The impact of financial leverage on risk of equity measured by loss-oriented risk measures: An option pricing approach

We investigate how financial leverage influences the risk of equity in companies with limited liability. In our study, the risk is measured by loss-oriented risk measures (VaR, downside deviation, etc.). Also, the dependence of the risk premium on risk is under consideration. VaR-based and downside risk measures are considered in similar frameworks, and risk premium is introduced which is symmetrical to these risk measures. The value of equity is modeled by the price of a call option. In most cases there is a positive relationship between the level of leverage measured by the debt ratio and the risk measured by the loss-oriented risk measures. However, there exist exceptions. The risk premium is not a linear function of the risk. Still, for a reasonable range of leverage, the dependence of the risk premium on risk is approximately linear in most cases.     

Factor risk quantification in annuity models

Calculation of risk contributions of sub-portfolios to total portfolio risk is essential for risk management in insurance companies. Thanks to risk capital allocation methods and linearity of the loss model, sub-portfolio (or position) contributions can be calculated efficiently. However, factor risk contribution theory in non-linear loss models has received little interest. Our concern is the determination of factor risk contributions to total portfolio risk where portfolio risk is a non-linear function of factor risks. We employ different approximations in order to convert the non-linear loss model into a linear one. We illustrate the theory on an annuity portfolio where the main factor risks are interest-rate risk and mortality risk.     

股市风险构成间接分解模型的改进及实证

对Campbell等提出的分析股市风险构成的间接分解模型进行改进,并运用改进模型研究中国股票市场1995年至2005年的风险构成和趋势。结果发现,公司风险是个股收益率平均风险的最大组成部分,其次是系统风险,行业风险的重要性相对较小;中国股市收益率的平均风险随时间存在下降的趋势,而公司风险和行业风险的重要性随时间在增加;总的协方差风险序列对个股收益率平均风险的影响,随时间不具有一致性。在分析股市风险构成时,不应忽略对协方差风险序列的研究。     

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。     

考虑两个风险情形的项目风险应对策略选择方法

项目风险应对是风险管理的一个值得关注的重要研究问题。本文是在文献[11]研究单一风险情形的项目风险应对策略选择方法的基础上,进一步给出了考虑两个风险情形的项目风险应对策略选择方法。在本文中,首先给出了项目风险应对策略的相关概念及数学描述;然后,考虑到针对一个风险所采取的应对策略会对另一个风险发生作用,给出了项目风险应对策略选择问题的分析,并在此基础上,构建了项目风险应对策略选择的优化模型,进而通过求解模型可进行选择最优风险应对策略;最后,通过一个实例分析说明了本文给出方法的可行性和有效性。     

均值-方差期望效用函数下的风险共担

借助Samuelson提出的风险汇合(Risk Adding)与风险分担(Risk Pooling)的概念,讨论了风险共担(Risk Sharing)机制产生的原理.在均值-方差效用函数下,给出了帕累托有效风险共担原则的具体形式,以及风险共担群体接纳新的个体,从而形成更大风险共担群体的条件.在此基础上,证明在均值-方差期望效用函数下,当考虑风险共担群体的形成条件以后,帕累托有效的风险共担原则等价于条件期望风险分配函数.从而在这一特殊效用函数下,建立了风险共担与风险分配函数之间的等价关系.     

考虑公众风险感知的突发事件风险传播模型及仿真研究

突发事件应对过程中,公众对突发事件的风险感知会在一定程度上决定其行为选择从而影响事件风险的传播。为此,本文通过分析突发事件风险信息、风险感知和风险传播的路径关系,在风险传播过程中引入传染病传播机制,构建基于微分方程的风险传播模型。综合考虑风险传播阈值、媒体报道力度、群体风险感知度、个人风险知识水平四类因素并结合仿真实验分析对风险感知和风险传播行为的影响。最后,通过实例研究表明模型结论的有效性。本文研究结论有助于为相关职能部门调节公众风险感知,制定风险防控措施提供理论依据与支持。     

市场风险值VaR的算法与应用

进行金融风险管理时可以将风险划分为四类，即信用风险、经营风险、流动性风险和市场风险。其中市场风险是指金融市场价格（包括股票价格、利率、汇率和大宗可交易商品的价格）波动而引起的未来收益的不确定性。市场风险值VaR(Value at Risk）就是用来评价给定资产所面临的市场风险大小。本文介绍了VaR的定义、相关的计算方法和在证券投资决策中的应用实例。     

The one-year non-life insurance risk

A major part of the literature on non-life insurance reserve risk has been devoted to the ultimo risk, the risk in the full run-off of the liabilities. This is in contrast to the short time horizon in internal risk models at insurance companies, and the one-year risk perspective taken in the Solvency II project of the European Community.This paper aims at clarifying the one-year risk concept and describing simulation approaches, in particular for the one-year reserve risk. We also discuss the one-year premium risk and its relation to the premium reserve.Finally, we initiate a discussion on the role of risk margins and discounting for the reserve and premium risk, with focus on the Cost-of-Capital method. We show that risk margins do not affect the reserve risk and show how reserve duration can be used for easy calculation of risk margins. ¹     

Variance computations for functional of absolute risk estimates

We present a simple influence function based approach for computing the variances of estimates of absolute risk and functions of absolute risk. We apply this approach to criteria that assess the impact of changes in the risk factor distribution on absolute risk for an individual and at the population level. As an illustration we use an absolute risk prediction model for breast cancer that includes modifiable risk factors in addition to standard breast cancer risk factors. Influence function based variance estimates for absolute risk and the criteria are compared to bootstrap variance estimates.     

基于ANP和模糊聚类的军人家属风险研究

军人家属风险是因军人履行职责而承担的连带风险, 是军人风险的重要组成部分。军人家属风险管理状况关系到军队的稳定性。由于军人家属风险属性上具备一定的模糊性, 当前缺乏规范的理论指导和实践管理经验。文章尝试通过构建ANP模型, 首先分析影响军人风险的因子指标及权重, 再以此为依据, 针对军人家属风险采用模糊聚类法与典型的人身风险、财产风险和责任风险进行聚类, 以期寻求最适宜的类别划分, 将典型风险的成熟管理模式和经验借鉴到军人家属风险领域, 并提出相应的管理建议。研究发现, 意外伤害风险、住房保障风险等13项指标是军人家属风险的主要影响因素; 军人家属风险在阈值0.95的水平上与责任风险聚为同一类型; 构建以军人家属风险为对象, 以军人家属社保和住房为重点内容, 军队保险、商业保险和军人互助保险三位一体的责任保险体系, 是完善军人家属风险管理的关键所在。     

高新技术项目区域风险多层次灰色评价

从区域产业风险、社会政治风险、政策法规风险、经济波动风险、金融与资本市场风险和人力资源风险等四个方面 ,设计了高新技术项目区域风险的综合评价指标体系 ,并描述了灰色系统理论应用于风险评价的基本过程 ,希望能有助于高新技术项目投资者的项目决策 .     

Risk taking with background risk under recursive rank-dependent utility

This paper examines how background risk affects risk taking under rank-dependent utility. I assume that a decision-maker facing a risk taking decision in the presence of background risk views these risks as composing a compound lottery, and recursively evaluates this compound lottery using rank-dependent utility. I show that adding background risk increases risk aversion whenever the utility-for-wealth function is risk vulnerable (Gollier and Pratt, 1996) in this model.     

Univariate and multivariate measures of risk aversion and risk premiums

This paper develops univariate and multivariate measures of risk aversion for correlated risks. We derive Rubinstein's measures of risk aversion from the risk premiums with correlated random initial wealth and risk. It is shown that these measures are not only consistent with those for uncorrelated or independent risks, but also have the corresponding local properties of the Arrow-Pratt measures of risk aversion. Thus Rubinstein's measures of risk aversion are the appropriate extension of the Arrow-Pratt measures of risk aversion in the univariate case. We also derive a risk aversion matrix from the risk premiums with correlated initial wealth and risk vectors. This matrix measure is the multivariate version of Rubinstein's measures and is also the generalization of Duncan's results for non-random initial wealth. The univariate and multivariate measures of risk aversion developed in this paper are applied to portfolio theory in Li and Ziemba [15].This research was partially supported by the National Research Council of Canada.     

New results on the relationship among risk aversion,prudence and temperance

This note studies the relationships between different aspects of agent’s preferences toward risk. We show that, under the assumptions of non-satiation and bounded marginal utility, prudence implies risk aversion (imprudence implies risk loving) and that temperance implies prudence (intemperance implies imprudence). The implications of these results for comparing risks in the cases of increase in risk, increase in downside risk and increase in outer risk are discussed.     

Risk measuring under liquidity risk

We present a general framework for measuring the liquidity risk. The theoretical framework defines risk measures that incorporate the liquidity risk into the standard risk measures. We consider a one-period risk measurement model. The liquidity risk is defined as the risk that a security or a portfolio of securities cannot be sold or bought without causing changes in prices. The risk measures are decomposed into two terms, one measuring the risk of the future value of a given position in a security or a portfolio of securities and the other the initial cost of this position. Within the framework of coherent risk measures, the risk measures applied to the random part of the future value of a position in a determinate security are increasing monotonic and convex cash sub-additive on long positions. The contrary, in certain situations, holds for the sell positions. By using convex risk measures, we apply our framework to the situation in which large trades are broken into many small ones. Dual representation results are obtained for both positions in securities and portfolios. We give many examples of risk measures and derive for each of them the respective capital requirement. In particular, we discuss the VaR measure.     

Extending dynamic convex risk measures from discrete time to continuous time: A convergence approach

We present an approach for the transition from convex risk measures in a certain discrete time setting to their counterparts in continuous time. The aim of this paper is to show that a large class of convex risk measures in continuous time can be obtained as limits of discrete time-consistent convex risk measures. The discrete time risk measures are constructed from properly rescaled (‘tilted’) one-period convex risk measures, using a d-dimensional random walk converging to a Brownian motion. Under suitable conditions (covering many standard one-period risk measures) we obtain convergence of the discrete risk measures to the solution of a BSDE, defining a convex risk measure in continuous time, whose driver can then be viewed as the continuous time analogue of the discrete ‘driver’ characterizing the one-period risk. We derive the limiting drivers for the semi-deviation risk measure, Value at Risk, Average Value at Risk, and the Gini risk measure in closed form.     

Optimal risk transfer for agents with germs

We introduce a new class of risk measures called generalized entropic risk measures (GERMS) that allow economic agents to have different attitudes towards different sources of risk. We formulate the problem of optimal risk transfer in terms of these risk measures and characterize the optimal transfer contract. The optimal contract involves what we call intertemporal source-dependent quotient sharing, where agents linearly share changes in the aggregate risk reserve that occur in response to shocks to the system over time, with scaling coefficients that depend on the attitudes of each agent towards the source of risk causing the shock. Generalized entropic risk measures are not dilations of a common base risk measure, so our results extend the class of risk measures for which explicit characterizations of the optimal transfer contract can be found.     

Risk measurement in the presence of background risk

A distortion-type risk measure is constructed, which evaluates the risk of any uncertain position in the context of a portfolio that contains that position and a fixed background risk. The risk measure can also be used to assess the performance of individual risks within a portfolio, allowing for the portfolio’s re-balancing, an area where standard capital allocation methods fail. It is shown that the properties of the risk measure depart from those of coherent distortion measures. In particular, it is shown that the presence of background risk makes risk measurement sensitive to the scale and aggregation of risk. The case of risks following elliptical distributions is examined in more detail and precise characterisations of the risk measure’s aggregation properties are obtained.     

供应链上两类不同信用风险的关联及传染效应研究

在一个典型的存在资金约束的二级供应链上,通常存在两类不同的信用风险:一是供应商向银行信用贷款所形成的信贷信用风险;二是供应商为零售商提供商业信用而形成的商业信用风险。本文针对上述两类不同信用风险之间的关联性及传染问题展开研究,揭示了两类风险之间的传染机理,度量了风险的传染强度,并分析了传染强度的影响因素。研究表明:两类不同信用风险之间的关联性,导致供应链上存在由非同类信用风险构成的关联信用风险(Different types of associated credit risk),本文简称为供应链上的D类关联信用风险。结合数值分析发现:D类关联信用风险的传染强度与供应商的生产成本及无风险利率正相关,而与商品的市场价格负相关。特别地,当市场需求服从指数分布时,关联信用风险的传染强度与商业信用成本和零售商的特质有关,供应商通过调整商业信用成本和选择零售商类型可以降低D类关联信用风险的传染强度,进而降低自身的银行信贷风险。本文将同类型信用风险之间的关联和传染问题引申到不同类型的信用风险之间,进一步深化和拓展了关联信用风险的内涵。