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Assessing Latent Risk Based on Joint Modelling of Multiple Health Insurance Outcomes of Mixed Types
IF 1.3 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-04-23 DOI: 10.1002/asmb.70012
Xingde Duan, Renjun Ma

Our research is motivated by an insurance study involving 788 insurance subscribers who made claims resulting from ischemic heart disease. Four different types of health services used by these subscribers as well as the corresponding total cost were observed for two years. Health care utilizations vary a lot even for subscribers of the same personal characteristics. The research question of primary interest is how to capture patient-specific latent risks beyond what can be explained by known personal characteristics. In this study, we characterize unobserved latent risks by random effects in our joint Tweedie mixed models for multiple health outcomes of mixed types. An optimal estimation of our model has been developed using the orthodox best linear unbiased predictors of random effects. Our approach is illustrated with the analysis of the health insurance study of 788 ischemic heart disease patients. Applying cluster analysis to the patient-specific latent risks predicted by our model, we were able to classify patients into a high risk group of 36 patients, a medium risk group of 256 patients and a low risk group of 496 patients. The finding is of important policy relevance since the losses suffered by a few are known to be spread over many in an insurance system. Grouping of patients and prioritization of specific groups based on subject-specific latent risks facilitates resource allocation and pricing.

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引用次数: 0
Designing Accelerated Degradation Tests Based on Wiener Process With a Positive Relation Between the Drift Rate and the Volatility
IF 1.3 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-04-09 DOI: 10.1002/asmb.70010
Daojiang He, Lei He, Jinming Ren

In this paper, we study the optimal design problem for constant-stress accelerated degradation tests using a new class of Wiener processes that effectively capture the positive relation between the drift rate and the volatility. Under the D$$ D $$-, A$$ A $$-, and c$$ c $$-optimality criteria, both the test stress levels and the allocation of test units at each stress level are explicitly determined. We provide a numerical example using carbon-film resistor data to validate our theoretical findings and perform a simulation study to highlight the advantages of our proposed designs. The numerical results suggest that the proposed designs outperform existing designs in terms of estimation accuracy.

在本文中,我们研究了恒定应力加速降解试验的优化设计问题,采用了一类新的维纳过程,有效地捕捉了漂移率和波动率之间的正相关关系。在 D $$ D $$ -、A $$ A $$ - 和 c $$ c $$ - 的最优标准下,试验应力水平和每个应力水平的试验单元分配都是明确确定的。我们提供了一个使用碳膜电阻器数据的数值示例,以验证我们的理论发现,并进行了模拟研究,以突出我们建议的设计的优势。数值结果表明,建议的设计在估计精度方面优于现有设计。
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引用次数: 0
Incorporating Asymmetric Loss for Real Estate Prediction With Area-Level Spatial Data
IF 1.3 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-04-02 DOI: 10.1002/asmb.70009
Vaidehi Dixit, Scott H. Holan, Christopher K. Wikle

We investigate two asymmetric loss functions, namely linear exponential (LINEX) loss and power divergence loss for optimal spatial prediction with area-level data. With our motivation arising from the real estate industry, namely in real estate valuation, we use the Zillow Home Value Index (ZHVI) for county-level values to show the change in prediction when the loss is different (asymmetric) from a traditional squared error loss (symmetric) function. Additionally, we discuss the importance of choosing the asymmetry parameter and propose a solution to this choice for a general asymmetric loss function. Since the focus is on area-level data predictions, we propose the methodology in the context of conditionally autoregressive (CAR) models. We conclude that the choice of the loss functions for spatial area-level predictions can play a crucial role and is heavily driven by the choice of parameters in the respective loss.

我们研究了两种非对称损失函数,即线性指数(LINEX)损失和幂发散损失,用于区域级数据的最优空间预测。我们的研究动机来自于房地产行业,即房地产估价,我们使用 Zillow 房屋价值指数(ZHVI)的县级数值来展示当损失与传统的平方误差损失(对称)函数不同(非对称)时预测的变化。此外,我们还讨论了选择非对称参数的重要性,并提出了针对一般非对称损失函数选择非对称参数的解决方案。由于重点是地区级数据预测,我们在条件自回归(CAR)模型的背景下提出了这一方法。我们的结论是,对于空间区域级预测,损失函数的选择可以起到至关重要的作用,并且在很大程度上受各自损失参数选择的影响。
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引用次数: 0
Hazard Rate Order Between Parallel Systems With Multiple Types of Scaled Components
IF 1.3 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-03-27 DOI: 10.1002/asmb.70008
Khaled Masoumifard, Abedin Haidari, Nuria Torrado

This study delves into the comparison of two parallel systems, each composed of multiple component types following the scale models with a shared baseline distribution. Under some assumptions imposed on the baseline distribution, it is shown that a restricted version of the p$$ p $$-larger order between the scale parameter vectors implies the hazard rate order between the system lifetimes, provided that the allocation vectors of the two systems are the same. Additionally, we explore scenarios where one system embodies heterogeneous scale parameters, whereas the other adopts homogeneous ones, examining the hazard rate order between their lifetimes. For the case when the scale vectors of the two systems are the same, it is shown under some assumptions on the baseline distribution that the weak supermajorization order between the allocation vectors results in the reversed hazard rate order between the system lifetimes. Under more restrictions on the allocation vectors, an extension of this result to the likelihood ratio order is also established. Our discussion also highlights the fulfillment of these assumptions by well-known lifetime distributions such as Feller-Pareto, generalized gamma, power-generalized Weibull, exponentiated Weibull, and half-normal distributions. The findings of this work contribute to addressing gaps in the understanding of stochastic orderings between parallel systems and further refine prior research in this domain. Furthermore, the results provide a foundation for practical applications, such as optimizing resource allocation and reliability assessment in engineering and operational contexts.

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引用次数: 0
No-Arbitrage Valuation of Contingent Claims Depending on an Untradeable Asset
IF 1.3 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-03-23 DOI: 10.1002/asmb.70007
Erindi Allaj

We consider an incomplete market situation with the presence of an untradeable asset and several tradeable assets. By an untradeable asset we mean an asset that cannot be traded on a public market. Typical examples of untradeable assets include real options and private credit/debt investments. We then exploit the relationship between the untradeable asset and tradeable assets to evaluate contingent claims depending on the untradeable asset. Under a multidimensional generalized Black–Scholes (GBS) framework, we study two different methods for pricing these kinds of contingent claims. The first is mean-variance hedging (MVH). The second is the method proposed in Jarrow (2023). We illustrate the two methods by applying them to two particular contingent claims: The option to defer and the spread option. No-arbitrage prices and admissible replicating trading strategies are derived. Lastly, we run simulations to test the performance of these replicating trading strategies.

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引用次数: 0
Digital Twins: A Revolution in Modeling and Simulation
IF 1.3 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-03-13 DOI: 10.1002/asmb.70006
Jean-Michel Poggi, Murat Caner Testik
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引用次数: 0
Pareto Optimal Proxy Metrics
IF 1.3 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-03-10 DOI: 10.1002/asmb.70003
Alessandro Zito, Dylan Greaves, Jacopo Soriano, Lee Richardson

North star metrics and online experimentation play a central role in how technology companies improve their products. In many practical settings, however, evaluating experiments based on the north star metric directly can be difficult. The two most significant issues are (1) low sensitivity of the north star metric and (2) differences between the short-term and long-term impact on it. A common solution is to rely on proxy metrics rather than the north star in experiment evaluation and launch decisions. Existing literature on proxy metrics concentrates mainly on the estimation of the long-term impact from short-term experimental data. In this article, instead, we focus on the trade-off between the estimation of the long-term impact and the sensitivity in the short term. In particular, we propose the Pareto optimal proxy metrics method, which simultaneously optimizes prediction accuracy and sensitivity. We also give a multi-objective optimization algorithm to solve our specific problem. We apply our methodology to experiments from a large industrial recommendation system, and found proxy metrics that are eight times more sensitive than the north star and consistently moved in the same direction, increasing the velocity and the quality of the decisions to launch new features.

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引用次数: 0
Is There a Future for Stochastic Modeling in Business and Industry in the Era of Machine Learning and Artificial Intelligence?
IF 1.3 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-03-10 DOI: 10.1002/asmb.70004
Fabrizio Ruggeri, David Banks, William S. Cleveland, Nicholas I. Fisher, Marcos Escobar-Anel, Paolo Giudici, Emanuela Raffinetti, Roger W. Hoerl, Dennis K. J. Lin, Ron S. Kenett, Wai Keung Li, Philip L. H. Yu, Jean-Michel Poggi, Marco S. Reis, Gilbert Saporta, Piercesare Secchi, Rituparna Sen, Ansgar Steland, Zhanpan Zhang

The paper arises from the experience of Applied Stochastic Models in Business and Industry which has seen, over the years, more and more contributions related to Machine Learning rather than to what was intended as a stochastic model. The very notion of a stochastic model (e.g., a Gaussian process or a Dynamic Linear Model) can be subject to change: What is a Deep Neural Network if not a stochastic model? The paper presents the views, supported by examples, of distinguished researchers in the field of business and industrial statistics. They are discussing not only whether there is a future for traditional stochastic models in the era of Machine Learning and Artificial Intelligence, but also how these fields can interact and gain new life for their development.

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引用次数: 0
Redundancy Allocation Problem in k-Out-Of-n Systems With Dependent and Heterogeneous Components
IF 1.3 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-03-03 DOI: 10.1002/asmb.2932
Zohreh Zare, Somayeh Zarezadeh, Mahmood Kharrati-Kopaei

The aim of this paper is to investigate the problem of one and two active redundant components allocation in a k-out-of-n system with dependent components. Here, some necessary and sufficient conditions are presented under which the redundancies are optimally allocated to the system components based on the usual stochastic order criterion. In addition, it is shown that, unlike the independence mode, a redundant component is not necessarily allocated to the weakest component. Further, in the case of the two redundant components, the weak (strong) redundant component is not necessarily allocated to the stronger (weaker) component of the system. Some algorithms are also presented for calculating the reliability of the considered system under the assumption of dependency between the main and redundant components. Using different copula functions for describing the dependencies between components, various examples are given to illustrate the optimal allocation of redundant components.

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引用次数: 0
Mean Distances and Dependence Structures for Lifetimes of Systems With Shared Components
IF 1.3 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-02-24 DOI: 10.1002/asmb.70002
Marco Capaldo, Antonio Di Crescenzo, Franco Pellerey

Distortion and copula functions represent powerful tools in the description of the reliability of some complex systems as functions of their components' reliability. On this aim, we study several pairs of reliability systems with one or more shared components, in the case when their lifetimes are independent and identically distributed or independent but not identically distributed. We focus on the dependence that arises from sharing components, often described by Marshall-Olkin copulas, making use of some distance measures related to the Gini's mean difference and its new recent generalizations. A special role is played by a new distortion function related to the ROC curve.

畸变函数和共轭函数是描述某些复杂系统可靠性的有力工具,是其组件可靠性的函数。为此,我们研究了具有一个或多个共享组件的几对可靠性系统,它们的寿命是独立且同分布的,或者是独立但非同分布的。我们将重点放在共享组件所产生的依赖性上,通常用马歇尔-奥尔金协方差来描述,并利用一些与基尼平均差及其最新概括相关的距离度量。与 ROC 曲线相关的新扭曲函数发挥了特殊作用。
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Applied Stochastic Models in Business and Industry
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