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Correlation analysis of degrading systems based on bivariate Wiener processes under imperfect maintenance 不完善维护条件下基于双变量维纳过程的退化系统相关性分析
IF 1.4 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-07-02 DOI: 10.1002/asmb.2883
Lucía Bautista, Inma T. Castro, Christophe Bérenguer, Olivier Gaudoin, Laurent Doyen
This article focuses on the correlation between the degradation levels of the two components that form a system. The degradation evolution of each component is modeled using Wiener processes. Both components are dependent and this dependence is described using the trivariate reduction method. To reduce the degradation and extend the system lifetime, preventive maintenance actions are periodically performed. These preventive maintenance actions are imperfect and they are modeled by using an arithmetic reduction of degradation of infinite order model with a determined maintenance efficiency parameter. The evolution of the maintained system is analysed by assessing the expectation and variance of both degradation processes at successive maintenance times. The novelty of this work is the analysis of the Pearson correlation coefficient between the degradation levels of the two components. Different properties of the monotonicity of the Pearson correlation coefficient between the two degradation paths are obtained by considering equal maintenance efficiency and equal general time scales functions for the two Wiener degradation processes associated to each degrading component.
本文重点讨论构成系统的两个组件的退化程度之间的相关性。每个组件的退化演化过程都使用维纳过程建模。两个组件之间存在依赖关系,这种依赖关系使用三变量还原法进行描述。为了减少退化并延长系统寿命,需要定期进行预防性维护。这些预防性维护行动是不完美的,它们是通过使用算术还原退化的无穷阶模型和一个确定的维护效率参数来建模的。通过评估连续维护时间内两个退化过程的期望值和方差,对维护系统的演变进行分析。这项工作的新颖之处在于分析了两个组件退化水平之间的皮尔逊相关系数。通过考虑与每个退化部件相关的两个维纳退化过程的相同维护效率和相同一般时间尺度函数,可以获得两个退化路径之间的皮尔逊相关系数的不同单调性。
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引用次数: 0
Comparing risk profiles of international stock markets as functional data: COVID-19 versus the global financial crisis 将国际股票市场的风险状况作为功能数据进行比较:COVID-19 与全球金融危机
IF 1.3 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-06-20 DOI: 10.1002/asmb.2879
Ryan Liam Shackleton, Sonali Das, Rangan Gupta

In this article, we aim to provide a detailed econometric analysis of the realized volatility in international stock markets of Brazil, China, Europe, India, the United Kingdom, and the United States, which represent a mix of large developing, and developed markets. For our purpose, we use the functional data analysis (FDA) framework, whence discrete volatility data were first transformed into continuous functions, and thereafter, derivatives of the continuous functions were investigated, and kinetic and potential energy associated is the volatility system were extracted. Results revealed that COVID-19 indeed had a significant effect on international financial market volatility for all the countries, with the exception of China. The realized volatility of the international financial markets did return to their pre-COVID levels in May 2020, and this recovery time was significantly faster than the 2008 financial crisis recovery period. Within the FDA framework, we further investigated the role of uncertainty on the realized volatility, specifically from an outbreak of an infectious disease (such as COVID-19) and a daily newspaper-based infectious disease index as the predictor. The regression analysis showed that the volatility of financial markets can be accurately modeled by this infectious disease index, but only for periods experiencing an epidemic or pandemic.

本文旨在对巴西、中国、欧洲、印度、英国和美国等国际股票市场的已实现波动率进行详 细的计量经济学分析,这些市场既有大型发展中市场,也有发达市场。为此,我们使用了函数数据分析(FDA)框架,首先将离散波动率数据转换为连续函数,然后研究连续函数的导数,并提取与波动率系统相关的动能和势能。结果显示,除中国外,COVID-19 对所有国家的国际金融市场波动率均有显著影响。国际金融市场的实际波动率确实在 2020 年 5 月恢复到了 COVID 前的水平,而这一恢复时间明显快于 2008 年金融危机的恢复期。在 FDA 框架内,我们进一步研究了不确定性对已实现波动率的作用,特别是来自传染病(如 COVID-19)爆发和基于日报的传染病指数作为预测因子的不确定性。回归分析表明,金融市场的波动性可以通过该传染病指数进行精确建模,但仅限于发生流行病或大流行的时期。
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引用次数: 0
Optimal designs of accelerated degradation tests with random shock failures and measurement errors 具有随机冲击故障和测量误差的加速降解试验的优化设计
IF 1.3 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-06-18 DOI: 10.1002/asmb.2878
Lin Wu, Xiao-Dong Zhou, Rong-Xian Yue

Accelerated degradation tests (ADTs) are widely used for assessing the reliability of long-life products. During an ADT, accelerated stresses not only expedite the degradation of test products but also increase the likelihood of encountering traumatic shocks. Moreover, it is important to acknowledge that measurement errors can be inevitable during the observation process of an ADT. Unfortunately, these errors are often overlooked in the optimal design of the ADT, especially when multiple competing failure modes are present. In this article, we propose a new approach to design ADTs when measurement errors exist and test products suffer from degradation failures and random shock failures. We utilize the Wiener process to model the degradation path, incorporating normally distributed measurement errors, and an exponential distribution to fit the time between random shock failures. Given the number of test products and the termination time, we optimize the ADT plans under three common design criteria. The equivalence theorem is used to verify the optimality of the optimal ADT plans. A real-life example and sensitivity analysis are provided to illustrate our proposed method. The results demonstrate that when competing failure modes are present, the optimal ADT plans, which account for measurement errors, differ significantly from those that do not consider such errors.

加速降解试验(ADT)被广泛用于评估长寿命产品的可靠性。在 ADT 过程中,加速应力不仅会加速测试产品的降解,还会增加遭遇创伤性冲击的可能性。此外,必须承认的是,在 ADT 观察过程中,测量误差是不可避免的。遗憾的是,这些误差往往在 ADT 的优化设计中被忽视,尤其是在存在多种竞争失效模式的情况下。在本文中,我们提出了一种新方法,用于在存在测量误差、测试产品遭受降级故障和随机冲击故障时设计 ADT。我们利用维纳过程对降解路径进行建模,其中包含正态分布的测量误差,并利用指数分布来拟合随机冲击故障之间的时间间隔。考虑到测试产品的数量和终止时间,我们根据三种常见的设计标准优化 ADT 计划。等价定理被用来验证最佳 ADT 计划的最优性。我们提供了一个实际案例和敏感性分析来说明我们提出的方法。结果表明,当存在相互竞争的故障模式时,考虑测量误差的最佳 ADT 计划与不考虑测量误差的最佳 ADT 计划差别很大。
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引用次数: 0
Estimation of VaR with jump process: Application in corn and soybean markets 利用跳跃过程估算 VaR:在玉米和大豆市场中的应用
IF 1.3 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-06-15 DOI: 10.1002/asmb.2880
Minglian Lin, Indranil SenGupta, William Wilson

Value at risk (VaR) is a quantitative measure used to evaluate the risk linked to the potential loss of investment or capital. Estimation of the VaR entails the quantification of prospective losses in a portfolio of investments, using a certain likelihood, under normal market conditions within a specific time period. The objective of this article is to construct a model and estimate the VaR for a diversified portfolio consisting of multiple cash commodity positions driven by standard Brownian motions and jump processes. Subsequently, a thorough analytical estimation of the VaR is conducted for the proposed model. The results are then applied to two distinct commodities—corn and soybean—enabling a comprehensive comparison of the VaR values in the presence and absence of jumps.

风险价值(VaR)是一种量化指标,用于评估与投资或资本潜在损失相关的风险。估算风险价值需要在特定时间段内的正常市场条件下,利用某种可能性对投资组合的预期损失进行量化。本文的目的是构建一个模型,并估算由标准布朗运动和跃迁过程驱动的多种现货商品仓位组成的多元化投资组合的风险价值。随后,对所提出的模型进行了全面的风险价值分析估算。然后将结果应用于两种不同的商品--玉米和大豆--对存在和不存在跳跃时的风险价值进行全面比较。
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引用次数: 0
Gender-inclusive financial and demographic literacy: Monetizing the gender mortality gap 性别包容的金融和人口扫盲:将性别死亡率差距货币化
IF 1.3 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-06-10 DOI: 10.1002/asmb.2876
Giovanna Apicella, Enrico De Giorgi, Emilia Di Lorenzo, Marilena Sibillo

Longevity crucially affects demand for pensions, insurance products and annuities. Consistent empirical evidence shows that women have historically experienced lower mortality rates than men. In this article, we study a measure of the gender gap in mortality rates, we call “Gender Gap Ratio”, across a wide range of ages and for four countries: France, Italy, Sweden, and USA. We show the stylized facts that characterize the trend of the Gender Gap Ratio, both in its historical evolution and future projection. Focusing on an example temporary life annuity contract, we give a monetary consistency to the Gender Gap Ratio. We show evidence that a Gender Gap Ratio that ranges between 1.5 and 2.5, depending on age, translates into a significant reduction of up to 23% in the benefits from a temporary life annuity contract for women with respect to men, against the same amount invested in the life annuity. The empirical evidence discussed in this article documents the crucial importance of working toward a more widespread demographic literacy, for example, a range of tools and strategies to raise longevity consciousness among individuals and policy-makers, in the framework of gender equality policies.

长寿对养老金、保险产品和年金的需求有着至关重要的影响。一致的经验证据表明,女性的死亡率历来低于男性。在本文中,我们研究了死亡率性别差异的衡量标准,我们称之为 "性别差异比",涉及四个国家的多个年龄段:法国、意大利、瑞典和美国。我们从性别差距比的历史演变和未来预测两方面展示了其趋势的典型事实。我们以临时年金合同为例,给出了性别差距比的货币一致性。我们展示的证据表明,性别差距比介于 1.5 和 2.5 之间(取决于年龄),意味着女性从临时人寿年金合同中获得的收益比男性大幅减少 23%,而投资于人寿年金的金额相同。本文讨论的经验证据表明,在性别平等政策框架内,努力普及人口知识至关重要,例如,通过一系列工具和战略来提高个人和政策制定者的长寿意识。
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引用次数: 0
Efficient pricing of path-dependent interest rate derivatives 路径依赖利率衍生品的有效定价
IF 1.3 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-06-01 DOI: 10.1002/asmb.2877
Allan Jonathan da Silva, Jack Baczynski, José V. M. Vicente

Interest rate derivative pricing is a critical aspect of fixed-income markets, where efficient methods are essential. This study introduces a novel approach to pricing path-dependent interest rate derivatives within a broad class of affine jumps. The study's particular setting is the Fourier-cosine series (COS) method adaptation, which offers an accurate and computationally efficient method for pricing interest rate derivatives. The Fourier-cosine series approach can be used to compute probability density functions and option pricing with a linear computing complexity and exponential convergence rate. The lack of a quick and precise pricing technique for Asian interest rate options in diverse fixed-income market scenarios is a research gap that is being addressed. This approach closes this gap by providing quasi-closed and closed-form equations for a range of density and characteristic functions, resulting in precise pricing. The results demonstrate the versatility of the COS method in interest rate markets. Similar to what has been previously reported for stock options, the numerical findings demonstrate the extreme precision and computing speed of the pricing and hedging estimations provided here. This method is an innovative approach to interest rate derivative pricing, offering researchers and practitioners a powerful tool for efficiently calculating prices and calibrating options across strikes and maturities.

利率衍生品定价是固定收益市场的一个重要方面,高效的定价方法至关重要。本研究介绍了一种新方法,用于在仿射跃迁的大类中对路径依赖利率衍生品进行定价。该研究的特定环境是傅立叶-余弦数列(COS)方法适应性,它为利率衍生品定价提供了一种精确且计算效率高的方法。傅立叶-余弦数列方法可用于计算概率密度函数和期权定价,计算复杂度为线性,收敛速度为指数。在各种固定收入市场情况下,亚洲利率期权缺乏快速精确的定价技术,这是一个正在解决的研究空白。这种方法为一系列密度和特征函数提供了准封闭和封闭式方程,从而实现了精确定价,填补了这一空白。研究结果证明了 COS 方法在利率市场中的多功能性。与之前关于股票期权的报告类似,数值结果表明本文提供的定价和对冲估算极其精确,计算速度极快。该方法是利率衍生品定价的一种创新方法,为研究人员和从业人员提供了一种有效计算价格和校准不同行权价和期限期权的强大工具。
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引用次数: 0
On optimal allocation of redundancies in random weighted k $$ k $$ -out-of- n $$ n $$ systems 论随机加权 k$$ k $$-out-of-n$ n $$ 系统中冗余的最优分配
IF 1.3 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-05-29 DOI: 10.1002/asmb.2875
Tanmay Sahoo, Nil Kamal Hazra

Random weighted k$$ k $$-out-of-n$$ n $$ systems are very useful in modeling the lifetimes of systems, wherein the success or failure of a system depends not only on its current operational status, but also on the contributions made by its components. In this paper, we consider random weighted k$$ k $$-out-of-n$$ n $$ systems with redundant components drawn randomly from a mixed population consisting of m$$ m $$ different subpopulations/substocks. We study different optimal allocation policies of active redundancies and minimal repair components in a random weighted k$$ k $$-out-of-n$$ n $$ system. Moreover, we investigate how the heterogeneity of subpopulations of items impacts the lifetime of a random weighted k$$ k $$-out-of-n$$ n $$ system. We also present some simulational results and a real data analysis for illustrative purpose.

随机加权损耗系统对系统寿命建模非常有用,因为系统的成败不仅取决于其当前的运行状况,还取决于其组件的贡献。在本文中,我们考虑的是随机加权 "缺失 "系统,其冗余组件是从由不同亚群/子群组成的混合群中随机抽取的。我们研究了随机加权出错系统中主动冗余和最小修复组件的不同最优分配策略。此外,我们还研究了项目子群的异质性如何影响随机加权出错系统的寿命。我们还介绍了一些模拟结果和真实数据分析,以作说明。
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引用次数: 0
K-Fuse: Credit card fraud detection based on a classification method with a priori class partitioning and a novel feature selection strategy K-Fuse:基于先验类别划分的分类方法和新型特征选择策略的信用卡欺诈检测
IF 1.3 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-05-24 DOI: 10.1002/asmb.2868
Mohammed Sabri, Rosanna Verde, Antonio Balzanella

Online transactions have become the dominant and most popular form of online payment in today's digital economy. Due to the growing popularity of e-commerce and the convenience it offers, both consumers and businesses are rapidly adopting online transactions. Notably, credit cards have become one of the most popular and standard online payment methods. However, it should be noted that credit card transactions are not without challenges. In particular, detecting and preventing fraudulent transactions is a major concern of the online payment system. It is difficult to find an effective detection model that can detect the new patterns created by fraudsters, due to the constant evolution of their methods to exploit the vulnerability of current security protocols. These fraud patterns are evolving and may not correspond to existing documented models, leading to a reduction in their identification. In addition, the customer's behavior can affect the model detection as it is susceptible to change based on factors such as economic conditions, trends, and individual circumstances. When consumers deviate from their typical behavior, the model may generate false alerts, thereby reducing its ability to differentiate between legitimate and fraudulent transactions. This article presents a new supervised detection model, called K-Fuse, which introduces an unsupervised phase in order to detect fraud patterns that may correspond to innovative models introduced by fraudsters. K-Fuse is a supervised classification method that fuses three steps consisting of (i)unsupervised clustering to identify hidden patterns of transactions in a dataset, (ii) a novel feature selection criterion based on the unsupervised results, and (iii) supervised classification to exploit the results of clustering and feature selection to predict new transactions as fraudulent or legitimate.

在线交易已成为当今数字经济中最主要、最流行的在线支付方式。由于电子商务的日益普及及其带来的便利,消费者和企业都在迅速采用在线交易。值得注意的是,信用卡已成为最受欢迎的标准在线支付方式之一。然而,应该指出的是,信用卡交易并非没有挑战。特别是,检测和防止欺诈交易是网上支付系统的一个主要问题。由于欺诈者利用当前安全协议漏洞的方法不断演变,因此很难找到一种有效的检测模式来检测欺诈者创造的新模式。这些欺诈模式不断演变,可能与现有的记录模式不符,导致识别率降低。此外,客户的行为也会影响模式检测,因为它很容易受经济状况、趋势和个人情况等因素的影响而发生变化。当消费者偏离其典型行为时,模型可能会产生错误警报,从而降低其区分合法交易和欺诈交易的能力。本文提出了一种新的监督检测模型,称为 K-Fuse,它引入了一个无监督阶段,以检测可能与欺诈者推出的创新模式相对应的欺诈模式。K-Fuse 是一种监督分类方法,它融合了三个步骤,包括(i)无监督聚类,以识别数据集中隐藏的交易模式;(ii)基于无监督结果的新颖特征选择标准;以及(iii)监督分类,利用聚类和特征选择的结果来预测新交易是欺诈还是合法。
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引用次数: 0
Sequential monitoring for conditional quantiles of general conditional heteroscedastic time series models 对一般条件异方差时间序列模型的条件定量进行序列监测
IF 1.3 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-05-13 DOI: 10.1002/asmb.2865
Sangyeol Lee, Chang Kyeom Kim

In this study, we introduce an online monitoring procedure designed to sequentially detect change points in the conditional quantiles of location-scale time series models. This statistical process control issue holds great significance in risk management, particularly in measuring the value-at-risk or expected shortfall of financial assets. Our approach employs suitable detectors, including cumulative sum statistics. We then define a stopping rule and determine control limits based on asymptotic theorems to signal an anomaly. To further evaluate the proposed methods, we conduct a comprehensive empirical study analyzing various aspects of our monitoring procedures when applied to location-scale time series models. Additionally, we perform a real data analysis using the daily returns of the Korea Composite Stock Price Index (KOSPI) and EuroStoxx 50 indices to affirm the adequacy of the proposed monitoring procedures in real-world applications.

在本研究中,我们介绍了一种在线监测程序,旨在依次检测位置尺度时间序列模型条件量级的变化点。这一统计过程控制问题在风险管理中具有重要意义,尤其是在衡量金融资产的风险价值或预期缺口时。我们的方法采用了合适的检测器,包括累积和统计量。然后,我们根据渐近定理定义停止规则并确定控制限值,以发出异常信号。为了进一步评估所提出的方法,我们进行了一项全面的实证研究,分析了我们的监控程序在应用于位置尺度时间序列模型时的各个方面。此外,我们还利用韩国综合股价指数(KOSPI)和 EuroStoxx 50 指数的日收益率进行了实际数据分析,以肯定所提出的监控程序在实际应用中的充分性。
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引用次数: 0
Accelerated failure time frailty model for modeling multiple systems subject to minimal repair 用于模拟受最小修复影响的多系统的加速故障时间虚弱模型
IF 1.3 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-05-02 DOI: 10.1002/asmb.2864
Edilenia Queiroz Pereira, Oilson Alberto Gonzatto Junior, Vera Lucia Damasceno Tomazella, Lia Hanna Martins Morita, Alex L. Mota, Francisco Louzada Neto

This article presents accelerated failure time models with and without frailty for modeling multiple systems subject to minimal repair. The study considers the conventional accelerated failure time model, the accelerated failure time model with Gamma frailty, and proposes the accelerated failure time model with weighted Lindley frailty, which has attractive properties such as a closed-form Laplace transform. The proposed model extends the accelerated failure time model with the intensity function of a power law process. It retains the direct physical interpretation of the original accelerated failure time model, in which the role of covariates is to accelerate or decelerate the time to each repair. This framework includes parametric approaches to model fitting, which we consider for estimating the vector of regression parameters under this model and the parameter in the baseline intensity functions. The methodology is illustrated with a simulation study and a toy example to demonstrate the applicability of these models in the industrial context.

本文提出了有脆性和无脆性的加速失效时间模型,用于对受到最小修复的多系统建模。研究考虑了传统的加速失效时间模型、带伽马虚弱的加速失效时间模型,并提出了带加权林德利虚弱的加速失效时间模型,该模型具有闭式拉普拉斯变换等吸引人的特性。所提出的模型利用幂律过程的强度函数扩展了加速失效时间模型。它保留了原始加速故障时间模型的直接物理解释,其中协变量的作用是加速或减速每次修复的时间。这个框架包括模型拟合的参数方法,我们考虑用这种方法来估计该模型下的回归参数向量和基线强度函数中的参数。我们通过一个模拟研究和一个玩具示例对该方法进行了说明,以展示这些模型在工业环境中的适用性。
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引用次数: 0
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Applied Stochastic Models in Business and Industry
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