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Automated machine learning in insurance 保险中的自动机器学习
IF 1.9 2区 经济学 Q2 ECONOMICS Pub Date : 2024-11-08 DOI: 10.1016/j.insmatheco.2024.10.002
Panyi Dong, Zhiyu Quan
Machine Learning (ML) has gained popularity in actuarial research and insurance industrial applications. However, the performance of most ML tasks heavily depends on data preprocessing, model selection, and hyperparameter optimization, which are considered to be intensive in terms of domain knowledge, experience, and manual labor. Automated Machine Learning (AutoML) aims to automatically complete the full life-cycle of ML tasks and provides state-of-the-art ML models without human intervention or supervision. This paper introduces an AutoML workflow that allows users without domain knowledge or prior experience to achieve robust and effortless ML deployment by writing only a few lines of code. This proposed AutoML is specifically tailored for the insurance application, with features like the balancing step in data preprocessing, ensemble pipelines, and customized loss functions. These features are designed to address the unique challenges of the insurance domain, including the imbalanced nature of common insurance datasets. The full code and documentation are available on the GitHub repository.1
机器学习(ML)在精算研究和保险行业应用中越来越受欢迎。然而,大多数 ML 任务的性能在很大程度上取决于数据预处理、模型选择和超参数优化,而这些都被认为是领域知识、经验和人工劳动的密集型工作。自动化机器学习(AutoML)旨在自动完成 ML 任务的整个生命周期,并在无需人工干预或监督的情况下提供最先进的 ML 模型。本文介绍了一种 AutoML 工作流程,让没有领域知识或先前经验的用户只需编写几行代码,就能轻松实现强大的 ML 部署。本文提出的 AutoML 专为保险应用量身定制,具有数据预处理中的平衡步骤、集合管道和自定义损失函数等功能。这些功能旨在应对保险领域的独特挑战,包括常见保险数据集的不平衡性。完整的代码和文档可在 GitHub 存储库中获取1。
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引用次数: 0
Pension funds with longevity risk: An optimal portfolio insurance approach 养老基金的长寿风险:最佳投资组合保险方法
IF 1.9 2区 经济学 Q2 ECONOMICS Pub Date : 2024-11-01 DOI: 10.1016/j.insmatheco.2024.10.001
Marina Di Giacinto , Daniele Mancinelli , Mario Marino , Immacolata Oliva
We present a unified framework designed to provide an optimal investment strategy for members of a defined contribution pension plan. Our model guarantees a minimum retirement savings level, expressed as a target annuity, by assuming uncertainty in interest rates, labor income, and mortality during the accumulation phase. To protect the accumulated retirement capital against both investment and longevity risks, the present value of the guaranteed lifetime annuity is regarded as the baseline wealth to hold upon reaching the retirement date, while a purpose-oriented proportion portfolio strategy is employed to invest the residual wealth. By applying standard dynamic programming techniques, we determine a closed-form solution to the stochastic control problem with the objective of maximizing the expected utility of the final surplus, defined as the difference between the accumulated wealth and the target annuity value. The theoretical findings are bolstered by a comprehensive numerical analysis designed to assess the impact of longevity on investment policies, highlighting the suitability of our proposal for managing defined contribution schemes.
我们提出了一个统一的框架,旨在为固定缴费养老金计划的成员提供最佳投资策略。我们的模型通过假设积累阶段的利率、劳动收入和死亡率的不确定性,保证最低退休储蓄水平,以目标年金来表示。为了保护积累的退休资本免受投资风险和长寿风险的影响,我们将保证终身年金的现值视为到达退休日期时应持有的基准财富,同时采用目标导向的比例投资组合策略来投资剩余财富。通过应用标准动态编程技术,我们确定了随机控制问题的闭式解,其目标是最大化最终盈余的预期效用,即累积财富与目标年金值之间的差额。我们进行了全面的数值分析,以评估长寿对投资政策的影响,突出了我们的建议对管理固定缴费计划的适用性,从而为理论研究成果提供了支持。
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引用次数: 0
A new characterization of second-order stochastic dominance 二阶随机优势的新特征
IF 1.9 2区 经济学 Q2 ECONOMICS Pub Date : 2024-10-11 DOI: 10.1016/j.insmatheco.2024.09.005
Yuanying Guan , Muqiao Huang , Ruodu Wang
We provide a new characterization of second-order stochastic dominance, also known as increasing concave order. The result has an intuitive interpretation that adding a risk with negative expected value in adverse scenarios makes the resulting position generally less desirable for risk-averse agents. A similar characterization is also found for convex order and increasing convex order. The proof techniques for the main result are based on properties of Expected Shortfall, a family of risk measures that is popular in banking and insurance regulation. Applications in risk management and insurance are discussed.
我们为二阶随机支配(又称递增凹阶)提供了一个新的特征。这一结果有一个直观的解释,即在不利情况下增加一个预期值为负的风险,会使风险规避者对由此产生的头寸普遍不感兴趣。凸序和递增凸序也有类似的特征。主要结果的证明技术基于预期缺口的特性,预期缺口是银行和保险监管中常用的风险度量系列。本文还讨论了风险管理和保险中的应用。
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引用次数: 0
Bivariate Tail Conditional Co-Expectation for elliptical distributions 椭圆分布的双变量尾部条件共期望
IF 1.9 2区 经济学 Q2 ECONOMICS Pub Date : 2024-10-01 DOI: 10.1016/j.insmatheco.2024.09.004
Roy Cerqueti , Arsen Palestini
In this paper, we consider a random vector X=(X1,X2) following a multivariate Elliptical distribution and we provide an explicit formula for E(X|XX˜), i.e., the expected value of the bivariate random variable X conditioned to the event XX˜, with X˜R2. Such a conditional expectation has an intuitive interpretation in the context of risk measures. Specifically, E(X|XX˜) can be interpreted as the Tail Conditional Co-Expectation of X (TCoES). Our main result analytically proves that for a large number of Elliptical distributions, the TCoES can be written as a function of the probability density function of the Skew Elliptical distributions introduced in the literature by the pioneering work of Azzalini (1985). Some numerical experiments based on empirical data show the usefulness of the obtained results for real-world applications.
在本文中,我们考虑了一个服从多元椭圆分布的随机向量 X=(X1,X2),并提供了一个明确的 E(X|X≤X˜) 公式,即以事件 X≤X˜ 为条件的二元随机变量 X 的期望值,其中 X˜∈R2。这种条件期望在风险度量中有着直观的解释。具体来说,E(X|X≤X˜) 可以解释为 X 的尾部条件共同期望(TCoES)。我们的主要结果通过分析证明,对于大量椭圆分布,TCoES 可以写成 Azzalini(1985 年)开创性工作中引入的斜椭圆分布概率密度函数的函数。一些基于经验数据的数值实验表明,所获得的结果在实际应用中非常有用。
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引用次数: 0
Egalitarian pooling and sharing of longevity risk a.k.a. can an administrator help skin the tontine cat? 平均分摊和分担长寿风险,又称 "管理人能否帮助猫剥皮"?
IF 1.9 2区 经济学 Q2 ECONOMICS Pub Date : 2024-09-30 DOI: 10.1016/j.insmatheco.2024.09.003
Jan Dhaene , Moshe A. Milevsky
This paper is concerned with the mathematical problem of allocating longevity-linked fund payouts in a pool where participants differ in both wealth (contributions) and health (mortality), particularly when these groups are relatively small in size. In other words, we offer a modelling framework for distributing longevity-risk pools' income and benefits (or “tontine winnings”) when participants are heterogeneous. Similar to the nascent literature on decentralized risk sharing (DRS), there are several equally plausible arrangements for sharing benefits (a.k.a. “skinning the tontine cat”) among survivors. We argue that the selected rule may depend on the extent of social cohesion within the longevity risk pool, ranging from solidarity and altruism to pure individualism. And, if actuarial fairness is a concern, we suggest introducing an administrator – which differs from a guarantor – to make the tontine pool payouts collectively actuarial fair. Fairness is in the sense that the group of participants will on average receive the same benefits as they collectively invested; and we provide the mathematical framework to implement that suggestion. One thing is for certain: actuarial science cannot offer design uniqueness for longevity-contingent claims; only a consistent methodology.
本文关注的是在参与者的财富(缴费)和健康(死亡率)都不同的情况下,尤其是当这些群体的规模相对较小时,如何分配与长寿挂钩的基金赔付的数学问题。换句话说,我们提供了一个模型框架,用于在参与人异质性的情况下分配长寿风险池的收入和收益(或 "通廷奖")。与有关分散风险分担(DRS)的新兴文献类似,在幸存者之间分配收益(又称 "剥通廷猫皮")也有几种同样合理的安排。我们认为,所选择的规则可能取决于长寿风险池中社会凝聚力的程度,从团结和利他主义到纯粹的个人主义。而且,如果精算公平是一个问题,我们建议引入一个管理人--不同于担保人--来使长寿风险池的支付集体精算公平。所谓公平,是指参与人平均获得的收益与他们集体投资的收益相同;我们提供了实现这一建议的数学框架。有一点是肯定的:精算学无法为与长寿相关的索赔提供设计上的独特性,只能提供一致的方法。
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引用次数: 0
A two-layer stochastic game approach to reinsurance contracting and competition 再保险合约和竞争的双层随机博弈方法
IF 1.9 2区 经济学 Q2 ECONOMICS Pub Date : 2024-09-27 DOI: 10.1016/j.insmatheco.2024.09.002
Zongxia Liang , Yi Xia , Bin Zou
We propose a two-layer stochastic game model to study reinsurance contracting and competition in a market with one insurer and two competing reinsurers. The insurer negotiates with both reinsurers simultaneously for proportional reinsurance contracts that are priced using the variance premium principle. The reinsurance contracting between the insurer and each reinsurer is modeled as a Stackelberg game. The two reinsurers compete for business from the insurer and optimize the so-called relative performance, instead of their own surplus, and their competition is settled by a noncooperative Nash game. We obtain a sufficient and necessary condition, related to the competition degrees of the two reinsurers, for the existence of an equilibrium. We show that the equilibrium, if exists, is unique, and the equilibrium strategy of each player is constant, fully characterized in semiclosed form. Furthermore, we obtain interesting sensitivity results for the equilibrium strategies through both analytical and numerical studies.
我们提出了一个双层随机博弈模型,以研究在一个有一个保险人和两个相互竞争的再保险人的市场中,再保险合同的签订和竞争问题。保险人同时与两个再保险人就比例再保险合同进行谈判,再保险合同采用方差溢价原则定价。保险人与每个再保险人之间的再保险合约被模拟为斯泰尔伯格博弈。两个再保险人争夺保险人的业务,优化所谓的相对业绩,而不是自身的盈余,他们之间的竞争通过非合作的纳什博弈来解决。我们得到了存在均衡的充分必要条件,该条件与两个再保险人的竞争程度有关。我们证明,均衡(如果存在)是唯一的,而且每个博弈方的均衡策略都是恒定的,完全以半封闭形式表征。此外,我们还通过分析和数值研究获得了均衡策略的有趣敏感性结果。
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引用次数: 0
Optimal insurance design under asymmetric Nash bargaining 非对称纳什谈判下的最优保险设计
IF 1.9 2区 经济学 Q2 ECONOMICS Pub Date : 2024-09-12 DOI: 10.1016/j.insmatheco.2024.08.006
Yichun Chi , Tao Hu , Zhengtang Zhao , Jiakun Zheng

This paper considers a risk-neutral insurer and a risk-averse individual who bargain over the terms of an insurance contract. Under asymmetric Nash bargaining, we show that the Pareto-optimal insurance contract always contains a straight deductible under linear transaction costs and that the deductible disappears if and only if the deadweight cost is zero, regardless of the insurer's bargaining power. We further find that the optimality of no insurance is consistent across all market structures. When the insured's risk preference exhibits decreasing absolute risk aversion, the optimal deductible and the insurer's expected loss decrease in the degree of the insured's risk aversion and thus increase in the insured's initial wealth. In addition, the effect of increasing the insurer's bargaining power on the optimal deductible is equivalent to a pure effect of reducing the initial wealth of the insured. Our results suggest that the well-documented preference for low deductibles could be the result of insurance bargaining.

本文考虑了一个风险中性的保险公司和一个风险规避者,他们就保险合同的条款进行讨价还价。在非对称纳什讨价还价条件下,我们证明了帕累托最优保险合同总是包含线性交易成本下的直接免赔额,而且无论保险人的讨价还价能力如何,只有当死重成本为零时,免赔额才会消失。我们进一步发现,不投保的最优性在所有市场结构中都是一致的。当被保险人的风险偏好呈现绝对风险厌恶程度递减时,最优免赔额和保险人的预期损失会随着被保险人风险厌恶程度的降低而降低,从而随着被保险人初始财富的增加而增加。此外,保险人议价能力的提高对最优免赔额的影响等同于减少被保险人初始财富的纯粹影响。我们的研究结果表明,有据可查的低免赔额偏好可能是保险讨价还价的结果。
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引用次数: 0
Valuation of guaranteed lifelong withdrawal benefit with the long-term care option 采用长期护理方案的有保障终身离职金估值
IF 1.9 2区 经济学 Q2 ECONOMICS Pub Date : 2024-09-07 DOI: 10.1016/j.insmatheco.2024.09.001
Yang Yang , Shaoying Chen , Zhenyu Cui , Zhimin Zhang

In this paper, under the stochastic interest rate framework, we consider the valuation of a Guaranteed Lifelong Withdrawal Benefit (GLWB) annuity product by explicitly incorporating the health state of the policyholder through the long-term care (LTC) option. The product provides policyholders with protection against longevity risk and market downturns, as well as financial support when facing LTC needs. Within the context of dynamic withdrawals, the valuation of the GLWB annuity with the LTC option is characterized as a stochastic optimal control problem. We introduce a novel bang-bang analysis approach without the usual convexity assumption in literature and prove that the optimal withdrawal strategies for the policyholder are constrained to a finite set. Furthermore, we perform a sensitivity analysis on the price determinants of GLWB annuities with and without the LTC option, and provide economic interpretations. Lastly, we investigate the impact of gender on the optimal withdrawal strategy and the fair fee of the annuity with the LTC option.

本文在随机利率框架下,通过长期护理(LTC)选项明确纳入投保人的健康状况,考虑了保证终身提取利益(GLWB)年金产品的估值问题。该产品为投保人提供长寿风险和市场低迷的保护,并在面临长期护理需求时提供财务支持。在动态提取的背景下,带有 LTC 选项的 GLWB 年金的估值被描述为一个随机最优控制问题。我们引入了一种新颖的 "砰砰 "分析方法,摒弃了文献中常见的凸性假设,并证明了投保人的最优提取策略受限于一个有限集合。此外,我们还对有无 LTC 选项的 GLWB 年金的价格决定因素进行了敏感性分析,并提供了经济学解释。最后,我们研究了性别对最优提取策略和带有长寿医疗保险选项的年金公平费用的影响。
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引用次数: 0
Optimal dividends and capital injection: A general Lévy model with extensions to regime-switching models 最优股息和注资:扩展到制度转换模型的一般莱维模型
IF 1.9 2区 经济学 Q2 ECONOMICS Pub Date : 2024-09-06 DOI: 10.1016/j.insmatheco.2024.08.007
Dante Mata López , Kei Noba , José-Luis Pérez , Kazutoshi Yamazaki

This paper studies a general Lévy process model of the bail-out optimal dividend problem with an exponential time horizon, and further extends it to the regime-switching model. We first show the optimality of a double barrier strategy in the single-regime setting with a concave terminal payoff function. This is then applied to show the optimality of a Markov-modulated double barrier strategy in the regime-switching model via contraction mapping arguments. We solve these for a general Lévy model with both positive and negative jumps, greatly generalizing the existing results on spectrally one-sided models.

本文研究了指数时间跨度下救助最优红利问题的一般莱维过程模型,并将其进一步扩展到制度转换模型。我们首先证明了在单一制度背景下,双障碍策略的最优性,其终端报酬函数为凹型。然后,我们通过收缩映射论证,证明了在制度转换模型中马尔可夫调制双障碍策略的最优性。我们为具有正跳和负跳的一般莱维模型解决了这些问题,极大地推广了光谱单边模型的现有结果。
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引用次数: 0
A unified theory of decentralized insurance 分散式保险的统一理论
IF 1.9 2区 经济学 Q2 ECONOMICS Pub Date : 2024-09-05 DOI: 10.1016/j.insmatheco.2024.08.008
Runhuan Feng , Ming Liu , Ning Zhang

Decentralized insurance can be used to describe risk sharing mechanisms under which participants trade risks among each other as opposed to passing risks mostly to an insurer in traditional centralized insurance. There are a wide range of decentralized practices in all kinds of forms developed around the world, including online mutual aid in East Asia, takaful in the Middle East, peer-to-peer insurance in the West, international catastrophe risk pooling by African, Caribbean and Central America countries, etc. There is also a rich literature of risk sharing in academia that offers theoretical bases of other decentralized mechanisms. This work presents a unified mathematical framework to describe the commonalities and the relationships of all these seemingly different business in practice and theoretical models in academia. Such a framework provides a fertile ground for the comparison of existing practices and the design and engineering of hybrid and innovative models.

分散式保险可以用来描述风险分担机制,在这种机制下,参与者相互之间进行风险交易,而不是像传统的集中式保险那样将风险主要转嫁给保险公司。世界各地发展了各种形式的分散实践,包括东亚的网上互助、中东的塔卡富、西方的点对点保险、非洲、加勒比和中美洲国家的国际巨灾风险共担等。学术界也有丰富的风险分担文献,为其他分散机制提供了理论基础。这项工作提出了一个统一的数学框架来描述所有这些看似不同的实践业务和学术界理论模型的共性和关系。这样一个框架为比较现有的实践以及设计混合创新模式提供了肥沃的土壤。
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引用次数: 0
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Insurance Mathematics & Economics
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