两类索赔相关风险模型的罚金折现期望函数

考虑两类索赔相关风险模型.两类索赔计数过程分别为独立的广义Poisson过程和广义Erlang(2)过程.得到了该风险模型的罚金折现期望函数满足的积分微分方程及该函数的Laplace变换的表达式,且当索赔额均服从指数分布时,给出了罚金折现期望函数及破产概率的明确表达式.     

风险资产市场组合的概率分布和均值估计

探讨CAPM中风险资产市场组合的概率分布和均值估计问题.在股票价格行为模型用维纳过程(又称布朗运动)表述的前提下,证明了CAPM中的市场组合服从加法逻辑正态分布的结论,进而给出了市场组合均值的3种估计.以此为基础进行CAPM的实证检验,才具有理论上的严密性.     

具有随机收入的一类更新风险模型中的期望折现罚函数北大核心CSCD

考虑了具有随机收入的索赔时间间距服从相型分布的保险风险模型.建立了期望折现罚函数所满足的积分方程,当年金收入量为指数分布时,得到了期望折现罚函数的拉普拉斯解.进一步当索赔数量分布属于有理函数族时,给出了期望折现罚函数的解析表达式.     

组合投资与资本资产定价模型

根据效用理论 ,投资者在期望效用最大化准则下选择组合投资方案 ,通过改进均值 -方差模型假定 ,在完全市场 ( perfect markets)条件下由组合投资模型推导出广义的资本资产定价模型 .并证明了在投资者具有二次效用 ,或者收益率服从联合正态分布的情形下 ,它与夏普 -林特纳的资本资产定价模型 ( CA PM)一致     

一类相依双险种风险模型的罚金折现期望函数

考虑索赔到达具有相依性的一类双险种风险模型,其中第一类险种的索赔计数过程为Poisson过程,第二类险种的索赔计数过程为其p-稀疏过程与广义Erlang(2)过程的和,利用更新论证得到了此风险模型的罚金折现期望函数满足的微积分方程及其Laplace变换的表达式.并就索赔额均服从指数分布的情形,给出了罚金函数及破产概率的精确表达式.     

马氏环境下带干扰Cox风险模型的罚金折现期望函数

研究了马氏环境下带干扰的Cox风险模型.首先给出了罚金折现期望函数满足的积分方程,然后给出了破产概率,破产前瞬时盈余、破产赤字的分布及各阶矩所满足的积分方程.最后给出当索赔额服从指数分布且理赔强度为两状态时的破产概率的拉普拉斯变换.     

有跳风险的随机利率与动态资产分配

在股票服从跳扩散模型及利率满足有随机跳的均值回复过程的不完全市场下,讨论了股票,债券和银行存款的组合选择投资问题.应用动态规划建立了终期财富效用期望最大化目标函数对应的H JB方程,并给出了投资策略的表达式,最后通过数值计算分析了投资策略与风险回避参数γ,跳到达强度参数λ等关系.     

应用复合极值理论计算VaR1

本文介绍了一种复合极值理论,并将其应用到VaR的计算上。实际中大的损失发生的频率也是风险的一种度量,在应用复合极值理论方法计算VaR时,我们第一次将在一定时期内金融资产的损失率超过一定阈值的次数的分布和收益率的分布结合了起来,对欧元/人民币、日元/人民币两种汇率进行了VaR的计算,经过实证分析,得到了一些有意义的结果。     

具有随机收入的一类更新风险模型中的期望折现罚函数

考虑了具有随机收入的索赔时间间距服从相型分布的保险风险模型.建立了期望折现罚函数所满足的积分方程,当年金收入量为指数分布时,得到了期望折现罚函数的拉普拉斯解.进一步当索赔数量分布属于有理函数族时,给出了期望折现罚函数的解析表达式.     

组合证券投资优化模型的比较研究

本文给出基于历史收益率数据的均值一极差和均值一离差型组合证券投资优化模型,并用实例对两模型的结果进行比较。     

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.     

Stochastic optimization for allocation problems with shortfall risk constraints

One of the crucial aspects in asset allocation problems is the assumption concerning the probability distribution of asset returns. Financial managers generally suppose normal distribution, even if extreme realizations usually have an higher frequency than in the Gaussian case. The aim of this paper is to propose a general Monte Carlo simulation approach able to solve an asset allocation problem with shortfall constraint, and to evaluate the exact portfolio risk‐level when managers assume a misspecified return behaviour. We assume that returns are generated by a multivariate skewed Student‐t distribution where each marginal can have different degrees of freedom. The stochastic optimization allows us to value the effective risk for managers. In the empirical application we consider a symmetric and heterogeneous case, and interestingly note that a multivariate Student‐t with heterogeneous marginal distributions produces in the optimization problem a shortfall probability and a shortfall return level that can be adequately approximated by assuming a multivariate Student‐t with common degrees of freedom. Thus, the proposed simulation‐based approach could be an important instrument for investors who require a qualitative assessment of the reliability and sensitivity of their investment strategies in the case their models could be potentially misspecified. Copyright © 2007 John Wiley & Sons, Ltd.     

沪深股市的相关结构分析与投资组合风险度量——基于ARFIMA-GARCH-Copula模型

金融资产收益率不仅具有尖峰厚尾性、异方差性,还具有长记忆性。基于此,本文建立ARFIMA-GARCH-Copula模型来研究沪深股市的相关结构和等权重投资组合风险值VaR,利用上证指数和深成指数收益率的组合来进行实证研究。首先采用经典R/S分析法检验各个资产收益率的长记忆性,经过分数阶差分后选用GARCH模型建模得到边缘分布。然后选择Copula函数来刻画两资产之间的相关结构,建立联合分布模型。进而采用Monte Carlo方法模拟产生各资产的收益率序列,计算出投资组合的风险值VaR。实证研究表明:沪深股市具有长记忆性,且两者具有对称的尾部相关性;Kupiec检验说明ARFIMA-GARCH-Copula模型较之于GARCH-Copula模型能更准确地度量投资组合风险。     

GH分布族下资产收益率分布拟合优度比较——基于中国证券指数高频数据的实证研究

资产收益率分布假设对期权定价、对冲,风险度量和组合资产优化的结果有着重要影响.但由于资产收益率的"程式化性质",经典正态分布假设不能很好拟合实际收益率分布.广义双曲线分布,作为子分布及极限分布非常丰富的分布族,在资产收益率分布拟合中已取得良好效果.在讨论第三类修正贝塞尔函数和广义逆高斯分布性质基础上,借助于正态均值-方差混合理论,得到广义双曲线分布及其极限分布.在McNeil,Frey和Embrechts(2005)算法框架内,以及WenBo Hu(2005)算法改进基础上,对参数估计的算法做了实质性改进:用两个重要参数χ和ψ的线性关系,代替了一个包含第三类修正贝塞尔函数的方程,避免了对该方程数值求解.在实证部分,选择了3个主要指数,利用GH分布的两个子分布和两个极限分布对过滤后的指数收益率进行拟合,并对它们的拟合优度和收敛速度做了比较.     

Portfolio insurance: Gap risk under conditional multiples

The research on financial portfolio optimization has been originally developed by Markowitz (1952). It has been further extended in many directions, among them the portfolio insurance theory introduced by Leland and Rubinstein (1976) for the “Option Based Portfolio Insurance” (OBPI) and Perold (1986) for the “Constant Proportion Portfolio Insurance” method (CPPI). The recent financial crisis has dramatically emphasized the interest of such portfolio strategies. This paper examines the CPPI method when the multiple is allowed to vary over time. To control the risk of such portfolio management, a quantile approach is introduced together with expected shortfall criteria. In this framework, we provide explicit upper bounds on the multiple as function of past asset returns and volatilities. These values can be statistically estimated from financial data, using for example ARCH type models. We show how the multiple can be chosen in order to satisfy the guarantee condition, at a given level of probability and for various financial market conditions.     

Asset management and surplus distribution strategies in life insurance: An examination with respect to risk pricing and risk measurement

In this paper, we investigate the impact of different asset management and surplus distribution strategies in life insurance on risk-neutral pricing and shortfall risk. In general, these feedback mechanisms affect the contract’s payoff and hence directly influence pricing and risk measurement. To isolate the effect of such strategies on shortfall risk, we calibrate contract parameters so that the compared contracts have the same market value and same default-value-to-liability ratio. This way, the fair valuation method is extended since, in addition to the contract’s market value, the default put option value is fixed. We then compare shortfall probability and expected shortfall and show the substantial impact of different management mechanisms acting on the asset and liability side.     

均值-ES框架下带交易费用的资本资产市场中均衡价格的存在性与确定

探讨具有有限多个风险资产和一个无风险资产、有多个投资者参与的资本资产市场中非负均衡价格的存在性条件与确定问题,从以下角度改进了现有结果:采用期望损失(Expected shortfall,简称ES)作为风险度量,保证了均值-ES框架下所得结果与期望效用极大化原理结果的一致性;对证券收益的联合分布不做假设;考虑了比例交易费用对价格的影响,所得结果更贴近现实的金融市场;不仅给出了非负均衡价格存在唯一的充要条件,而且导出了其具体表达式;在对比分析其与现有结果异同的同时,还讨论了所给充要条件与定价公式的应用与经济解释.     

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。