Quantitative Structural Models to Assess Credit Risk on Individuals

Default Probabilities quantitatively measures the credit risk that a borrower will be unable or unwilling to repay its debt. An accurate model to estimate, as a function of time, these default probabilities is of crucial importance in the credit derivatives market. In this work, we adapt Merton’s [1] original works on credit risk, consumption and portfolio rules to model an individual wealth scenario, and apply it to compute this individual default probabilities. Using our model, we also compute the time depending individual default intensities, recovery rates, hazard rate and risk premiums. Hence, as a straight-forward application, our model can be used as novel way to measure the credit risk of individuals.

Predicting lymph node metastasis in colorectal cancer:An analysis of influencing factors to develop a risk model

BACKGROUND Colorectal cancer(CRC)is a significant global health issue,and lymph node metastasis(LNM)is a crucial prognostic factor.Accurate prediction of LNM is essential for developing individualized treatment strategies for patients with CRC.However,the prediction of LNM is challenging and depends on various factors such as tumor histology,clinicopathological features,and molecular characteristics.The most reliable method to detect LNM is the histopathological examination of surgically resected specimens;however,this method is invasive,time-consuming,and subject to sampling errors and interobserver variability.AIM To analyze influencing factors and develop and validate a risk prediction model for LNM in CRC based on a large patient queue.METHODS This study retrospectively analyzed 300 patients who underwent CRC surgery at two Peking University Shenzhen hospitals between January and December 2021.A deep learning approach was used to extract features potentially associated with LNM from primary tumor histological images while a logistic regression model was employed to predict LNM in CRC using machine-learning-derived features and clinicopathological variables as predictors.RESULTS The prediction model constructed for LNM in CRC was based on a logistic regression framework that incorporated machine learning-extracted features and clinicopathological variables.The model achieved high accuracy(0.86),sensitivity(0.81),specificity(0.87),positive predictive value(0.66),negative predictive value(0.94),area under the curve for the receiver operating characteristic(0.91),and a low Brier score(0.10).The model showed good agreement between the observed and predicted probabilities of LNM across a range of risk thresholds,indicating good calibration and clinical utility.CONCLUSION The present study successfully developed and validated a potent and effective risk-prediction model for LNM in patients with CRC.This model utilizes machine-learning-derived features extracted from primary tumor histology and clinicopathological variables,demonstrating superior performance and clinical applicability compared to existing models.The study provides new insights into the potential of deep learning to extract valuable information from tumor histology,in turn,improving the prediction of LNM in CRC and facilitate risk stratification and decision-making in clinical practice.

Short-term and long-term risk factors in gastric cance

While in chronic diseases, such as diabetes, mortalityrates slowly increases with age, in oncological seriesmortality usually changes dramatically during thefollow-up, often in an unpredictable pattern. Forinstance, in gastric cancer mortality peaks in thefirst two years of follow-up and declines thereafter.Also several risk factors, such as TNM stage, largelyaffect mortality in the first years after surgery, whileafterward their effect tends to fade. Temporal trendsin mortality were compared between a gastric cancerseries and a cohort of type 2 diabetic patients. Forthis purpose, 937 patients, undergoing curativegastrectomy with D1/D2/D3 lymphadenectomy forgastric cancer in three GIRCG （Gruppo Italiano RicercaCancro Gastrico = Italian Research Group for GastricCancer） centers, were compared with 7148 type 2diabetic patients from the Verona Diabetes Study. Inthe early/advanced gastric cancer series, mortality fromrecurrence peaked to 200 deaths per 1000 personyears1 year after gastrectomy and then declined,becoming lower than 40 deaths per 1000 person-yearsafter 5 years and lower than 20 deaths after 8 years.Mortality peak occurred earlier in more advanced Tand N tiers. At variance, in the Verona diabetic cohort overall mortality slowly increased during a 10-yearfollow-up, with ageing of the type 2 diabetic patients.Seasonal oscillations were also recorded, mortalitybeing higher during winter than during summer. Alsothe most important prognostic factors presented adifferent temporal pattern in the two diseases： whilethe prognostic significance of T and N stage markedlydecrease over time, differences in survival amongpatients treated with diet, oral hypoglycemic drugsor insulin were consistent throughout the follow-up.Time variations in prognostic significance of main riskfactors, their impact on survival analysis and possiblesolutions were evaluated in another GIRCG series of568 patients with advanced gastric cancer, undergoingcurative gastrectomy with D2/D3 lymphadenectomy.Survival curves in the two different histotypes （intestinaland mixed/diffuse） were superimposed in the first threeyears of follow-up and diverged thereafter. Likewise,survival curves as a function of site （fundus vs body/antrum） started to diverge after the first year. On thecontrary, survival curves differed among age classesfrom the very beginning, due to different post-operativemortality, which increased from 0.5% in patients aged65-74 years to 9.9% in patients aged 75-91 years;this discrepancy later disappeared. Accordingly, theproportional hazards assumption of the Cox modelwas violated, as regards age, site and histology. Tocope with this problem, multivariable survival analysiswas performed by separately considering either thefirst two years of follow-up or subsequent years.Histology and site were significant predictors only aftertwo years, while T and N, although significant bothin the short-term and in the long-term, became lessimportant in the second part of follow-up. Increasingage was associated with higher mortality in the firsttwo years, but not thereafter. Splitting survival timewhen performing survival analysis allows to distinguishbetween short-term and long-term risk factors.Alternative statistical solutions could be to excludepost-operative mortality, to introduce in the modeltime-dependent covariates or to stratify on variablesviolating proportionality assumption.

个体化预测脓毒血症患儿并发急性肾损伤列线图模型的建立及验证

目的构建及验证脓毒血症患儿并发急性肾损伤(AKI)的列线图预测模型,并进行验证。方法本研究设计为回顾性研究,收集2019年8月至2021年8月在我院治疗的108例脓毒症患儿的临床资料。通过单因素和多因素Logistic回归分析脓毒血症患儿并发AKI的独立危险因素,利用R软件(R 4.0.3)构建列线图模型,采用Bootstrap法进行内部验证,采用校正曲线、Hosmer-Lemeshow检验和ROC曲线评价模型的预测能力。结果108例脓毒症患儿中,30例(27.78%)并发AKI(AKI组),78例(72.22%)无发生AKI(无AKI组)。AKI组与无AKI组的机械通气时间、急性生理与慢性健康评分(APACHEⅡ评分)、降钙素原(PCT)、C-反应蛋白(CRP)、白蛋白(ALB)、肌酸激酶(CK)等比较,差异均有统计学意义(均P<0.05)。多因素Logistic回归分析显示,机械通气时间(OR=1.245,95%CI:1.004~1.545)、APACHEⅡ评分(OR=1.529,95%CI:1.068~2.187)、PCT(OR=1.597,95%CI:1.237~2.061)、CRP(OR=1.046,95%CI:1.012~1.080)、ALB(OR=0.815,95%CI:0.721~0.979)、CK(OR=0.814,95%CI:0.730~0.942)是脓毒血症患儿并发AKI的独立影响因素(P<0.05)。基于上述影响因素建立列线图预测模型,经内部验证,校准曲线的平均绝对误差(MAE)为0.031,预测值与实际值基本一致;Hosmer-Lemeshow拟合优度检验显示模型拟合度较好(χ2=2.134,P=0.976)。曲线下面积(AUC)为0.965(95%CI:0.932~0.996),灵敏度为0.867,特异度为0.949。结论机械通气时间、APACHEⅡ评分、PCT、CRP、ALB、CK是脓毒血症患儿并发AKI的独立影响因素,基于上述因素建立的脓毒血症患儿并发AKI列线图预测模型具有良好的校准度和区分度,可为临床早期筛查脓毒血症并发AKI的高风险患儿及个体化干预方案的制定提供参考依据。

Nomogram prediction model called“ADPLCP”for predictinglinezolid-associated thrombocytopenia in elderly individuals

Background:Linezolid-associated thrombocytopenia(LAT)leads to drug withdrawal associated with a poor prognosis.Some risk factors for LAT have been identified;however,the sample size of previous studies was small,data from elderly individuals are limited,and a simple risk score scale was not established to predict LAT at anearly stage,making it difficult to identify and intervene in LAT at an early stage.Methods:In this single-center retrospective case-control study,we enrolled elderly patients treated with linezolidin the intensive care unit from January 2015 to December 2020.All the data of enrolled patients,includingdemographic information and laboratory findings at baseline,were collected.We analyzed the incidence andrisk factors for LAT and established a nomogram risk prediction model for LAT in the elderly population.Results:A total of 428 elderly patients were enrolled,and the incidence of LAT was 35.5%(152/428).Age≥80 years old(OR=1.980;95%CI:1.179–3.325;P=0.010),duration of linezolid≥10 days(OR=1.100;95%CI:1.050–1.152;P<0.0001),platelet count at baseline(100–149×10^(9)/L vs.≥200×10^(9)/L,OR=8.205,95%CI:4.419–15.232,P<0.0001;150–199×10^(9)/L vs.≥200×10^(9)/L,OR=3.067,95%CI:1.676–5.612,P<0.001),leukocytecount at baseline≥16×10^(9)/L(OR=2.580;95%CI:1.523–4.373;P<0.0001),creatinine clearance<50 mL/min(OR=2.323;95%CI:1.388–3.890;P=0.001),and total protein<60 g/L(OR=1.741;95%CI:1.039–2.919;P=0.035)were associated with LAT.The nomogram prediction model called“ADPLCP”(age,duration,platelet,leukocyte,creatinine clearance,protein)was established based on logistic regression.The area under the curve(AUC)of ADPLCP was 0.802(95%CI:0.748–0.856;P<0.0001),with 78.9%sensitivity and 69.2%specificity(cut-off was 108).Risk stratification for LAT was performed based on“ADPLCP.”Total points of<100 were defined as low risk,and the possibility of LAT was<32.0%.Total points of 100–150 were defined as medium risk,and the possibility of LAT was 32.0–67.5%.A total point>150 was defined as high risk,and the probability ofLAT was>67.5%.Conclusions:We created the ADPLCP risk score scale to predict the occurrence of LAT in elderly individuals.ADPLCP is simple and feasible and is helpful for the early determination of LAT to guide drug withdrawal orearly intervention.

Storage reliability assessment model based on competition failure of multi-components in missile

The degradation data of multi-components in missile is derived by periodical testing. How to use these data to assess the storage reliability (SR) of the whole missile is a difficult problem in current research. An SR assessment model based on competition failure of multi-components in missile is proposed. By analyzing the missile life profile and its storage failure feature, the key components in missile are obtained and the characteristics voltage is assumed to be its key performance parameter. When the voltage testing data of key components in missile are available, a state space model (SSM) is applied to obtain the whole missile degradation state, which is defined as the missile degradation degree (DD). A Wiener process with the time-scale model (TSM) is applied to build the degradation failure model with individual variability and nonlinearity. The Weibull distribution and proportional risk model are applied to build an outburst failure model with performance degradation effect. Furthermore, a competition failure model with the correlation between degradation failure and outburst failure is proposed. A numerical example with a set of missiles in storage is analyzed to demonstrate the accuracy and superiority of the proposed model.

Recursions for the Individual Risk Model

In the actuarial literature, several exact and approximative recursive methods have been proposed for calculating the distribution of a sum of mutually independent compound Bernoulli distributed random variables. In this paper, we give an overview of these methods. We compare their performance with the straight- forward convolution technique by counting the number of dot operations involved in each method. It turns out that in many practicle situations, the recursive methods outperform the convolution method.

Precise Large Deviations for a Customer-based Individual Risk Model

In this paper, we propose a customer-based individual risk model, in which potential claims by customers are described as i.i.d, heavy-tailed random variables, but different insurance policy holders are allowed to have different probabilities to make actual claims. Some precise large deviation results for the prospectiveoss process are derived under certain mild assumptions, with emphasis on the case of heavy-tailed distribution function class ERV （extended regular variation）. Lundberg type limiting results on the finite time ruin probabilities are also investigated.

个体化预测育龄期子宫肌瘤患者宫腔镜术后复发风险列线图模型构建与验证

目的探讨个体化预测育龄期子宫肌瘤患者宫腔镜术后复发风险列线图模型的构建与验证。方法选取2016年1月至2018年4月在苏州九龙医院行宫腔镜下子宫肌瘤剔除术的育龄期患者289例,术后3年内定期随访,最终纳入随访资料齐全的236例患者为研究对象。收集所有纳入患者的临床资料,根据随访期间患者是否复发,分为复发组(n=49)和未复发组(n=187)。通过单因素和多因素logistic回归分析,确定影响术后复发的危险因素,随后建立列线图模型并进行验证。结果纳入的236例患者中,3年内复发率为20.76%(49/236)。单因素分析显示,两组患者宫腔黏连、肌瘤数目、肌瘤分型、肌瘤直径、血清雌激素受体、孕酮受体、B淋巴细胞瘤-2基因水平水平比较,差异有统计学意义(P<0.05)。多因素logistic回归分析显示,宫腔黏连、肌瘤数目、肌瘤分型、肌瘤直径、ER、PR、Bcl-2水平均为育龄期子宫肌瘤患者宫腔镜术后复发的独立危险因素(P<0.05)。根据上述7项独立危险因素构建列线图模型及验证发现,列线图模型预测育龄期子宫肌瘤患者术后复发风险的AUC为0.971(95%CI:0.951~0.990)、灵敏度为0.898、特异度为0.936;Hosmer-Lemeshow偏差性检验显示,χ2=2.866(P=0.943);Bootstrap内部验证显示,该列线图模型校准曲线的MAE为0.015。结论育龄期子宫肌瘤患者术后复发危险因素构建列线图模型具有较好的区分度、校准度及预测能力,可为宫腔镜下子宫肌瘤剔除术后复发高危患者筛查和干预方案提供参考。

Stochastic loss reserving using individual information model with over-dispersed Poisson

For stochastic loss reserving,we propose an individual information model(IIM)which accom-modates not only individual/micro data consisting of incurring times,reporting developments,settlement developments as well as payments of individual claims but also heterogeneity among policies.We give over-dispersed Poisson assumption about the moments of reporting developments and payments of every individual claims.Model estimation is conducted under quasi-likelihood theory.Analytic expressions are derived for the expectation and variance of outstanding liabilities,given historical observations.We utilise conditional mean square error of prediction(MSEP)to measure the accuracy of loss reserving and also theoretically prove that when risk portfolio size is large enough,IIM shows a higher prediction accuracy than individ-ual/micro data model(IDM)in predicting the outstanding liabilities,if the heterogeneity indeed influences claims developments and otherwise IIM is asymptotically equivalent to IDM.Some simulations are conducted to investigate the conditional MSEPs for IIM and IDM.A real data analysis is performed basing on real observations in health insurance.

用SAFETI定量评价液氯泄漏事故的风险

基于液氯储运过程中的安全现状分析和事故统计,结合挪威船级社的定量风险分析软件SAFETI(Software forAssessment of Flammable,Explosive and Toxic Impacts),分析了氯气的危险特性以及液氯储运过程中因泄漏而导致的毒害危险性,归纳出了液氯储运过程中可能发生的各种泄漏事故类型;并运用SAFETI软件对某液氯槽车发生泄漏后的毒性危害后果及风险进行定量评价,建立具针对性的评价模型,模拟预测事故后果及风险,取得了液氯泄漏毒害事故危害程度和范围及造成的个人风险和社会风险的计算机模拟图表及报告等,对预测、预防液氯泄漏毒害事故以及减少事故造成的人员伤亡和财产损失具有工程应用价值.

个人信用卡信用风险评价体系与模型研究

分析了国内个人信用卡信用评价的现状和不足;探讨了建立个人信用指标体系的原则和方法;建立了一套包括个人还贷能力和还贷意愿共2大类15个指标的个人信用卡信用风险评价指标体系,并设计了负债情况等3项具有双向影响作用的指标;运用隶属度原理和层次分析法,确定了各类指标的评分函数和权重;建立了个人信用卡信用风险评价模型.确定了划分信用等级的两个阈值,解决了以往信用分级缺乏依据的问题.

基于神经网络的慢性病危险因素人体模型的建模方法

本研究的目的是运用神经网络反向传播(BP)学习算法,建立一种个体化慢性病危险因素人体模型的方法,为状态控制研究提供人体模型基础。该模型以运动状况、饮食习惯(包括盐、谷类、蔬菜、水果、肉禽类、蛋类、鱼虾类、豆类、奶类、油脂、动物内脏等的摄入量)、饮酒和吸烟等为输入量,输出量包括与慢性病密切相关的收缩压、舒张压、血糖、心率、BMI等生理参数,并用残差分析检验所建模型的可靠性。通过13例志愿者的受试试验,有9例实测参数和估计参数的符合率超过80%。研究结果表明,所提出的基于神经网络的个体化慢性病危险因素预测模型的建模方法,在总体上是可行的,为个体化设计危险因素控制策略提供了依据。

食源性致病菌单细胞观测与预测的研究进展

微生物在单细胞水平下的生长普遍具有随机性和变异性,同时低菌量污染食品所造成的危害风险亦不可忽视,因此食源性致病菌单细胞的生长观测及预测研究逐渐成为食品预测微生物学及食源性致病菌风险评估的研究热点。在分析现有相关文献的基础上,将目前主要的食源性致病菌单细胞生长观测研究分为间接推断和直接观测两类方法;同时对食源性致病菌单细胞生长预测的模型参数与建模过程进行概述,比较了传统预测微生物的决定模型与微生物单细胞的随机模型二者之间的区别,强调了单细胞生长模型需在随机建模的基础上开展,并通过个体建模方法进一步联系其与所在食品环境之间的关系。最后,分析了食源性致病菌单细胞生长观测与预测的现状,并展望了其未来与食品安全风险评估相结合的发展趋势。

不完全信息下的信贷风险决策模型

从银行信贷资金风险极小化的角度出发 ,通过引入激励机制设计的理论和方法 ,建立了银行信贷风险决策模型 .指出了在此模型下 ,当两类企业向银行提供等值的抵押品时 ,高、低风险企业的利率也相同 .这说明 ,当抵押品作为鉴别企业风险类型的手段失效时 ,银行无法根据利率来判断企业项目风险 .研究结果表明 ,当两类企业向银行提供非等值的抵押品时 ,高风险企业愿意接受更高的贷款利率而提供更低的抵押品价值 ;低风险企业则愿意接受更低的贷款利率而提供更高的抵押品价值 .

个人住房抵押贷款提前还款风险因素实证研究

以个人住房抵押贷款的微观数据为基础,运用比例风险模型,探讨影响个人住房抵押贷款提前还款风险的显著因素.针对提前还款买权,引入了一种新定义的买权价值.实证研究结果不仅表明新定义的买权价值与提前还款风险显著相关,而且还得到了与国外同类研究不完全相同的结论,例如借款人收入与提前还款风险显著负相关,借款人年龄与提前还款风险非显著相关等.通过对显著因素的分析,提出借款人保守的负债消费观念、自有资金没有更好的投资渠道、对住宅价格预期的降低以及抵押住宅的出售是引发我国提前还款风险的可能原因.

基于probit模型的超压引发多米诺效应定量风险评价研究

为定量评价化工园区相邻设备之间由于事故传播而导致的事故多米诺效应及其风险,基于Monte-Carlo方法及probit模型建立超压导致的事故多米诺效应定量风险评价模型。对液化石油气(LPG)蒸气云爆炸(VCE)过程中储罐泄漏数学模型中的随机参数进行Monte-Carlo模拟,通过概率方法对超压等扩展向量导致的多米诺效应的事故场景进行分析,并以常压容器的probit模型计算二次目标设备的损坏概率,以英国HSE的人员伤亡评估probit标准对事故多米诺效应后果进行定量化分析。结果表明:在液化石油气VCE中超压是导致多米诺效应的主要因素,可以忽略碎片的影响;在液化石油气VCE中虽然考虑多米诺效应时的个人风险及社会风险比不考虑时的大,但在二次事故局限于池火的情况下,由超压导致的池火事故对个人风险的影响较小。

天然气输气管道泄漏事故热辐射危害风险分析

针对天然气输气管道泄漏事故,结合Pasquill-Gifford扩散模型,建立合适的泄漏源模型,考虑天然气泄漏的初始动量和浮力的影响,获得不同位置处的天然气浓度分布。在此基础上,对天然气泄漏事故喷射火焰的热辐射危害进行风险分析,绘制了相应的社会风险曲线图,研究了可能导致的个人风险及社会风险。

个体风险模型的Poisson复合模型近似

本文在近乎最一般的假定下,简述了个体风险模型的Poisson复合模型近似。特别地,借助风险间停止损失保费的总差异给出了这一近似的精度。

个别风险模型中总索赔额分布函数的界值及应用

根据单个保单索赔额分布函数的一些性质,本文研究了个别风险模型中总索赔额分布函数的界值问题,并给出了计算实例和应用。