资者在构造投资策略时考虑跳跃风险可以显著增加其效用水平;同时,随着博弈竞争的加剧,投资者为了在竞争中取得更好的表现,往往会采取更加激进的投资策略,增加对风险资产的投资。     

基于随机基准的最优投资组合选择问题研究

本文研究基于随机基准的最优投资组合选择问题. 假设投资者可以投资于一种无风险资产和一种风险股票,并且选择某一基准作为目标. 基准是随机的, 并且与风险股票相关. 投资者选择最优的投资组合策略使得终端期望绝对财富和基于基准的相对财富效用最大. 首先, 利用动态规划原理建立相应的HJB方程, 并在幂效用函数下,得到最优投资组合策略和值函数的显示表达式. 然后,分析相对业绩对投资者最优投资组合策略和值函数的影响. 最后, 通过数值计算给出了最优投资组合策略和效用损益与模型主要参数之间的关系.     

有交易费时的欧式期权定价

本文考虑存款与借款利率不同且对股票的交易有交易费要求时的欧式期权定价问题。我们假定投资者的投资目的是使自己的期望效用最大化。对于市场给出的期权价格,投资者将选择最优的资产组合。在投资者的这种行为下,可以认为市场是投资者的对手,而期权的市场价格将会这样给出：投资者在这个价格下,他的最大期望效用将达到最小。本文在假定投资者的效用函数为风险中性时,给出了有交易费时欧式期权价格的显式表达式。     

CEV模型下家庭最优投资决策问题

考虑固定收入下具有随机支出风险的家庭最优投资组合决策问题.在假设投资者拥有工资收入的同时将财富投资到一种风险资产和一种无风险资产,其中风险资产的价格服从CEV模型,无风险利率采用Vasicek随机利率模型.当支出过程是随机的且服从跳-扩散风险模型时,运用动态规划的思想建立了使家庭终端财富效用最大化的HJB方程,采用Legendre-对偶变换进行求解,得到最优策略的显示解,并通过敏感性分析进行验证表明,家庭投资需求是弹性方差系数的减函数,解释了家庭流动性财富的增加对最优投资比例呈现边际效用递减趋势.     

奈特不确定下资产收益率发生紊乱的最优投资策略

在部分信息且市场利率非零的情形下,应用α-极大极小期望效用(α-MEU)模型区别投资者的含糊和含糊态度,研究资产预期收益率发生紊乱(disorder)时的投资组合问题.首先,利用倒向随机微分方程理论刻画了α-MEU.其次,给出紊乱时刻的后验概率过程满足的随机微分方程(SDE),以及价值过程所满足的倒向随机微分方程(BSDE).最后,应用鞅论解出指数效用时的最优交易策略和价值过程的明确表达式.     

考虑相对业绩的最优投资选择博弈问题研究

研究了具有相互作用的两个竞争机构投资者之间的离散时间最优投资选择博弈问题,每个机构投资者都考虑其竞争对手的相对业绩.机构投资者可以投资于相同的无风险资产和不同的具有相关关系的风险股票,以反映投资的资产专门化.机构投资者选择投资组合策略使得期望终端绝对财富和相对财富的效用最大.首先,定义了Nash均衡投资组合选择策略.然后,在机构投资者具有指数效用函数的假设下,得到了Nash均衡投资组合选择策略和值函数的显示表达式,分析了机构投资者之间的竞争对Nash均衡投资组合选择策略的影响.最后,通过数值计算给出了各种情况下Nash均衡投资组合选择策略和值函数与模型主要参数之间的关系.结果表明:机构投资者之间的竞争会影响其对风险的承担,投资机会集对机构投资者的Nash均衡投资组合选择策略和值函数与模型主要参数之间的关系会产生很大的影响.     

国际投资商组合投资决策模型研究(英文)

在国际金融市场上,投资商参与风险资产投资,国际投资商的投资行为不仅受风险资产价格变动的影响,而且受外汇市场汇率波动风险的影响,在投资者效用最大化的标准下,本文研究了国际金融市场的投资者投资决策模型．在确定性系数下,提供了反馈形式的消费投资公式,并就股价或汇率变动对投资者行为的影响进行了理论分析．分析表明,我们的模型从理论上可以解释１９９７ 年以东南亚为起点的金融危机对国际资本流动的影响     

位置-尺度分布族中均值-方差准则与期望效用理论的一致性

证明了当决策集为位置-尺度分布族时,期望效用理论与均值-方差准则是一致的.从而就可以将马克威茨的均值-方差准则中的正态假设减弱为位置-尺度分布族.这不仅扩大了均值-方差准则的应用范围,而且巩固了组合投资理论与资本资产定价理论的基础.     

Moments of utility functions and their applications

This paper presents moments and cross-moments of utility functions and measures of utility dependence. We start with an interpretation of the nth moment of a utility function, and describe methods for its assessment in practice and consistency checks that need to be satisfied for any assessed moments. We then show how moments of a utility function (i) provide a new method to determine the parameters of a given functional form of a utility function and (ii) to derive the functional form of a utility function that satisfies some given moment assessments. Next, we derive a fundamental formula that relates the expected utility of a joint distribution to the expected utility of the marginal distributions for multiattribute utility functions. We use this formulation to provide an intuitive interpretation for cross-moments of utility functions and illustrate their use in (i) constructing multiattribute utility functions that incorporate utility dependence and (ii) in providing necessary conditions for utility independence in decisions with multiple attributes. We end with a new measure of utility dependence for multiattribute utility functions and work through several examples to illustrate the approach.     

Representing risk preferences in expected utility based decision models

Users of expected utility based decision models frequently find it useful or necessary to specify a functional form that represents the risk preferences of a decision maker. Having additional functional forms from which to choose would be helpful. The literature so far has provided several such functional forms for the utility function itself. The discussion presented here indicates that providing a functional form for the marginal utility function is an alternate and equally useful way to represent risk preferences. Furthermore, functional forms for marginal utility are easier to provide, and there exist functional forms for marginal utility that represent simple risk preferences for which there is no associated functional form for the utility function. Several functional forms for marginal utility are suggested, and the class of isoelastic risk preferences is identified and discussed.     

企业及市场经营效用函数形式研究

鉴于经营效用是企业制订战略决策和发展策略的重要影响因素,研究其基本效用类型,提出对应的函数形式,并在此基础上提出市场总体的综合经营效用测度方法。企业经营效用由自身经营效用和同业比较效用两部分线性合成,效用变量分别为企业单位盈利指标加权合成值及单位盈利水平与行业平均值的差,效用函数通过原点且单调,因此需将效用理论中对应于各种效用类型的对数函数、指数函数等进行坐标变换、旋转或对称。保守型和冒险型效用在定义域内分别为凹函数和凸函数,共组合为9种效用类型含81种基本函数形式,并给出各效用类型含义、经营特征和定价倾向。以市场份额作为各企业经营效用权重,构建幂平均效用合成模型作为市场总体综合经营效用测度。     

基于2可加模糊测度的多线性效用函数建模和求解

构建合适的多属性效用函数是多属性效用分析的关键。针对不同偏好假设,文献从可加独立、效用独立、效用依赖等分别进行了多属性效用函数构建的研究。然而,由于求解的复杂性,多属性效用理论的应用绝大部分限于可加效用函数和多乘效用函数。提出一种基于2可加模糊测度的多线性效用函数建模和求解方法。首先,证明多线性效用函数和基于模糊测度的多线性模型之间的等价性,提出利用基于模糊测度的多线性模型对多线性效用函数进行表示。其次,针对多线性模型的特点和模糊测度识别的复杂性,利用Banzhaf交互指数和2可加模糊测度对多线性模型进行表示,并利用最小方法差进行模糊测度和Banzhaf交互指数识别,进而实现多线性效用函数的求解。最后,将方法用于某可穿戴医疗设备基于顾客需求的多属性效用函数构建,确认了可行性。方法为多线性效用函数的求解提供了一种新思路。     

Objective comparisons of the optimal portfolios corresponding to different utility functions

This paper considers the effects of some frequently used utility functions in portfolio selection by comparing the optimal investment outcomes corresponding to these utility functions. Assets are assumed to form a complete market of the Black–Scholes type. Under consideration are four frequently used utility functions: the power, logarithm, exponential and quadratic utility functions. To make objective comparisons, the optimal terminal wealths are derived by integration representation. The optimal strategies which yield optimal values are obtained by the integration representation of a Brownian martingale. The explicit strategy for the quadratic utility function is new. The strategies for other utility functions such as the power and the logarithm utility functions obtained this way coincide with known results obtained from Merton’s dynamic programming approach.     

基于效用函数的模糊数的比较与排序

对相同的模糊数进行比较,不同风险偏好的决策者,会得到不同的结论.效用函数是对风险偏好的度量,因此,模糊数的比较与排序的方法,一定要结合决策者的效用函数来构造.为此,根据效用函数定义了模糊效用函数,在此基础上定义了效用序.之后,证明效用序为全序,进一步利用结构元理论对效用序进行表述.根据效用函数反映风险偏好的程度,对效用序进行分类.这样,决策者对模糊数进行比较时,依据自身对风险偏好程度来选择效用序.     

Sensitivity analysis incorporating fuzzy evaluation for scaling constants of multiattribute utility functions

A multiattribute utility function can be represented by a function of single-attribute utility functions if the decision maker’s preference satisfies additive independence or mutually utility independence. Additive independence is a preference condition stronger than mutually utility independence, and the multiattribute utility function is in the additive form if the former condition is satisfied, otherwise it is in the multiplicative form. In this paper, we propose a method for sensitivity analysis of multiattribute utility functions in multiplicative form, taking into account the imprecision of the decision maker’s judgment in the procedures for determining scaling constants (attribute weights).     

Optimal Control for Utility Portfolio Selection with Liability

In this paper we use stochastic optimal control theory to investigate a dynamic portfolio selection problem with liability process, in which the liability process is assumed to be a geometric Brownian motion and completely correlated with stock prices. We apply dynamic programming principle to obtain Hamilton-Jacobi-Bellman (HJB) equations for the value function and systematically study the optimal investment strategies for power utility, exponential utility and logarithm utility. Firstly, the explicit expressions of the optimal portfolios for power utility and exponential utility are obtained by applying variable change technique to solve corresponding HJB equations. Secondly, we apply Legendre transform and dual approach to derive the optimal portfolio for logarithm utility. Finally, numerical examples are given to illustrate the results obtained and analyze the effects of the market parameters on the optimal portfolios.     

An efficient algorithm for mining high utility itemsets with negative item values in large databases

Utility itemsets typically consist of items with different values such as utilities, and the aim of utility mining is to identify the itemsets with highest utilities. In the past studies on utility mining, the values of utility itemsets were considered as positive. In some applications, however, an itemset may be associated with negative item values. Hence, discovery of high utility itemsets with negative item values is important for mining interesting patterns like association rules. In this paper, we propose a novel method, namely HUINIV (High Utility Itemsets with Negative Item Values)-Mine, for efficiently and effectively mining high utility itemsets from large databases with consideration of negative item values. To the best of our knowledge, this is the first work that considers the concept of negative item values in utility mining. The novel contribution of HUINIV-Mine is that it can effectively identify high utility itemsets by generating fewer high transaction-weighted utilization itemsets such that the execution time can be reduced substantially in mining the high utility itemsets. In this way, the process of discovering all high utility itemsets with consideration of negative item values can be accomplished effectively with less requirements on memory space and CPU I/O. This meets the critical requirements of temporal and spatial efficiency for mining high utility itemsets with negative item values. Through experimental evaluation, it is shown that HUINIV-Mine outperforms other methods substantially by generating much less candidate itemsets under different experimental conditions.     

Unbounded expected utility and continuity

This paper develops an axiom system for expected utility in a setting wherepreferences are defined directly on probability distributions of outcomes. The axioms do not imply boundedness of the utility function. The approach is topological, and conditions for continuity of the utility function are brought out.