一个非对称线性风险函数与证券组合投资分析

在分析Jia&D yer的风险-价值理论基础上,给出了一个基于预先给定的目标收益的非对称线性风险函数.该风险函数是低于参考点的离差和高于参考点的离差的加权和,它利用一阶"上偏矩"来修正一阶下偏矩,进一步建立了在此非对称风险函数下的线性规划证券投资组合模型;并证明了该模型与二阶随机占优准则的一致性;最后通过上海证券市场的实际数据验证了该模型的有效性和实用性.     

与TSD准则一致的组合证券投资分析

基于预先给定的目标收益率,利用投资者对低于目标收益率的风险损失和高于目标收益率的风险报酬之间的权衡,给出了一些非对称风险度量模型,特别其中一种风险度量是低于参考点的方差和高于参考点的方差的加权和,它利用二阶上偏矩来修正二阶下偏矩,进一步建立了在该非对称风险度量下的组合投资优化模型,并证明了该模型在三阶随机占优的意义下是有效的.此外,还给出了其它3个模型与三阶随机占优准则是否一致的结论,并对所给出的几个组合证券投资模型的求解方法及其应用进行了分析.以上研究和分析为投资者在选择投资模型时避免盲目性、任意性提供了有益的决策参考.     

不完全信息下损失风险的研究

在获得损失分布不完全信息情况下,提出用方差和熵共同度量损失风险的方法.在不完全信息条件下,通过最大熵原理在最不确定的情况下得到最大熵损失分布,并获得了损失分布的熵函数值.用熵值度量损失分布对于均匀分布的离散程度,从而度量概率波动带来的风险;用方差度量损失对于均值的离散程度,从而度量状态波动带来的风险.由于熵是与损失变量更高阶矩信息相联系的,所以新方法是从更全面的角度对损失风险的预测.通过算例,进一步看出在获得高阶矩信息下,熵参与风险度量的必要性.     

基于矩分析的资产组合选择

在风险资产收益分布为非正态的情景下,通过矩分析,研究其收益的高阶矩对资产组合选择的影响.首先,假设风险资产收益存在有限阶矩,泰勒展开边际财富期望效用,获得静态资产组合选择的近似解;其次,假设收益过程的跳跃产生收益分布的非正态性,运用随机控制方法获得动态资产组合选择的近似解析解,从高阶矩角度解释其特征。分析表明,超出峰度的存在导致减少风险资产投资,正(负)的偏度导致增加(减少)风险资产投资,该影响性随着它们及风险规避系数的增大而增强;可预测性导致资产组合存在正或负的对冲需求,取决于相关系数的符号和风险规避系数;跳跃性总体上减少风险资产投资;可预测性和跳跃性对动态资产组合选择的影响具有内在关联性。     

基于超前倒向随机微分方程的动态风险度量

本文研究了基于超前倒向随机微分方程的时间相容的过程的动态凸(一致性)风险度量的问题.利用对超前倒向随机微分方程生成元的适当假设,建立超前倒向随机微分方程生成元与过程的动态凸(一致性)风险度量的对应模型,证明了超前倒向随机微分方程的解可以定义时间相容的过程的风险度量.得到了基于超前倒向随机微分方程的风险度量,推广了基于倒向随机微分方程的动态风险度量.由于超前倒向随机微分方程生成元中包含当前时刻和未来时刻的解,因此本文的结论对风险的预测更加可靠.     

投资者情绪对上证50ETF隐含分布偏度影响的实证研究

从期权价格中提取信息的传统做法是借助于隐含波动率,然而,通过与标的资产的历史数据对比发现,隐含波动率并不能比历史波动率提供更多的市场预期信息。考虑隐含波动率是利用Black-Scholes模型所导出,意味着模型设定风险也可能会影响到结论的客观性与准确性。为了克服传统方法的不足,本文尝试从一种无模型的视角,利用矩方法展开相关研究。该方法不依赖于任何模型和假设,避免了对定价核以及中性概率分布的讨论,直接由期权价格得到股票收益的隐含分布,利用状态价格来确定市场预期收益与风险厌恶。在分布曲线足够光滑(可导)的条件下,通过对行权价格求导得到标的资产未来收益的隐含风险中性概率密度,并测算出隐含分布的高阶矩特征。     

考虑借款企业决策行为的供应链CVaR利率决策模型

贷款利率是银行和其他金融机构用于权衡风险和收益的重要指标之一.考虑借款企业的决策行为,采用CVaR的风险度量准则作为决策标准,建立了基于条件风险价值最小的银行贷款利率决策模型,得到了权衡风险和收益条件下的最优利率.通过模型求解和数值分析发现:决策者的风险容忍水平直接对利率决策产生影响,CVaR风险度量准则可以帮助银行权衡收益和风险:借款企业利润率和自有资金是银行规避风险时需要着重考虑的关键因素.     

一种多目标条件风险值数学模型

研究了一种多目标条件风险值(CVaR)数学模型理论.先定义了一种多目标损失函数下的α-VaR和α-CVaR值,给出了多目标CVaR最优化模型.然后证明了多目标意义下的α-VaR和α-CVaR值的等价定理,并且给出了对于多目标损失函数的条件风险值的一致性度量性质.最后,给出了多目标CVaR模型的近似求解模型.     

金融风险度量的建模理论与方法的一些进展及其应用

本文综述了金融风险度量的建模的理论和方法最近的发展。介绍了常用的矩度量和现代风险度量技术,包括在险价值VaR、预期不足ES和期望分位数Expectile等现代风险度量技术和方法,以及复杂风险因素下的非/半参数风险度量方法。违约概率和违约相关性是信用风险度量中的两个基本概念,本文还介绍了信用违约风险中违约概率和违约相关性的常用度量方法。最后,通过一些应用案例介绍如何在金融风险度量中应用现代风险度量技术度量和识别风险。     

PLS情绪指数对中国股市风险收益关系的影响研究

从行为金融学角度研究投资者情绪对中国股市风险收益关系的影响,或有助于更好的解释风险收益关系.采用偏最小二乘法(PLS)构建新的投资者情绪综合指数,同时在对风险的度量中运用个股平均相关性代替总体方差来度量市场风险.研究结果表明PLS情绪指数比常用的主成分分析法所构建的情绪指数及单个情绪代理变量能更好的解释股市收益;平均相关性比市场波动更适合作为市场风险的度量指标;投资者情绪对风险收益关系有显著影响,其中在低情绪期风险和收益之间的相关性不显著,而高情绪期风险和收益之间呈现显著的负相关关系.由实证结果可知中国股市投资者存在非理性行为,应从行为金融的角度去考虑资产定价,同时对各指标的准确度量更有利于完善行为资产定价理论.     

双侧风险度量方法及其在投资组合优化模型中的应用

现有的资产风险度量方法不能合理的反映收益的向上波动给投资者带来的风险感受,针对这一不足,本文提出了一种新的风险度量方法,这一方法综合考虑了投资者对于损失的规避和对超额收益的偏好,能够更为真实的反映投资者对于资产收益双侧波动的不同风险感受.同时本文结合新的风险度量方法给出了投资组合优化模型,并对模型的解从不同角度进行了分析.研究结果表明,新的风险度量方法可以为投资者提供更有效的投资决策依据,并且投资者的风险态度对于投资组合有效前沿和最优投资组合都有显著的影响.     

新型风险投资组合选择模型

为克服现有关于风险投资的投资组合选择研究所存在的诸如相关参量在实际中不易确定、对投资风险的刻画过于粗糙等不足,本文依据风险投资的特点,提出了直接基于对风险投资项目的综合评价值来预测其未来投资效益与风险的新方法,给出了两种更合理的风险度量,并由此导出了相应的新型风险投资的投资组合选择模型,模拟结果说明了新度量和模型的合理性和实用价值.     

Market price-based convex risk measures: A distribution-free optimization approach

In Cont (2006) [1], a convex risk measure was proposed to measure the impact of uncertainty resulting from the misspecification of derivative models. Evaluation of the risk measures was illustrated on finite families of probability measures. In this paper, we consider the case of infinite families of measures that share common moments, e.g. mean and variance for European-style options. We show that the risk measure can still be efficiently evaluated based on semi-infinite programming. Examples are given that illustrate the benefits of evaluating the risk measure with infinite families of measures and shed light on the limitations of considering only finite families of measures.     

First return probabilities of birth and death chains and associated orthogonal polynomials

For a birth and death chain on the nonnegative integers, integral representations for first return probabilities are derived. While the integral representations for ordinary transition probabilities given by Karlin and McGregor (1959) involve a system of random walk polynomials and the corresponding measure of orthogonality, the formulas for the first return probabilities are based on the corresponding systems of associated orthogonal polynomials. Moreover, while the moments of the measure corresponding to the random walk polynomials give the ordinary return probabilities to the origin, the moments of the measure corresponding to the associated polynomials give the first return probabilities to the origin.

As a by-product we obtain a new characterization in terms of canonical moments for the measure of orthogonality corresponding to the first associated orthogonal polynomials. The results are illustrated by several examples.

     

Optimal Financial Portfolios

The classes of reward‐risk optimization problems that arise from different choices of reward and risk measures are considered. In certain examples the generic problem reduces to linear or quadratic programming problems. An algorithm based on a sequence of convex feasibility problems is given for the general quasi‐concave ratio problem. Reward‐risk ratios that are appropriate in particular for non‐normal assets return distributions and are not quasi‐concave are also considered.     

Portfolio value-at-risk optimization for asymmetrically distributed asset returns

We propose a new approach to portfolio optimization by separating asset return distributions into positive and negative half-spaces. The approach minimizes a newly-defined Partitioned Value-at-Risk (PVaR) risk measure by using half-space statistical information. Using simulated data, the PVaR approach always generates better risk-return tradeoffs in the optimal portfolios when compared to traditional Markowitz mean–variance approach. When using real financial data, our approach also outperforms the Markowitz approach in the risk-return tradeoff. Given that the PVaR measure is also a robust risk measure, our new approach can be very useful for optimal portfolio allocations when asset return distributions are asymmetrical.     

TSD-consistent performance assessment of mutual funds

This paper presents three new data envelopment analysis-based approaches to assess the relative efficiency of mutual funds (MFs). Each model considers an appropriate risk measure as input and an appropriate return measure as output. The risk and return measures have been chosen so that the proposed models are consistent with third-order stochastic dominance (TSD) rules. This means that the MFs found efficient by the proposed models are also, in a necessity condition sense, TSD efficient and therefore of highest consideration for all non-satiated, risk averse investors that also have decreasing absolute risk aversion. The proposed approach is illustrated with real data on a set of Spanish MFs and compared with existing approaches from the literature based on Mean–Variance and Mean–Variance–Skewness models.     

Robust reward–risk ratio optimization with application in allocation of generation asset

In this article, we study reward–risk ratio models under partially known message of random variables, which is called robust (worst-case) performance ratio problem. Based on the positive homogenous and concave/convex measures of reward and risk, respectively, the new robust ratio model is reduced equivalently to convex optimization problems with a min–max optimization framework. Under some specially partial distribution situation, the convex optimization problem is converted into simple framework involving the expectation reward measure and conditional value-at-risk measure. Compared with the existing reward–risk portfolio research, the proposed ratio model has two characteristics. First, the addressed problem combines with two different aspects. One is to consider an incomplete information case in real-life uncertainty. The other is to focus on the performance ratio optimization problem, which can realize the best balance between the reward and risk. Second, the complicated optimization model is transferred into a simple convex optimization problem by the optimal dual theorem. This indeed improves the usability of models. The generation asset allocation in power systems is presented to validate the new models.     

A new class of coherent risk measures based on p‐norms and their applications

To exercise better control on the lower tail of the loss distribution and to easily describe the investor's risk attitude, a new class of coherent risk measures is proposed in this paper by taking the minimization of p‐norms of lower losses with respect to some reference point. We demonstrate that the new risk measure has satisfactory mathematical properties such as convexity, continuity with respect to parameters included in its definition, the relations between two new risk measures are also examined. The application of the new risk measures for optimal portfolio selection is illustrated by using trade data from the Chinese stock markets. Empirical results not only support our theoretical conclusions, but also show the practicability of the portfolio selection model with our new risk measures. Copyright © 2006 John Wiley & Sons, Ltd.