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Mortality models incorporating long memory for life table estimation: a comprehensive analysis 结合长记忆的寿命表估计死亡率模型:综合分析
IF 1.7 Q3 BUSINESS, FINANCE Pub Date : 2021-02-02 DOI: 10.1017/S1748499521000014
Hongxuan Yan, G. Peters, J. Chan
Abstract Mortality projection and forecasting of life expectancy are two important aspects of the study of demography and life insurance modelling. We demonstrate in this work the existence of long memory in mortality data. Furthermore, models incorporating long memory structure provide a new approach to enhance mortality forecasts in terms of accuracy and reliability, which can improve the understanding of mortality. Novel mortality models are developed by extending the Lee–Carter (LC) model for death counts to incorporate a long memory time series structure. To link our extensions to existing actuarial work, we detail the relationship between the classical models of death counts developed under a Generalised Linear Model (GLM) formulation and the extensions we propose that are developed under an extension to the GLM framework known in time series literature as the Generalised Linear Autoregressive Moving Average (GLARMA) regression models. Bayesian inference is applied to estimate the model parameters. The Deviance Information Criterion (DIC) is evaluated to select between different LC model extensions of our proposed models in terms of both in-sample fits and out-of-sample forecasts performance. Furthermore, we compare our new models against existing models structures proposed in the literature when applied to the analysis of death count data sets from 16 countries divided according to genders and age groups. Estimates of mortality rates are applied to calculate life expectancies when constructing life tables. By comparing different life expectancy estimates, results show the LC model without the long memory component may provide underestimates of life expectancy, while the long memory model structure extensions reduce this effect. In summary, it is valuable to investigate how the long memory feature in mortality influences life expectancies in the construction of life tables.
死亡率预测和预期寿命预测是人口统计学和寿险建模研究的两个重要方面。我们在这项工作中证明了死亡率数据中存在长记忆。此外,结合长记忆结构的模型为提高死亡率预测的准确性和可靠性提供了一种新的方法,可以提高人们对死亡率的认识。通过扩展李-卡特(LC)死亡计数模型以纳入长记忆时间序列结构,开发了新的死亡模型。为了将我们的扩展与现有的精算工作联系起来,我们详细介绍了在广义线性模型(GLM)公式下开发的经典死亡计数模型与我们提出的在时间序列文献中称为广义线性自回归移动平均(GLARMA)回归模型的广义线性模型(GLM)框架的扩展下开发的扩展之间的关系。采用贝叶斯推理对模型参数进行估计。根据样本内拟合和样本外预测性能,评估偏差信息准则(DIC)以在我们提出的模型的不同LC模型扩展之间进行选择。此外,我们将我们的新模型与文献中提出的现有模型结构进行比较,并将其应用于分析来自16个国家(按性别和年龄组划分)的死亡计数数据集。在编制生命表时,将死亡率估计数应用于计算预期寿命。通过比较不同的预期寿命估计,结果表明,不考虑长记忆成分的LC模型可能会低估预期寿命,而长记忆模型结构扩展会降低这种影响。综上所述,在生命表的构建中,研究死亡率中的长记忆特征对预期寿命的影响是有价值的。
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引用次数: 7
Dynamic importance allocated nested simulation for variable annuity risk measurement 可变年金风险度量的动态重要性分配嵌套模拟
IF 1.7 Q3 BUSINESS, FINANCE Pub Date : 2020-11-27 DOI: 10.2139/ssrn.3738777
Ou Dang, M. Feng, M. Hardy
Abstract Estimating tail risk measures for portfolios of complex variable annuities is an important enterprise risk management task which usually requires nested simulation. In the nested simulation, the outer simulation stage involves projecting scenarios of key risk factors under the real-world measure, while the inner simulations are used to value pay-offs under guarantees of varying complexity, under a risk-neutral measure. In this paper, we propose and analyse an efficient simulation approach that dynamically allocates the inner simulations to the specific outer scenarios that are most likely to generate larger losses. These scenarios are identified using a proxy calculation that is used only to rank the outer scenarios, not to estimate the tail risk measure directly. As the proxy ranking will not generally provide a perfect match to the true ranking of outer scenarios, we calculate a measure based on the concomitant of order statistics to test whether further tail scenarios are required to ensure, with given confidence, that the true tail scenarios are captured. This procedure, which we call the dynamic importance allocated nested simulation approach, automatically adjusts for the relationship between the proxy calculations and the true valuations and also signals when the proxy is not sufficiently accurate.
摘要估计复杂变量年金投资组合的尾部风险度量是一项重要的企业风险管理任务,通常需要嵌套模拟。在嵌套模拟中,外部模拟阶段涉及在真实世界衡量标准下预测关键风险因素的情景,而内部模拟用于在风险中性衡量标准下,在不同复杂性的保证下评估回报。在本文中,我们提出并分析了一种有效的模拟方法,该方法将内部模拟动态分配给最有可能产生更大损失的特定外部场景。这些场景是使用代理计算来识别的,该计算仅用于对外部场景进行排名,而不是直接估计尾部风险度量。由于代理排名通常不会提供与外部场景的真实排名的完美匹配,我们基于伴随的订单统计来计算一个度量,以测试是否需要进一步的尾部场景来确保在给定的置信度下捕获真实的尾部场景。这个过程,我们称之为动态重要性分配嵌套模拟方法,自动调整代理计算和真实估值之间的关系,并在代理不够准确时发出信号。
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引用次数: 2
A spatial machine learning model for analysing customers’ lapse behaviour in life insurance 用于分析寿险客户失效行为的空间机器学习模型
IF 1.7 Q3 BUSINESS, FINANCE Pub Date : 2020-11-10 DOI: 10.1017/S1748499520000329
Sen Hu, A. O'Hagan, James Sweeney, Mohammadhossein Ghahramani
Abstract Spatial analysis ranges from simple univariate descriptive statistics to complex multivariate analyses and is typically used to investigate spatial patterns or to identify spatially linked consumer behaviours in insurance. This paper investigates if the incorporation of publicly available spatially linked demographic census data at population level is useful in modelling customers’ lapse behaviour (i.e. stopping payment of premiums) in life insurance policies, based on data provided by an insurance company in Ireland. From the insurance company’s perspective, identifying and assessing such lapsing risks in advance permit engagement to prevent such incidents, saving money by re-evaluating customer acquisition channels and improving capital reserve calculation and preparation. Incorporating spatial analysis in lapse modelling is expected to improve lapse prediction. Therefore, a hybrid approach to lapse prediction is proposed – spatial clustering using census data is used to reveal the underlying spatial structure of customers of the Irish life insurer, in conjunction with traditional statistical models for lapse prediction based on the company data. The primary contribution of this work is to consider the spatial characteristics of customers for life insurance lapse behaviour, via the integration of reliable government provided census demographics, which has not been considered previously in actuarial literature. Company decision-makers can use the insights gleaned from this analysis to identify customer subsets to target with personalized promotions to reduce lapse rates, and to reduce overall company risk.
摘要空间分析从简单的单变量描述性统计到复杂的多变量分析,通常用于调查空间模式或识别保险中空间关联的消费者行为。本文根据爱尔兰一家保险公司提供的数据,调查了在人口层面纳入公开的空间关联人口普查数据是否有助于在人寿保险单中模拟客户的失误行为(即停止支付保费)。从保险公司的角度来看,提前识别和评估此类失误风险可以防止此类事件的发生,通过重新评估客户获取渠道和改进资本准备金的计算和准备来节省资金。将空间分析纳入时差建模有望改善时差预测。因此,提出了一种失效预测的混合方法——使用人口普查数据的空间聚类来揭示爱尔兰人寿保险公司客户的潜在空间结构,并结合基于公司数据的失效预测的传统统计模型。这项工作的主要贡献是通过整合可靠的政府提供的人口普查人口统计数据,考虑人寿保险失效行为的客户空间特征,这在精算文献中以前没有考虑过。公司决策者可以利用从该分析中收集的见解来确定个性化促销的目标客户子集,以降低失误率,并降低公司的整体风险。
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引用次数: 12
Clustering driving styles via image processing 基于图像处理的驾驶风格聚类
IF 1.7 Q3 BUSINESS, FINANCE Pub Date : 2020-10-27 DOI: 10.1017/S1748499520000317
Rui Zhu, M. Wüthrich
Abstract It has become of key interest in the insurance industry to understand and extract information from telematics car driving data. Telematics car driving data of individual car drivers can be summarised in so-called speed–acceleration heatmaps. The aim of this study is to cluster such speed–acceleration heatmaps to different categories by analysing similarities and differences in these heatmaps. Making use of local smoothness properties, we propose to process these heatmaps as RGB images. Clustering can then be achieved by involving supervised information via a transfer learning approach using the pre-trained AlexNet to extract discriminative features. The K-means algorithm is then applied on these extracted discriminative features for clustering. The experiment results in an improvement of heatmap clustering compared to classical approaches.
从远程信息处理汽车驾驶数据中理解和提取信息已成为保险行业关注的焦点。远程信息处理汽车驾驶数据的个别汽车司机可以总结在所谓的速度-加速度热图。本研究的目的是通过分析这些热图的相似性和差异性,将这些速度-加速度热图聚类到不同的类别。利用局部平滑特性,我们建议将这些热图处理为RGB图像。然后,通过使用预训练的AlexNet提取判别特征的迁移学习方法,通过涉及监督信息来实现聚类。然后将K-means算法应用于这些提取的判别特征进行聚类。实验结果表明,与经典方法相比,该方法对热图聚类有了改进。
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引用次数: 5
Imprecise credibility theory 不精确可信度理论
IF 1.7 Q3 BUSINESS, FINANCE Pub Date : 2020-10-23 DOI: 10.1017/S1748499521000117
Liang Hong, Ryan Martin
Abstract The classical credibility theory is a cornerstone of experience rating, especially in the field of property and casualty insurance. An obstacle to putting the credibility theory into practice is the conversion of available prior information into a precise choice of crucial hyperparameters. In most real-world applications, the information necessary to justify a precise choice is lacking, so we propose an imprecise credibility estimator that honestly acknowledges the imprecision in the hyperparameter specification. This results in an interval estimator that is doubly robust in the sense that it retains the credibility estimator’s freedom from model specification and fast asymptotic concentration, while simultaneously being insensitive to prior hyperparameter specification.
摘要经典可信度理论是经验评级的基石,特别是在财产保险领域。将可信度理论付诸实践的一个障碍是将可用的先验信息转换为关键超参数的精确选择。在大多数实际应用中,缺乏证明精确选择所需的信息,因此我们提出了一个不精确的可信度估计器,它诚实地承认超参数规范中的不精确。这使得区间估计具有双重鲁棒性,因为它保留了可信度估计量不受模型规范和快速渐近集中的影响,同时对先验超参数规范不敏感。
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引用次数: 0
Mortality forecasting using a Lexis-based state-space model 使用基于Lexis的状态空间模型进行死亡率预测
IF 1.7 Q3 BUSINESS, FINANCE Pub Date : 2020-09-11 DOI: 10.1017/S1748499520000275
Patrik Andersson, M. Lindholm
Abstract A new method of forecasting mortality is introduced. The method is based on the continuous-time dynamics of the Lexis diagram, which given weak assumptions implies that the death count data are Poisson distributed. The underlying mortality rates are modelled with a hidden Markov model (HMM) which enables a fully likelihood-based inference. Likelihood inference is done by particle filter methods, which avoids approximating assumptions and also suggests natural model validation measures. The proposed model class contains as special cases many previous models with the important difference that the HMM methods make it possible to estimate the model efficiently. Another difference is that the population and latent variable variability can be explicitly modelled and estimated. Numerical examples show that the model performs well and that inefficient estimation methods can severely affect forecasts.
摘要介绍了一种预测死亡率的新方法。该方法基于Lexis图的连续时间动力学,它给出的弱假设意味着死亡计数数据是泊松分布的。潜在死亡率采用隐马尔可夫模型(HMM)建模,该模型可实现完全基于似然的推断。通过粒子滤波方法进行似然推断,避免了近似假设,并提出了自然的模型验证方法。所提出的模型类包含了许多以前的模型作为特殊情况,其重要区别在于HMM方法可以有效地估计模型。另一个不同之处在于,总体和潜在变量可变性可以被明确地建模和估计。数值算例表明,该模型性能良好,但低效的估计方法会严重影响预测结果。
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引用次数: 2
A review on Poisson, Cox, Hawkes, shot-noise Poisson and dynamic contagion process and their compound processes 泊松、Cox、Hawkes、弹噪声泊松和动态传染过程及其复合过程综述
IF 1.7 Q3 BUSINESS, FINANCE Pub Date : 2020-09-09 DOI: 10.1017/S1748499520000287
Jiwook Jang, Rosy Oh
Abstract The Poisson process is an essential building block to move up to complicated counting processes, such as the Cox (“doubly stochastic Poisson”) process, the Hawkes (“self-exciting”) process, exponentially decaying shot-noise Poisson (simply “shot-noise Poisson”) process and the dynamic contagion process. The Cox process provides flexibility by letting the intensity not only depending on time but also allowing it to be a stochastic process. The Hawkes process has self-exciting property and clustering effects. Shot-noise Poisson process is an extension of the Poisson process, where it is capable of displaying the frequency, magnitude and time period needed to determine the effect of points. The dynamic contagion process is a point process, where its intensity generalises the Hawkes process and Cox process with exponentially decaying shot-noise intensity. To facilitate the usage of these processes in practice, we revisit the distributional properties of the Poisson, Cox, Hawkes, shot-noise Poisson and dynamic contagion process and their compound processes. We provide simulation algorithms for these processes, which would be useful to statistical analysis, further business applications and research. As an application of the compound processes, numerical comparisons of value-at-risk and tail conditional expectation are made.
泊松过程是向复杂的计数过程(如Cox(“双随机泊松”)过程、Hawkes(“自激”)过程、指数衰减的单噪声泊松(简称“单噪声泊松”)过程和动态传染过程)移动的重要组成部分。Cox过程提供了灵活性,使强度不仅取决于时间,而且允许它是一个随机过程。Hawkes过程具有自激特性和聚类效应。短噪声泊松过程是泊松过程的扩展,它能够显示确定点的影响所需的频率、幅度和时间周期。动态传染过程是一个点过程,其强度推广了弹噪声强度呈指数衰减的Hawkes过程和Cox过程。为了便于在实践中使用这些过程,我们重新讨论了泊松、Cox、Hawkes、散噪声泊松和动态传染过程及其复合过程的分布性质。我们提供了这些过程的模拟算法,这将有助于统计分析,进一步的商业应用和研究。作为复合过程的应用,对风险值和尾部条件期望进行了数值比较。
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引用次数: 9
Multifactorial disorders and polygenic risk scores: predicting common diseases and the possibility of adverse selection in life and protection insurance – CORRIGENDUM 多因素障碍和多基因风险评分:预测常见疾病和人寿保险和保障保险中逆向选择的可能性——CORRIGENDUM
IF 1.7 Q3 BUSINESS, FINANCE Pub Date : 2020-09-08 DOI: 10.1017/s1748499520000299
Jessye Maxwell, Richard A. Russell, H. Wu, N. Sharapova, Peter Banthorpe, Paul F O'Reilly, C. Lewis
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引用次数: 0
AI in actuarial science – a review of recent advances – part 2 精算学中的人工智能——最新进展综述——第2部分
IF 1.7 Q3 BUSINESS, FINANCE Pub Date : 2020-08-26 DOI: 10.1017/S174849952000024X
Ronald Richman
Abstract Rapid advances in artificial intelligence (AI) and machine learning are creating products and services with the potential not only to change the environment in which actuaries operate, but also to provide new opportunities within actuarial science. These advances are based on a modern approach to designing, fitting and applying neural networks, generally referred to as “Deep Learning”. This paper investigates how actuarial science may adapt and evolve in the coming years to incorporate these new techniques and methodologies. Part 1 of this paper provides background on machine learning and deep learning, as well as an heuristic for where actuaries might benefit from applying these techniques. Part 2 of the paper then surveys emerging applications of AI in actuarial science, with examples from mortality modelling, claims reserving, non-life pricing and telematics. For some of the examples, code has been provided on GitHub so that the interested reader can experiment with these techniques for themselves. Part 2 concludes with an outlook on the potential for actuaries to integrate deep learning into their activities. Finally, a supplementary appendix discusses further resources providing more in-depth background on machine learning and deep learning.
摘要人工智能(AI)和机器学习的快速发展正在创造产品和服务,这些产品和服务不仅有可能改变精算师的经营环境,而且有可能在精算科学领域提供新的机会。这些进步是基于设计、拟合和应用神经网络的现代方法,通常被称为“深度学习”。本文研究了精算科学在未来几年如何适应和发展,以纳入这些新技术和方法。本文的第1部分提供了机器学习和深度学习的背景,以及精算师可能从应用这些技术中受益的启发。论文的第2部分调查了人工智能在精算科学中的新兴应用,包括死亡率建模、索赔准备金、非人寿定价和远程信息处理。对于其中一些示例,GitHub上提供了代码,以便感兴趣的读者可以自己尝试这些技术。第2部分最后展望了精算师将深度学习融入其活动的潜力。最后,补充附录讨论了进一步的资源,为机器学习和深度学习提供了更深入的背景。
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引用次数: 18
AI in actuarial science – a review of recent advances – part 1 精算科学中的人工智能-最新进展综述-第1部分
IF 1.7 Q3 BUSINESS, FINANCE Pub Date : 2020-08-26 DOI: 10.1017/S1748499520000238
Ronald Richman
Abstract Rapid advances in artificial intelligence (AI) and machine learning are creating products and services with the potential not only to change the environment in which actuaries operate but also to provide new opportunities within actuarial science. These advances are based on a modern approach to designing, fitting and applying neural networks, generally referred to as “Deep Learning.” This paper investigates how actuarial science may adapt and evolve in the coming years to incorporate these new techniques and methodologies. Part 1 of this paper provides background on machine learning and deep learning, as well as an heuristic for where actuaries might benefit from applying these techniques. Part 2 of the paper then surveys emerging applications of AI in actuarial science, with examples from mortality modelling, claims reserving, non-life pricing and telematics. For some of the examples, code has been provided on GitHub so that the interested reader can experiment with these techniques for themselves. Part 2 concludes with an outlook on the potential for actuaries to integrate deep learning into their activities. Finally, a supplementary appendix discusses further resources providing more in-depth background on machine learning and deep learning.
摘要人工智能(AI)和机器学习的快速发展正在创造产品和服务,这些产品和服务不仅有可能改变精算师的经营环境,而且有可能在精算科学领域提供新的机会。这些进步是基于设计、拟合和应用神经网络的现代方法,通常被称为“深度学习”。本文研究了精算科学在未来几年如何适应和发展,以融入这些新技术和方法。本文的第1部分提供了机器学习和深度学习的背景,以及精算师可能从应用这些技术中受益的启发。论文的第2部分调查了人工智能在精算科学中的新兴应用,包括死亡率建模、索赔准备金、非人寿定价和远程信息处理。对于其中一些示例,GitHub上提供了代码,以便感兴趣的读者可以自己尝试这些技术。第2部分最后展望了精算师将深度学习融入其活动的潜力。最后,补充附录讨论了进一步的资源,为机器学习和深度学习提供了更深入的背景。
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引用次数: 21
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Annals of Actuarial Science
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