证券组合M-V有效前沿旋移分析的进一步研究

在市场上存在无风险资产且允许卖空的条件下,研究了新增加k种证券后对原有效前沿的影响.引入了有效证券和无效证券,给出了M-V证券组合有效前沿旋移的方向.研究结果表明新增加证券后有效前沿的斜率变大.     

基于Copula函数的组合资产条件相依性模型研究

条件概率分布常用来研究马尔科夫序列相依模型的构建,组合资产的相依结构受多方面的影响,资产之间的相互影响与时间上的记忆效应是组合资产两类主要的相依关系.结合条件概率的理论建立基于Copula函数相依关系模型,研究组合资产之间同期相依关系及时间上的短期相依关系,提出了模型参数的三阶段极大似然估计方法.     

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．     

不同均值-风险准则下的资产组合有效前沿比较研究

本文根据V aR和CV aR风险度量方法,对马克维茨的均值-方差资产组合选择模型进行拓展,研究在均值-风险准则下更具有一般性的资产组合选择问题.并在正态分布假设条件下,证明当不存在无风险资产时和存在无风险资产时,基于方差、V aR和CV aR风险度量准则的资产组合有有沿之间的关系,指出根据均值-V aR准则和均值-CV aR准则求解有效资产组合时,置信水平必须满足的条件     

不允许卖空的组合投资决策

本建立了一定置信水平下最小收益最大准则下的组合投资决策模型，该模型不仅适用于风险规避，也适用于风险偏好，在风险资产的收益率联合服从正态分布的假设下，给出不容许卖空情形下的求解有效资产组合的算法，并给出一个算例。     

证券数目变化时受到扰动的M-V有效前沿分析

基于M-V证券组合模型,在证券市场上不存在无风险资产且允许卖空条件下,探讨了证券数增加k种后原n种证券协方差矩阵发生改变情形下M-V证券组合有效前沿的漂移问题。通过引入扰动因子和扰动矩阵,给出了M-V证券组合有效前沿的漂移方向及其开口大小的变化情况．研究结果表明证券数增加了k种后有效前沿向左漂移以及它的开口变大,原证券组合的有效前沿完全落在新的证券组合可行集内．     

一类投资组合选择的线性规划方法研究

如何在摩擦市场下构建最优组合一直是一个非常有意义的问题.人们通常在有效前沿上选择最优的投资组合,但是值得注意的是,如果我们考虑摩擦因素,原本的有效组合将不再有效.探讨如何在无风险借贷利率不同的摩擦市场下构建投资组合模型.为了得到最优策略,我们先利用Karush-Kuhn-Tucker条件给出一类线性规划问题求解方法,然后具体阐述如何将投资决策问题转化为可以求解的线性规划问题,最后给出在无风险借贷利率不同的情况下投资组合的有效边界.     

带交易费的最优投资组合选择的极大极小方法

研究不允许卖空时不相关资产的最优投资选择问题.在风险资产收益率不能确切知道的情况下,建立了投资组合选择问题的极大极小模型.将交易费引入到极大极小模型中,交易费假定为新旧投资组合之差的V型函数.推导出有效投资组合与有效前沿的解析表达式.     

静态证券组合理论与CAPM—金融理论及其应用（Ⅱ）

1 前言在静态证券组合理论中,我们假定投资者是依据收益率的均值和方差来决定证券组合的.亦即使均值增大、方差减小的投资.这个资产选择的均值方差模型,从大约40年前的Markowitz(1952)以来,大量地被运用于金融中,其理由,并不在于其假定的一般性,而是在于其优良的解析性.而且,如果在均值方差模型上附加上供需均衡条件,就可以导出被称为资产期望收益率的资本性资产评价模型(Capital Asset Pricing Model(CAPM)),这在现今都是一个最重要的资产评价模型. 本文将简洁地说明静态证券组合理论,导出关于均衡中的资产期望收益率的结果.另外,作为CAPM的应用.介绍资本预算法及其对证券投资的应用.本文的构成:第2节是静态证券组合理论;第3节是为引入CAPM的前沿证券组合的数理;第4节是CAPM;第5节是CAPM的应用;最后是结论.     

不允许卖空证券组合选择的有效子集

证券组合选择的有效子集是指它可取代原有的基本证券集来生成Markowits有效组合前沿.本文给出一个证券集的子集在不允许卖空的条件下是全集的有效子集的充要条件。     

An option-theoretic model of a reputation network

This paper constructs a new theory of social networks based on reputation. The model assumes that reputation is an asset and that individuals connect by buying options on the reputation of others. In networking, individuals construct portfolios of call options to leverage the reputations of others and put options to hedge the connections with others. A network then consists of portfolios of reputation options. The option model confers advantages not present in existing models. First, the payoff to connecting is the payoff on a portfolio of reputation options. Second, the network forms as individuals take option positions; the network evolves as individuals adjust those positions. Third, networking strategies become option strategies. The model allows for insights into network structure, the price of connecting and the value of connecting.     

Outperformance and Tracking: Dynamic Asset Allocation for Active and Passive Portfolio Management

ABSTRACT

Portfolio management problems are often divided into two types: active and passive, where the objective is to outperform and track a preselected benchmark, respectively. Here, we formulate and solve a dynamic asset allocation problem that combines these two objectives in a unified framework. We look to maximize the expected growth rate differential between the wealth of the investor’s portfolio and that of a performance benchmark while penalizing risk-weighted deviations from a given tracking portfolio. Using stochastic control techniques, we provide explicit closed-form expressions for the optimal allocation and we show how the optimal strategy can be related to the growth optimal portfolio. The admissible benchmarks encompass the class of functionally generated portfolios (FGPs), which include the market portfolio, as the only requirement is that they depend only on the prevailing asset values. Finally, some numerical experiments are presented to illustrate the risk–reward profile of the optimal allocation.     

t-分布与不同风险度量下有效投资组合及其边缘的相互关系研究

In order to study the effect of different risk measures on the efficient portfolios (frontier) while properly describing the characteristic of return distributions in the stock market, it is assumed in this paper that the joint return distribution of risky assets obeys the multivariate t-distribution. Under the mean-risk analysis framework, the interrelationship of efficient portfolios (frontier) based on risk measures such as variance, value at risk (VaR), and expected shortfall (ES) is analyzed and compared. It is proved that, when there is no riskless asset in the market, the efficient frontier under VaR or ES is a subset of the mean-variance (MV) efficient frontier, and the efficient portfolios under VaR or ES are also MV efficient; when there exists a riskless asset in the market, a portfolio is MV efficient if and only if it is a VaR or ES efficient portfolio. The obtained results generalize relevant conclusions about investment theory, and can better guide investors to make their investment decision.     

STUDY ON THE INTERRELATION OF EFFICIENT PORTFOLIOS AND THEIR FRONTIER UNDER t DISTRIBUTION AND VARIOUS RISK MEASURES

In order to study the effect of different risk measures on the efficient portfolios (frontier) while properly describing the characteristic of return distributions in the stock market, it is assumed in this paper that the joint return distribution of risky assets obeys the multivari-ate t-distribution. Under the mean-risk analysis framework, the interrelationship of efficient portfolios (frontier) based on risk measures such as variance, value at risk (VaR), and expected shortfall (ES) is analyzed and compared. It is proved that, when there is no riskless asset in the market, the efficient frontier under VaR or ES is a subset of the mean-variance (MV) efficient frontier, and the efficient portfolios under VaR or ES are also MV efficient; when there exists a riskless asset in the market, a portfolio is MV efficient if and only if it is a VaR or ES efficient portfolio. The obtained results generalize relevant conclusions about investment theory, and can better guide investors to make their investment decision.     

STUDY ON THE INTERRELATION OF EFFICIENT PORTFOLIOS AND THEIR FRONTIER UNDER t DISTRIBUTION AND VARIOUS RISK MEASUREgS

In order to study the effect of different risk measures on the efficient portfolios （fron- tier） while properly describing the characteristic of return distributions in the stock market, it is assumed in this paper that the joint return distribution of risky assets obeys the multivariate t-distribution. Under the mean-risk analysis framework, the interrelationship of efficient portfolios （frontier） based on risk measures such as variance, value at risk （VaR）, and expected shortfall （ES） is analyzed and compared. It is proved that, when there is no riskless asset in the market, the efficient frontier under VaR or ES is a subset of the mean-variance （MV） efficient frontier, and the efficient portfolios under VaR or ES are also MV efficient; when there exists a riskless asset in the market, a portfolio is MV efficient if and only if it is a VaR or ES efficient portfolio. The obtained results generalize relevant conclusions about investment theory, and can better guide investors to make their investment decision.     

Sharp Upper and Lower Bounds for Basket Options

Given a basket option on two or more assets in a one‐period static hedging setting, the paper considers the problem of maximizing and minimizing the basket option price subject to the constraints of known option prices on the component stocks and consistency with forward prices and treat it as an optimization problem. Sharp upper bounds are derived for the general n‐asset case and sharp lower bounds for the two‐asset case, both in closed forms, of the price of the basket option. In the case n = 2 examples are given of discrete distributions attaining the bounds. Hedge ratios are also derived for optimal sub and super replicating portfolios consisting of the options on the individual underlying stocks and the stocks themselves.     

选择资产组合的EP-MV模型及最优解的解析表示

本文提出了存在无风险资产贷出或借入时的有效投资组合模型(EP-MV模型)，研究了不允许卖空(投资比例非负)约束条件下，EP-MV优化模型的算法，给出了有效投资组合投资比例的解析表示．在资产收益由多因素模型产生的基础上，得到了资产与有效投资组合的期望收益及风险的估计，便于实际应用．     

Large deviations theorems for optimal investment problems with large portfolios

The thrust of this paper is to develop a new theoretical framework, based on large deviations theory, for the problem of optimal asset allocation in large portfolios. This problem is, apart from being theoretically interesting, also of practical relevance; examples include, inter alia, hedge funds where optimal strategies involve a large number of assets. In particular, we also prove the upper bound of the shortfall probability (or the risk bound) for the case where there is a finite number of assets. In the two-assets scenario, the effects of two types of asymmetries (i.e., asymmetry in the portfolio return distribution and asymmetric dependence among assets) on optimal portfolios and risk bounds are investigated. We calibrate our method with international equity data. In sum, both a theoretical analysis of the method and an empirical application indicate the feasibility and the significance of our approach.     

不存在无风险资产的投资组合灵敏度分析

本文研究了M－V证券投资组合灵敏度分析方法。考虑了不存在无险资产时证券预睡益率和协方差矩阵存在扰动的情形，给出了最优投资组合有效边缘的漂移方程及组合扩展路径。     

Portfolio Selection and Transactions Costs

This paper deals with the portfolio selection problem of risky assets with a diagonal covariance matrix, upper bounds on all assets and transactions costs. An algorithm for its solution is formulated which terminates in a number of iterations that is at most three times the number of assets. The efficient portfolios, under appropriate assumptions, are shown to have the following structure. As the risk tolerance parameter increases, an asset's holdings increases to its target, then stays there for a while, then increases to its upper bound, reaches it and stays there. Then the holdings of the asset with the next highest expected return proceeds in a similar way and so on.