Solvency II,regulatory capital,and optimal reinsurance: How good are Conditional Value-at-Risk and spectral risk measures?

We study the problem of optimal reinsurance as a means of risk management in the regulatory framework of Solvency II under Conditional Value-at-Risk and, as its natural extension, spectral risk measures. First, we show that stop-loss reinsurance is optimal under both Conditional Value-at-Risk and spectral risk measures. Spectral risk measures thus constitute a more general class of suitable regulatory risk measures than specific Conditional Value-at-Risk. At the same time, the established type of stop-loss reinsurance can be maintained as the optimal risk management strategy that minimizes regulatory capital. Second, we derive the optimal deductibles for stop-loss reinsurance. We show that under Conditional Value-at-Risk, the optimal deductible tends towards restrictive and counter-intuitive corner solutions or “plunging”, which is a serious objection against its use in regulatory risk management. By means of the broader class of spectral risk measures, we are able to overcome this shortcoming as optimal deductibles are now interior solutions. Especially, the recently discussed power spectral risk measures and the Wang risk measure are shown to avoid any plunging. They yield a one-to-one correspondence between the risk parameter and the optimal deductible and, thus, provide economically plausible risk management strategies.     

Some Finite Time Ruin Problems in Markov-Modulated Risk Model

This paper studies the distribution of finite-time ruin quantities. It gives the probability mass function of finite time number of claims, and find the distribution function of aggregate claims by using discretise method and compared with exact distribution function, which shows that the approximation works very well. In addition, by applying decomposition for density function, it gives the explicit expression for joint density of ruin time and deficit at ruin.     

Bayesian Analysis of Extreme Values by Mixture Modeling

Modeling of extreme values in the presence of heterogeneity is still a relatively unexplored area. We consider losses pertaining to several related categories. For each category, we view exceedances over a given threshold as generated by a Poisson process whose intensity is regulated by a specific location, shape and scale parameter. Using a Bayesian approach, we develop a hierarchical mixture prior, with an unknown number of components, for each of the above parameters. Computations are performed using Reversible Jump MCMC. Our model accounts for possible grouping effects and takes advantage of the similarity across categories, both for estimation and prediction purposes. Some guidance on the specification of the prior distribution is provided, together with an assessment of inferential robustness. The method is illustrated throughout using a data set on large claims against a well-known insurance company over a 15-year period.     

负二项分布的优良特性及其在风险管理中的应用

孟生旺．负二项分布的优良特性及其在风险管理中的应用．数理统计与管理，１９９８，１７（２），９～１２．负二项分布之所以在风险管理中被广泛应用是由其优良特性所决定的。本文主要讨论了其中三个方面的问题：第一，负二项分布在描述风险集体中任意风险的索赔次数时表现为伽玛分布对泊松分布按参数变化的加权平均；第二，负二项分布在描述某些风险的累积索赔额时具有复合泊松分布的形式；第三，负二项分布是当风险的索赔频率强度之间存在正向传染时索赔次数的分布     

保单个数为Poisson分布的总理赔额分布函数的界值研究

根据单个保单理赔额分布函数F(z)的一些特殊性质,研究了开放个别风险模型在保单个数N为Poisson分布下,总理赔额分布函数F_S(x)对任意x(x≥0)的界值问题,得到一些实用的、便于数值计算的界值结果,具有重要的应用价值．     

桑蚕种良卵率调查中样本间卵粒数的偏差控制方法

桑蚕种良卵率是蚕种质量检验的重要指标,控制样本间卵粒数的偏差是保证良卵率准确性的关键。通过对桑蚕卵粒重的调查分析,得出其分布服从正态分布。若从一批蚕种中抽取1g卵作为样本,则来自同一总体的2个样本的卵粒数之差不超过16粒,其置信概率为95%;当置信概率取99%时,两个样本的卵粒数之差不超过21粒。文章为蚕业生产提供了一种实用的克卵粒数偏差控制方法。     

离散时间不完全金融市场中未定权益的定价

对一类连续时间不完全市场（其中的股票价格由Brown运动驱动），ElKarouiandQuenez[1]讨论了一般的不可达未定权益的定价问题．本文利用FollmerandKabanov[2]建立的分解定理，证明[1]中关于买方与卖方价格过程的结果与方法适用于一般的离散时间不完全金融市场（定理1）．特别，关于买方与卖方价格我们给出另一种合理的解释（定理3）．     

标的资产价格服从跳-扩散过程的具有随机寿命的未定权益定价

本文在假设被终止或取消的风险与重大信息导致的标的资产价格跳跃的风险为非系统风险的情况下,应用无套利资本资产定价,推导出了标的的资产的价格服从跳-扩散过程具有随机寿命的未定权益满足的偏微分方程,然后应用Feynman-kac公式获得了未定权益的定价公式.     

Calibrating software reliability models when the test environment does not match the user environment

Software failures have become the major factor that brings the system down or causes a degradation in the quality of service. For many applications, estimating the software failure rate from a user's perspective helps the development team evaluate the reliability of the software and determine the release time properly. Traditionally, software reliability growth models are applied to system test data with the hope of estimating the software failure rate in the field. Given the aggressive nature by which the software is exercised during system test, as well as unavoidable differences between the test environment and the field environment, the resulting estimate of the failure rate will not typically reflect the user‐perceived failure rate in the field. The goal of this work is to quantify the mismatch between the system test environment and the field environment. A calibration factor is proposed to map the failure rate estimated from the system test data to the failure rate that will be observed in the field. Non‐homogeneous Poisson process models are utilized to estimate the software failure rate in both the system test phase and the field. For projects that have only system test data, use of the calibration factor provides an estimate of the field failure rate that would otherwise be unavailable. For projects that have both system test data and previous field data, the calibration factor can be explicitly evaluated and used to estimate the field failure rate of future releases as their system test data becomes available. Copyright © 2002 John Wiley & Sons, Ltd.