基于贝叶斯极值估计的商业银行内部欺诈风险度量研究

内部欺诈风险是我国商业银行面临的一个重大风险来源。本文针对内部欺诈具有的低频率高损失的特点,采用不同分布分段刻画其损失统计分布规律,对于低于和高于门限值的样本点,采用Box-Cox变换和全Paretian分布模型进行分析,然后采用贝叶斯估计对全Paretian分布模型的参数进行估计,接着在此基础上对建立了一个内部欺诈风险度量模型,然后使用所构建的风险度量模型对操作风险在险风险值、经济资本和最大可能损失进行了测算,最后提出了防范操作风险的政策建议。     

商业银行操作风险计量模型的Bayes估计

对于商业银行来讲,一个很重要的问题是损失数据缺乏,而损失数据缺乏会影响模型参数的估计,用Bayes估计解决了这一问题.Bayes估计的方法利用商业银行专家提供的意见确定先验分布,能够有效地解决损失数据缺乏的问题.实证分析的结果表明,Bayes估计与极大似然估计的结果.不考虑存在着一定的差距.不考虑各部分风险之间的相关性,基于Bayes估计与极大似然估计时VaR与ES的大部分结果相差不大.     

尖峰厚尾保险损失数据的统计建模

保险损失数据的一个重要特点是尖峰厚尾性,即既有大量的小额损失,又有少量的高额损失,使得通常的损失分布模型很难拟合此类数据,从而出现了对各种损失分布模型进行改进的尝试.改进后的模型一方面要有较高的峰度,另一方面又要有较厚的尾部.最近几年文献中出现的改进模型主要是组合模型,即把一个具有非零众数的模型(如对数正态分布或威布尔分布)与一个厚尾分布模型(如帕累托分布或广义帕累托分布)进行组合.讨论了这些组合模型的性质和特点,并与偏t正态分布和偏t分布进行了比较分析,最后应用MCMC方法估计模型参数,并通过一个实际损失数据的拟合分析,表明偏t分布对尖峰厚尾损失数据的拟合要优于目前已经提出的各种组合模型.     

Levy分布参数估计的损失函数和风险函数的Bayes推断

给出了在共轭先验分布下,L evy分布参数估计的损失函数和风险函数的Bayes估计及其为保守估计的一般条件,说明了该条件的合理性,并用S&P 500$close数据进行了实证分析支持我们的结论.     

基于蒙特卡罗模拟的供应链风险估计研究

以市场需求波动风险为例,基于蒙特卡罗模拟研究了供应链风险估计问题.首先,对市场需求波动风险及其损失度量进行理论分析,利用市场需求波动风险情境下的供应链系统库存成本损失来度量市场需求波动风险的损失.其次,选择供应链末端需求为蒙特卡罗方法待模拟的随机变量,基于需求建立了市场需求波动风险概率测度模型和风险损失度量模型,确定了市场需求波动风险概率和风险损失为需求的相关量.然后,通过实例的仿真求解验证了模型.最后,给出了利用本模型方法进行供应链风险估计时需要注意的问题及进一步研究的问题.研究表明:蒙特卡罗方法对供应链风险估计具有较强的鲁棒性.     

失真风险保费的最优经验厘定

研究了贝叶斯模型中失真风险保费的经验厘定问题.通过引入分布函数的加权积分损失函数,利用信度理论的方法最小化期望损失得到分布函数的最优线性估计,进而得到失真风险保费的两个信度估计,并对信度估计的统计性质进行了比较.文章还讨论了失真函数和权重函数的选取问题,给出了结构参数的估计方法,证明了估计的无偏性和相合性.最后,利用数值模拟的方法验证了估计的收敛情况,并对不同失真函数下的收敛情况进行了比较.     

基于贝叶斯分析的中国商业银行内部欺诈分析

内部欺诈事件类型是中国商业银行最严重的操作风险类型。但由于操作风险本质特征和中国商业银行内部欺诈损失数据收集年度较短,数据匮乏,小样本数据容易导致参数结果不稳定。为了在小样本数据下进行更准确的度量,本文采用贝叶斯马尔科夫蒙特卡洛模拟方法,在损失分布法框架下,假设损失频率服从泊松-伽马分布,而损失强度服从广义帕累托-混合伽马分布,分析后验分布的形式,获得中国商业银行不同业务线的内部欺诈损失频率和损失强度的后验分布估计,并进行蒙特卡罗模拟获得不同业务线内部欺诈的风险联合分布。结果表明,拟合结果很好,与传统极值分析法相比,基于利用贝叶斯的分析获得的后验分布可以作为未来的先验分布,有利于在较小样本下获得较真实的参数估计,本方法有助于银行降低监管资本要求。     

基于藤Copula方法的巨灾风险条件VaR预测

为准确预测巨灾风险的条件VaR,应用藤Copula方法刻画巨灾损失变量间的相关结构,进而得到损失变量间的联合分布和条件分布函数,最终实现对条件VaR的估计.对全球洪水的损失数据进行实证分析,利用核密度估计检验法从常用多元Copula中选出最优的Copula作为比较对象,回测检验结果表明:准确刻画相关结构是精确估计条件VaR的关键,藤Copula方法对巨灾风险条件VaR的预测能力要优于常用多元Copula方法.     

基于分段损失分布法和Copula的银行操作风险集成度量

多个风险单元的集成度量是银行操作风险管理的关键步骤之一。立足于操作风险的“厚尾”、“截断”性,从分段损失分布法的视角出发,探讨操作风险集成度量的模式和数值方法。首先,引入两阶段损失分布法来拟合单个风险单元边际损失分布,用双截尾分布代替传统的完整分布来刻画“高频低损”损失数据的双截断特性,利用POT模型捕获“低频高损”事件的厚尾特性。再次,基于分段建模思路,对传统度量过程中边际分布为单一、完整分布的Copula模型进行了扩展,研究边际分布为分段分布、截尾分布条件下使用Copula函数集成度量操作风险的框架和步骤,并设计了Monte Carlo模拟算法。最后,以实证分析的形式验证所构建模型。通过对中国商业银行416个操作风险损失数据的实证分析,结果表明分段分布、截尾分布能对单个风险单元边际分布有更好的拟合效果,能减小由于分布选择不当而引发的模型风险。分段度量视角下Copula函数的引入能灵活处理多个操作风险单元间的相依结构,使风险度量结果更为合理。     

基于POT方法的商业银行操作风险极端值估计

对于商业银行而言,操作风险已经成为与市场风险和信用风险同样重要的风险。本文利用极值理论超越样本的估计能力,采用极值理论中对数据要求量较少,可以进行单步预测的超阈值(POT)方法对我国商业银行操作损失极端值分布进行估计,以均值超额函数图和拟合直线的交点确定阈值,估计出给定置信水平之下操作风险损失的分位数,从而使得国内商业银行操作风险监管资本的计算成为可能。     

核估计在医疗费用分布研究中的应用

医疗费用的分布是健康保险的精算基础之一.本文研究了某团体一年的住院医疗费用记录,运用非参数模型中的核密度估计方法,对每次住院费用对数的分布密度进行了估计,并用它进一步估计了每次住院费用的均值和方差,取得了较好的效果.在此基础上,本文对拟合结果及其对健康保险的启示作了一些讨论.     

A health insurance pricing model based on prevalence rates: Application to critical illness insurance

The Italian health insurance market is currently undersized. The paucity of assured data and the discontinuous statistical surveys carried out by the National Institute of Statistics (ISTAT) represent one of the main obstacles to the insurance market development. The paper sets forth a parametric model to estimate technical basis for health insurance policies when data are limited and only aggregated information on mortality and morbidity is available. The probabilistic framework is based on a multiple state continuous and time inhomogeneous Markov model. We provide an estimate of transition intensities from the healthy state to the sickness state when only prevalence rates of sickness are available, according to an extension and modification of the methodology proposed in Olivieri (1996) for Long Term Care insurance. We assume that mortality intensity of both healthy and sick lives is modelled by two independent Gompertz–Makeham models.     

Health shock risk,critical illness insurance,and housing services

This paper studies a consumption–investment problem involving health shock risk, perishable consumption, and consumption of housing services. Additionally to a risk-free asset and a stock index, the agent can invest in real estate. I analyze the impact of health shocks on the optimal consumption and investment decisions in model specifications with and without the possibility to buy critical illness insurance. I discuss the influence of critical illness insurance on the optimal strategy and analyze the drivers of the optimal critical illness insurance demand. The results indicate that health shock risk has potentially devastating consequences, especially for young agents. It turns out that critical illness insurance is an excellent instrument for hedging health shock risk and for consumption smoothing across different health states. Optimal critical illness insurance demand is decreasing in financial wealth and increasing in human wealth. Real estate prices have a minor influence on optimal critical illness insurance demand.     

基于医保规制和消费者效用的双渠道医药供应链竞争策略

医药消费者在面对双渠道零售时,会明显受到实体渠道医保报销政策的影响。基于这一现象,本文构建了同时考虑医保规制政策和消费者效用的双渠道医药供应链博弈模型,研究了医保报销比例和电商佣金比例对双渠道定价、供应链绩效以及社会福利的影响规律。研究结果表明:医药双渠道定价会同时随着平台收费标准和医保报销比例的增加而降低;医保报销比例的增加会提高社会福利、降低供应链绩效,同时会弱化网络渠道低价优势,能够有效抑制渠道蚕食现象;电商平台佣金比例的增加虽然在一定程度上提高了社会福利,但是会严重瓜分渠道利润,加剧渠道竞争,导致供应链绩效降低。     

Simulation of a health insurance market with adverse selection

A health insurance market is examined in which individuals with a history of high utilization of health care services tend to select fee-for-service (FFS) insurance when offered a choice between FFS and health maintenance organizations (HMOs). In addition, HMOs are assumed to practice community rating of employee groups. Based on these observations and health plan enrollment and premium data from Minneapolis-St. Paul, a deterministic simulation model is constructed to predict equilibrium market shares and premiums for HMO and FFS insurers within a firm. Despite the fact that favorable selection enhances their ability to compete with FFS insurers, the model predicts that HMOs maximize profits at less than 100% market share, and at a lower share than they could conceivably capture. That is, HMOs would not find it to their advantage to drive FFS insurers from the market even if they could. In all cases, however, the profit-maximizing HMO premium is greater than the experience-rated premium and, thus, the average health insurance premium per employee in firms offering both HMOs and FFS insurance is predicted to be greater than in firms offering one experience-rated plan. The model may be used to simulate the effects of varying the employer's method of contributing to health insurance premiums. Several contribution methods are compared. Employers who offer FFS and HMO insurance and pay the full cost of the lowest-cost plan are predicted to have lower average total premiums (employer plus employee contributions) than employers who pay any level percent of the cost of each plan.     

失能收入损失保险定价方法研究

失能收入损失保险定价方法研究对于丰富健康保险精算理论、促进健康保险发展有重要的理论意义和应用价值。文中从失能收入损失保险的三状态模型出发,分析了国外失能收入损失保险的定价方法,并提出了一种新的失能收入损失保险定价方法,力图为我国失能收入损失保险精算提供参考。     

Estimation of the ruin probability of an insurance company operating on a BS-market

We obtain an estimate for the ruin probability of an insurance company that invests a part of its capital in stocks and puts the rest of the capital in a bank account. An insurance premium is established depending on the capital of the insurance company. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 11, pp. 1443–1453, November, 2007.     

To borrow or insure? Long term care costs and the impact of housing

We assess the impact of housing, the availability of reverse mortgages and long-term care (LTC) insurance on a retiree’s optimal portfolio choice and consumption decisions using a multi-period life cycle model that takes into consideration individual longevity risk, health shocks and house price risk. We determine how much an individual should borrow against their home equity and how much to insure health care costs with LTC insurance. We introduce an endogenous grid method, along with a regression based approach, to improve computational efficiency and avoid the curse of dimensionality. Our results confirm that borrowing against home equity provides higher consumption in earlier years and longevity insurance. LTC insurance transfers wealth from healthy states to disabled states, but reduces early consumption because of the payment of insurance premiums. Housing is an illiquid asset that is important in meeting bequest motives, and it reduces the demand for LTC insurance for the wealthy. We show that the highest welfare benefits come from combining a reverse mortgage with LTC insurance because of strong complementary effects between them. This result highlights the benefits of innovative products that bundle these two products together.     

Hidden regular variation under full and strong asymptotic dependence

Data exhibiting heavy-tails in one or more dimensions is often studied using the framework of regular variation. In a multivariate setting this requires identifying specific forms of dependence in the data; this means identifying that the data tends to concentrate along particular directions and does not cover the full space. This is observed in various data sets from finance, insurance, network traffic, social networks, etc. In this paper we discuss the notions of full and strong asymptotic dependence for bivariate data along with the idea of hidden regular variation in these cases. In a risk analysis setting, this leads to improved risk estimation accuracy when regular methods provide a zero estimate of risk. Analyses of both real and simulated data sets illustrate concepts of generation and detection of such models.     

Premium rates based on genetic studies: How reliable are they?

Underwriting the risk of rare disorders in long-term insurance often relies on rates of onset estimated from quite small epidemiological studies. These estimates can have considerable sampling uncertainty and any function based upon them, such as a premium rate, is also an estimate subject to uncertainty. This is particularly relevant in the case of genetic disorders, because the acceptable use of genetic information may depend on establishing its reliability as a measure of risk. The sampling distribution of a premium rate is hard to estimate without access to the original data, which is rarely possible. From two studies of adult polycystic kidney disease (APKD) we obtain, not the original data, but the cases and exposures used for Kaplan-Meier estimates of the survival probability. We use three resampling methods with these data, namely: (a) the standard bootstrap; (b) the weird bootstrap; and (c) simulation of censored random lifetimes. Rates of onset were obtained from each simulated sample using kernel-smoothed Nelson-Aalen estimates, hence critical illness insurance premium rates for a mutation carrier or a member of an affected family. From 10,000 such samples we estimate the sampling distributions of the premium rates, finding considerable uncertainty. Very careful consideration should be given before using small-sample epidemiological data to deal with insurance problems.