Insurance Mathematics & Economics最新文献

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PowerBurr regression model for heavy-tailed loss data and its application 重尾损失数据的PowerBurr回归模型及其应用

IF 2.2 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2026-01-23 DOI: 10.1016/j.insmatheco.2026.103224

Yu Liu, Shengwang Meng

Statistical modeling of heavy-tailed loss data is a crucial foundation for catastrophe risk management. The PowerBurr distribution, as a novel multi-parameter heavy-tailed distribution, has promising applications in catastrophe risk management. This paper explores the statistical properties of the PowerBurr distribution in depth, including its special distributional forms under specific parameter settings and the limiting distributions at the boundaries of the parameter space. We further extend the concept to a family of PowerBurr distributions and analyze the tail properties of various distributions within this family. Building upon this foundation, the present study constructs a general linear regression model by specifying functional relationships between the reparameterized scale and shape parameters of the PowerBurr distribution and a set of explanatory variables. Methods for parameter estimation and model validation are provided. The commonly used Lomax regression model is a special case of this regression model. Finally, the PowerBurr-based regression model is applied to earthquake loss data in China and compared with regression models based on other heavy-tailed distributions. The results demonstrate that the new model improves the model’s goodness-of-fit and predictive performance, providing a new and effective tool for modeling heavy-tailed loss data.

重尾损失数据的统计建模是巨灾风险管理的重要基础。PowerBurr分布作为一种新型的多参数重尾分布，在巨灾风险管理中具有广阔的应用前景。本文深入探讨了PowerBurr分布的统计性质，包括其在特定参数设置下的特殊分布形式和参数空间边界处的极限分布。我们进一步将该概念扩展到一系列PowerBurr分布，并分析该家族中各种分布的尾部特性。在此基础上，本研究通过确定PowerBurr分布的重参数化尺度与形状参数之间的函数关系以及一组解释变量，构建了一般线性回归模型。给出了参数估计和模型验证的方法。常用的Lomax回归模型就是这种回归模型的特例。最后，将基于powerburr的回归模型应用于中国地震损失数据，并与基于其他重尾分布的回归模型进行了比较。结果表明，新模型提高了模型的拟合优度和预测性能，为重尾损失数据建模提供了一种新的有效工具。

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引用次数: 0

Optimal annuitization and asset allocation with fixed transaction costs 具有固定交易成本的最优年金化与资产配置

IF 2.2 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2026-01-21 DOI: 10.1016/j.insmatheco.2026.103223

Junyi Guo , Xiaoqing Liang , Yang Shen , Jie Xiong

In this paper, we examine optimal annuitization and asset allocation strategies for a utility-maximizing retiree with constant absolute risk aversion (CARA). The retiree can invest in a market consisting of one risky asset and one risk-free asset and is also allowed to purchase life annuities, with each purchase of life annuities incurring a fixed transaction cost. By using a stochastic control approach and duality techniques, we find that the optimal annuitization strategy is a barrier strategy involving a lower and an upper barrier on the retiree’s wealth. Once the wealth reaches the upper barrier, the retiree purchases additional annuity income to reduce the wealth to the lower one. Furthermore, we provide several numerical examples to illustrate our results and analyze the sensitivity of various parameters. We also compare these optimal strategies with those in the constrained Merton model and the scenario without transaction costs. Numerical results indicate that transaction costs cannot only postpone the retiree’s decision on annuitizing additional wealth, but also result in underspending and slow drawdown rate in the decumulation phases, which provides further explanations for the annuity puzzle, retirement-consumption puzzle and retirement-savings puzzle. Finally, we conduct perturbation analysis and find an asymptotic approximation of the value function when the transaction fee is small.

本文研究了具有恒定绝对风险厌恶（CARA）的效用最大化退休人员的最优年金化和资产配置策略。退休人员可以投资于由一种风险资产和一种无风险资产组成的市场，也可以购买终身年金，每次购买终身年金产生固定的交易成本。利用随机控制方法和对偶技术，我们发现最优年化策略是一种涉及退休人员财富的上下障碍的障碍策略。一旦财富达到较高的障碍，退休人员购买额外的年金收入来减少财富到较低的障碍。此外，我们还提供了几个数值例子来说明我们的结果，并分析了各种参数的灵敏度。我们还将这些最优策略与约束默顿模型和无交易成本情况下的最优策略进行了比较。数值结果表明，交易成本不仅会推迟退休人员对额外财富的年金化决策，而且会导致退休人员在累积阶段的支出不足和缓慢的提取速度，这进一步解释了年金难题、退休-消费难题和退休-储蓄难题。最后，我们进行了扰动分析，找到了交易费用较小时的值函数的渐近逼近。

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引用次数: 0

Mitigating ambiguity in earthquake catastrophe insurance pricing: A model averaging and α-Maxmin approach 减轻地震巨灾保险定价中的模糊性：模型平均和α-Maxmin方法

IF 2.2 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2026-01-13 DOI: 10.1016/j.insmatheco.2026.103222

Yunxian Li , Xinmei Yang , Zhilan Zi , Hefei Liu

Ambiguity poses a key challenge in the pricing of catastrophe insurance, as it leads to higher premiums compared to unambiguous risks. This paper proposes a novel approach that integrates model averaging (MA) techniques with an extended α-maxmin framework to address ambiguity in insurance pricing decisions. Specifically, we introduce three MA weighting strategies within a quantile regression setting to mitigate estimation uncertainty and extend the α-maxmin framework to formally incorporate both the insurer’s ambiguity aversion and survival constraints into the pricing process. Using earthquake loss data from China (1974-2023), we show that MA improves predictive accuracy and mitigates affordability issues by reducing ambiguity-induced premium inflation, with jackknife model averaging lowering net premiums by 15.69%. Sensitivity analyzes indicate that stronger ambiguity aversion (higher α), tighter survival constraints (lower θ), and a higher cost of capital (higher δ) all necessitate larger capital reserves to counter bankruptcy risk, thereby raising premiums, with the first two factors exerting a more pronounced influence. The paper offers a coherent toolkit for integrating model uncertainty into catastrophe insurance pricing with practical relevance for risk management and regulation.

模糊性对巨灾保险的定价构成了一个关键挑战，因为与明确的风险相比，模糊性导致更高的保费。本文提出了一种将模型平均（MA）技术与扩展的α-maxmin框架相结合的新方法来解决保险定价决策中的模糊性问题。具体而言，我们在分位数回归设置中引入了三种MA加权策略，以减轻估计的不确定性，并扩展α-maxmin框架，将保险人的歧义厌恶和生存约束正式纳入定价过程。利用中国1974-2023年的地震损失数据，我们发现MA通过减少模糊性导致的保费通胀，提高了预测准确性，并缓解了可负担性问题，折刀模型平均降低了15.69%的净保费。敏感性分析表明，更强的歧义厌恶（较高的α）、更严格的生存约束（较低的θ）和更高的资本成本（较高的δ）都需要更大的资本储备来应对破产风险，从而提高保费，其中前两个因素的影响更为显著。本文提供了一个连贯的工具包，将模型不确定性整合到巨灾保险定价中，与风险管理和监管具有实际意义。

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引用次数: 0

Efficient pricing and Greeks estimation for variable annuities under a multivariate OUSV model 多元OUSV模型下可变年金的有效定价与希腊人估计

IF 2.2 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2026-01-07 DOI: 10.1016/j.insmatheco.2026.103220

Shaoying Chen , Zhenyu Cui , Yang Yang , Zhimin Zhang

As the understanding of GMxB-related risks deepens, insurance companies are increasingly seeking efficient annuity risk management systems. This paper is the first to extend the Karhunen-Loève (KL) expansion method to the pricing and Greeks estimation of the GMxB variable annuities written on multiple sub-account funds, under the multivariate Ornstein-Uhlenbeck stochastic volatility model. Additionally, the simulation-based pathwise (PW) and likelihood ratio (LR) methods are generalized for efficient Greeks computation within the multi-asset annuity framework. Through asymptotic analysis, we address a theoretical gap in the original KL expansion sampling framework. Numerical experiments demonstrate that the proposed method achieves computational efficiency and robustness, providing a practical and reliable framework for the risk management of complex multi-asset variable annuities.

随着对gmxb相关风险认识的加深，保险公司越来越寻求高效的年金风险管理系统。本文首次将karhunen - lo (KL)展开方法推广到多元Ornstein-Uhlenbeck随机波动率模型下的GMxB型多子账户型可变年金的定价和希腊估计。此外，基于模拟的路径（PW）和似然比（LR）方法被推广用于多资产年金框架内的有效希腊人计算。通过渐近分析，我们解决了原始KL展开抽样框架的理论缺陷。数值实验表明，该方法具有较好的计算效率和鲁棒性，为复杂多资产变量年金的风险管理提供了一个实用可靠的框架。

引用次数: 0

Subgame perfect Nash equilibria in large reinsurance markets 大型再保险市场的子博弈完全纳什均衡

IF 2.2 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2026-01-07 DOI: 10.1016/j.insmatheco.2025.103210

Maria Andraos , Mario Ghossoub , Michael B. Zhu

We consider a model of a reinsurance market consisting of multiple insurers on the demand side and multiple reinsurers on the supply side, thereby providing a unifying framework and extension of the recent literature on optimality and equilibria in reinsurance markets. Each insurer has preferences represented by a general Choquet risk measure and can purchase coverage from any or all reinsurers. Each reinsurer has preferences represented by a general Choquet risk measure and can provide coverage to any or all insurers. Pricing in this market is done via a nonlinear pricing rule given by a Choquet integral. We model the market as a sequential game in which the reinsurers have the first-move advantage. We characterize the Subgame Perfect Nash Equilibria in this market in some cases of interest, and we examine their Pareto efficiency. In addition, we consider two special cases of our model that correspond to existing models in the related literature, and we show how our findings extend these previous results. Finally, we illustrate our results in a numerical example.

我们考虑了一个再保险市场的模型，该模型由多个保险公司在需求侧和多个再保险公司在供给侧组成，从而提供了一个统一的框架，并扩展了最近关于再保险市场最优性和均衡的文献。每个保险公司都有一个通用的Choquet风险度量代表的偏好，并且可以从任何或所有再保险公司购买保险。每个再保险公司都有一个通用的Choquet风险度量代表的偏好，并可以向任何或所有保险公司提供保险。该市场的定价是通过由Choquet积分给出的非线性定价规则来完成的。我们将市场建模为一个连续博弈，其中再保险公司具有先发优势。在某些情况下，我们描述了这个市场上的子博弈完全纳什均衡，并检验了它们的帕累托效率。此外，我们考虑了我们的模型对应于相关文献中现有模型的两个特殊情况，并展示了我们的发现如何扩展了这些先前的结果。最后，我们用一个数值例子来说明我们的结果。

引用次数: 0

Hedging universal life insurance policies 对冲万能寿险保单

IF 2.2 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2026-01-07 DOI: 10.1016/j.insmatheco.2026.103221

Emmanuel Hamel , Frédéric Godin , Patrice Gaillardetz

This study explores hedging procedures for Universal Life (UL) insurance contracts. Risk related to guarantees embedded in UL policies are typically managed through conventional means by insurers, such as reserving, capital buffers, and the use of natural hedges. We outline that hedging can be a useful risk management tool to mitigate risk associated with UL policies. We explore two hedging approaches: a static hedging procedure based on a portfolio of zero-coupons bonds and a dynamic hedging approach relying on the sequential rebalancing of liquid swap portfolios. Both strategies are shown to successfully reduce loss variability, even when relying on a low number of hedging instruments. In our setting, the dynamic approach provides the best performance.

本研究探讨万能人寿（UL）保险合约的套期保值程序。保险公司通常通过传统手段管理与UL保单中嵌入的担保相关的风险，例如准备金、资本缓冲和使用自然对冲。我们概述了套期保值可以是一种有用的风险管理工具，以减轻与UL政策相关的风险。我们探讨了两种套期保值方法：基于零息债券组合的静态套期保值程序和依赖于流动性掉期组合的顺序再平衡的动态套期保值方法。这两种策略都被证明可以成功地减少损失的可变性，即使依赖于低数量的对冲工具。在我们的设置中，动态方法提供了最佳性能。

引用次数: 0

Probabilistic loss reserving prediction via denoising diffusion model 基于去噪扩散模型的概率损失保留预测

IF 2.2 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2026-01-03 DOI: 10.1016/j.insmatheco.2025.103208

Shiying Gao, Yuning Zhang, Ruikun Li, S.T. Boris Choy, Junbin Gao

This paper introduces an innovative approach to predicting loss reserves in the insurance industry through a revised diffusion model. This model leverages run-off triangles of claim data as graphical representations, highlighting the interconnections among data points within the triangle. Unlike the traditional cross-classified over-dispersed Poisson (ccODP) model, our proposed diffusion model not only enhances accuracy and efficiency but also provides probabilistic forecasts. Through comprehensive simulation and empirical studies, we demonstrate the superior forecasting capabilities of our diffusion model compared to existing methods. These findings indicate that using network-based interactions within run-off triangles can significantly improve loss reserve forecasting.

本文介绍了一种通过修正的扩散模型来预测保险业损失准备金的创新方法。该模型利用索赔数据的输出三角形作为图形表示，突出显示三角形内数据点之间的相互连接。与传统的交叉分类过分散泊松（codp）模型不同，我们提出的扩散模型不仅提高了精度和效率，而且提供了概率预测。通过综合模拟和实证研究，我们证明了我们的扩散模型与现有方法相比具有优越的预测能力。这些发现表明，在径流三角形中使用基于网络的交互可以显著改善损失储备预测。

引用次数: 0

The demand for insurance with ambiguous recovery rate 赔偿率模糊的保险需求

IF 2.2 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2026-01-01 DOI: 10.1016/j.insmatheco.2025.103209

Yichun Chi , Yuxia Huang , Sheng Chao Zhuang

It is not uncommon for insurance contracts to fail performing as intended. In practice, the default recovery rate is rather difficult to be evaluated precisely by insureds at the inception of the insurance contract. Thus, in this paper we assume ambiguous recovery rates and study optimal insurance demand for an insured. Under the insured’s identifiable smooth ambiguity preference, we derive conditions for the optimality of full insurance, partial insurance, or no insurance. In particular, we find that the introduction of ambiguity on the recovery rate raises the trigger level for full insurance to be optimal under actuarially fair contract pricing. We further carry out comparative statics to analyze the effect of the change in the degree of the insured’s ambiguity aversion or ambiguity level on the insurance demand. The insurance demand is reduced for a higher degree of ambiguity aversion or greater ambiguity, if certain conditions are imposed on the insurance pricing and the insured’s risk preference and ambiguity preference. We also examine the impact of the insured’s initial wealth, and find that the ambiguity reinforces the wealth effect when her coefficient of relative risk aversion is less than one.

保险合同未能按预期履行并不罕见。在实践中，被保险人很难在保险合同成立之初就准确评估违约回收率。因此，在本文中，我们假设不明确的回收率和研究最优保险需求的投保人。在被保险人可识别的平滑模糊偏好下，我们推导出全额保险、部分保险和不保险的最优性条件。特别是，我们发现，在精算公平的合同定价下，引入回收率的模糊性提高了全额保险的最优触发水平。我们进一步进行比较统计，分析被保险人歧义厌恶程度或歧义程度的变化对保险需求的影响。如果对保险定价和被保险人的风险偏好和模糊性偏好施加一定的条件，则对模糊性厌恶程度越高或模糊性越大，保险需求就会减少。我们还考察了被保险人初始财富的影响，发现当其相对风险厌恶系数小于1时，模糊性强化了财富效应。

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引用次数: 0

The ultimate drawdown insurance and its state-dependent premium 终极提款保险及其依赖于国家的保费

IF 2.2 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2026-01-01 DOI: 10.1016/j.insmatheco.2025.103201

Duo Xu, Shu Li

The analysis of drawdown risk is attracting growing interest thanks to its valuable insights into risk management. In this paper, we analyze an insurance contract designed to provide protection against the risk of market drawdown, where the claim is triggered by an ultimate drawdown. The concept of the ultimate drawdown was introduced in Li and Zhou (2022), which occurs either when the drawdown size exceeds a soft barrier for an extended period (so-called the Parisian drawdown), or when the drawdown size exceeds a significantly hard barrier. We propose the state-dependent premium structure for the ultimate drawdown insurance, where the premium are collected when the underlying process is in the financial non-distress state. Under the Lévy insurance framework, we analytically derive the fair market premium for the proposed premium structure. Furthermore, we explore the policyholder’s optimal surrender strategy when the contract allows for a cancellation feature. We demonstrate the merits of the proposed premium structure on the surrender risk, by comparing it to the constant premium structure. Numerical examples are provided for illustration. In addition, we examine some drawdown-related penalty functions of interest.

由于其对风险管理的宝贵见解，对收缩风险的分析正吸引着越来越多的兴趣。在本文中，我们分析了一种保险合同，该合同旨在提供对市场收缩风险的保护，其中索赔是由最终收缩触发的。Li和Zhou（2022）提出了最终缩减的概念，它要么发生在缩减规模长期超过软障碍（所谓的巴黎缩减）时，要么发生在缩减规模超过明显的硬障碍时。我们提出了最终提取保险的状态依赖保费结构，其中保费在基础过程处于财务非困境状态时收取。在lsamvy保险框架下，我们分析得出了所提出的保费结构的公平市场保费。此外，我们探讨了当合约允许取消功能时，投保人的最优退保策略。通过与不变保费结构的比较，我们证明了所提出的保费结构对退保风险的优点。给出了数值算例进行说明。此外，我们还研究了一些与降相关的惩罚函数。

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Stochastic orderings for set-valued risk measures 集值风险度量的随机排序

IF 2.2 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2026-01-01 DOI: 10.1016/j.insmatheco.2025.103180

Elisa Mastrogiacomo , Marco Tarsia

This paper explores the portfolio aggregation problem within the framework of set-valued risk measures, with a specific emphasis on maximal correlation risk measures, as introduced in this work. We propose a novel stochastic ordering concept for random vectors and establish consistency properties for maximal correlation risk measures in this setting. Furthermore, we demonstrate convex-type consistency for a specific subclass of law-invariant convex set-valued risk measures, highlighting both their theoretical foundations and practical significance.

本文探讨了集值风险度量框架内的投资组合聚集问题，特别强调了在本工作中引入的最大相关风险度量。我们提出了一种新的随机向量的随机排序概念，并建立了在这种情况下最大相关风险度量的一致性。在此基础上，我们进一步证明了一类特定的律不变凸集值风险测度的凸型一致性，突出了其理论基础和实际意义。

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