Insurance Mathematics & Economics最新文献_第6页

Optimal reinsurance design under convex premium principles and distortion risk measures 凸保费原则和失真风险措施下的最优再保险设计

IF 2.2 2区经济学

Insurance Mathematics & Economics Pub Date : 2026-01-01 Epub Date: 2025-12-19 DOI: 10.1016/j.insmatheco.2025.103202

Yiying Zhang , Wenjun Jiang

{"title":"Optimal reinsurance design under convex premium principles and distortion risk measures","authors":"Yiying Zhang , Wenjun Jiang","doi":"10.1016/j.insmatheco.2025.103202","DOIUrl":"10.1016/j.insmatheco.2025.103202","url":null,"abstract":"<div><div>This paper studies an optimal reinsurance problem from an insurer’s perspective under convex premium principles. The insurer’s preference is assumed to be dictated by the distortion risk measure. When doing business with only one reinsurer, the general form of the optimal indemnity function for the insurer is derived by jointly applying the calculation of variation and marginal indemnification function approaches. We demonstrate that the optimal indemnity function for the insurer takes the form of a limited stop-loss when the insurer adopts a Range Value-at-Risk preference. In contrast, when the insurer applies strictly convex distortion risk measures, we show that, under mild conditions, the optimal indemnity function may include a co-insurance component. We also extend the results to the case of multiple reinsurers through a representative reinsurer lens, and present a sufficient condition under which the representative reinsurer’s premium principle is of the same mathematical form of the convex premium principle studied in this paper. We also show the connection between the optimal reinsurance problems under the certainty-equivalent premium principle and under the convex premium principle. Some interesting results are presented for the problem between one insurer and multiple reinsurers when each reinsurer applies an <em>i</em>th-moment premium principle.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"126 ","pages":"Article 103202"},"PeriodicalIF":2.2,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145883660","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Bayesian CART models for aggregate claim modeling 用于总索赔建模的贝叶斯CART模型

IF 2.2 2区经济学

Insurance Mathematics & Economics Pub Date : 2025-11-01 Epub Date: 2025-07-30 DOI: 10.1016/j.insmatheco.2025.103136

Yaojun Zhang , Lanpeng Ji , Georgios Aivaliotis , Charles C. Taylor

{"title":"Bayesian CART models for aggregate claim modeling","authors":"Yaojun Zhang , Lanpeng Ji , Georgios Aivaliotis , Charles C. Taylor","doi":"10.1016/j.insmatheco.2025.103136","DOIUrl":"10.1016/j.insmatheco.2025.103136","url":null,"abstract":"<div><div>This paper proposes three types of Bayesian CART (or BCART) models for aggregate claim amount, namely, frequency-severity models, sequential models and joint models. We propose a general framework for BCART models applicable to data with multivariate responses, which is particularly useful for the joint BCART models with a bivariate response: the number of claims and the aggregate claim amount. To facilitate frequency-severity modeling, we investigate BCART models for the right-skewed and heavy-tailed claim severity data using various distributions. We discover that the Weibull distribution is superior to gamma and lognormal distributions, due to its ability to capture different tail characteristics in tree models. Additionally, we find that sequential BCART models and joint BCART models, which can incorporate more complex dependence between the number of claims and severity, are beneficial and thus preferable to the frequency-severity BCART models in which independence is commonly assumed. The effectiveness of these models' performance is illustrated by carefully designed simulations and real insurance data.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"125 ","pages":"Article 103136"},"PeriodicalIF":2.2,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144749841","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Modelling seasonal mortality: An age–period–cohort approach 季节性死亡率建模：一种年龄时期队列方法

IF 2.2 2区经济学

Insurance Mathematics & Economics Pub Date : 2025-11-01 Epub Date: 2025-09-30 DOI: 10.1016/j.insmatheco.2025.103162

Jean-François Bégin , Mathieu Boudreault , Thomas Landry

{"title":"Modelling seasonal mortality: An age–period–cohort approach","authors":"Jean-François Bégin , Mathieu Boudreault , Thomas Landry","doi":"10.1016/j.insmatheco.2025.103162","DOIUrl":"10.1016/j.insmatheco.2025.103162","url":null,"abstract":"<div><div>Age–period–cohort (APC) mortality models have become the standard approach in actuarial science to project mortality improvements for uses such as pricing annuities and setting contributions in pension plans. Annual mortality rates are sufficient for such long-term applications; yet, for understanding excess mortality due to, e.g., epidemics and heat waves, annual observations have important limitations, and <em>high-frequency</em> data need to be used. This study introduces a seasonal overlay that can be used in the context of APC models. Based on a periodic spline, this extra layer allows the model to capture seasonal features parsimoniously. In an empirical application, we fit a CBDX variant of the APC family to daily mortality data from the province of Quebec in Canada. Our dataset covers over 3.6 million individuals aged at least 60 between 1996 and 2019. Our results show significant seasonal patterns consistent with the flu season, which are similar between males and females. We also test different parametric models and find that the shape of seasonality remained constant over time for most age groups. As part of a sensitivity analysis, we investigate intra-annual mortality patterns between subgroups and report that the local climate, scheme of urbanization, and individual socio-economic status do not affect seasonal patterns. Excess mortality during 2020–2022 is also explored using our modelling framework.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"125 ","pages":"Article 103162"},"PeriodicalIF":2.2,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145332458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Avoiding a longevity catastrophe: Harnessing longevity indices to mitigate individual, institutional and systemic longevity risks 避免长寿灾难：利用长寿指数来减轻个人、机构和系统的长寿风险

IF 2.2 2区经济学

Insurance Mathematics & Economics Pub Date : 2025-11-01 Epub Date: 2025-08-19 DOI: 10.1016/j.insmatheco.2025.103153

Guy Coughlan

{"title":"Avoiding a longevity catastrophe: Harnessing longevity indices to mitigate individual, institutional and systemic longevity risks","authors":"Guy Coughlan","doi":"10.1016/j.insmatheco.2025.103153","DOIUrl":"10.1016/j.insmatheco.2025.103153","url":null,"abstract":"<div><div>This paper considers the financial implications of an extreme increase in life expectancy for: (i) individuals with defined contribution pension plans and other forms of retirement savings; (ii) institutions such as defined benefit pension plans, insurance companies and reinsurers; and (iii) the financial system and economy as a whole. An extreme longevity scenario, as the IMF first acknowledged in 2006, is a long-term systemic risk that could impair the operation of the financial system with severe ramifications for the global economy. It also poses a significant risk to individuals who might live beyond the time that their retirement savings can support them. This paper explores one under-utilised way to mitigate these risks, viz., longevity index hedges, which can transfer longevity risk simply, rapidly and transparently away from where it is concentrated to a much broader set of organisations with appropriate levels of risk capital. For the market in these index hedges to grow requires a shared understanding of the hedges and their risk reduction potential by the insurance industry and regulators.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"125 ","pages":"Article 103153"},"PeriodicalIF":2.2,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144906892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A note on bequest preferences in utility maximisation for modern tontines 关于现代时代效用最大化中的遗赠偏好的注释

IF 2.2 2区经济学

Insurance Mathematics & Economics Pub Date : 2025-11-01 Epub Date: 2025-08-25 DOI: 10.1016/j.insmatheco.2025.103151

Thomas Bernhardt

引用次数: 0

Robust parameter estimation for the Lee-Carter family: A probabilistic principal component approach 李-卡特族的鲁棒参数估计：一种概率主成分方法

IF 2.2 2区经济学

Insurance Mathematics & Economics Pub Date : 2025-11-01 Epub Date: 2025-10-01 DOI: 10.1016/j.insmatheco.2025.103164

Yiping Guo , Johnny Siu-Hang Li

{"title":"Robust parameter estimation for the Lee-Carter family: A probabilistic principal component approach","authors":"Yiping Guo , Johnny Siu-Hang Li","doi":"10.1016/j.insmatheco.2025.103164","DOIUrl":"10.1016/j.insmatheco.2025.103164","url":null,"abstract":"<div><div>Although the impact of outliers on stochastic mortality modelling has been examined, previous studies on this topic focus on how outliers in the estimated time-varying indexes may be detected and/or modelled, with little attention being paid to the adverse effects of outliers on estimation robustness, particularly that pertaining to age-specific parameters. In this paper, we propose a robust estimation method for the Lee-Carter model, through a reformulation of the model into a probabilistic principal component analysis with multivariate <em>t</em>-distributions and an efficient expectation-maximization algorithm for implementation. The proposed method yields significantly more robust parameter estimates, while preserving the fundamental interpretation for the bilinear term in the model as the first principal component and the flexibility of pairing the estimated time-varying parameters with any appropriate time-series process. We also extend the proposed method for use with multi-population generalizations of the Lee-Carter model, allowing for a wider range of applications such as quantification of population basis risk in index-based longevity hedges. Using a combination of real and pseudo datasets, we demonstrate the superiority of the proposed method relative to conventional estimation approaches such as singular value decomposition and maximum likelihood.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"125 ","pages":"Article 103164"},"PeriodicalIF":2.2,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145265697","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Risk measures on Musielak-Orlicz spaces: A state-dependent perspective for insurance Musielak-Orlicz空间的风险度量：保险的状态依赖视角

IF 2.2 2区经济学

Insurance Mathematics & Economics Pub Date : 2025-11-01 Epub Date: 2025-11-07 DOI: 10.1016/j.insmatheco.2025.103174

Francesco Strati

{"title":"Risk measures on Musielak-Orlicz spaces: A state-dependent perspective for insurance","authors":"Francesco Strati","doi":"10.1016/j.insmatheco.2025.103174","DOIUrl":"10.1016/j.insmatheco.2025.103174","url":null,"abstract":"<div><div>This paper introduces a novel framework for risk measures defined on Musielak-Orlicz spaces, incorporating state-dependent Young functions to address the limitations of traditional uniform risk models in capturing heterogeneous tail behaviors. Extending the foundational work of Cheridito and Li [2009] on Orlicz hearts, the study establishes a robust representation theorem for convex monetary risk measures, demonstrating their expression as a maximum over penalized expectations adjusted by state-specific penalty functions. This result accommodates unbounded risks with spatially or temporally varying profiles, a critical enhancement for applications in insurance and finance where heterogeneity is prevalent. The framework subsumes coherent measures as a special case and provides a characterization of optimal probability measures, ensuring computational feasibility. Practical implications are explored through connections to insurance mathematics, including links to star-shaped risk measures, variable annuities via the <em>Q</em>⊙<em>P</em> measure, and a state-dependent generalization of the Haezendonck-Goovaerts risk measure. Additionally, an aggregation technique for portfolio risk across diverse states is proposed, accompanied by illustrative examples such as the Transformed Norm and Entropic Risk Measures. By integrating theoretical rigor with practical relevance, this study offers a versatile tool for risk assessment under complex, state-varying conditions.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"125 ","pages":"Article 103174"},"PeriodicalIF":2.2,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145528230","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An observation-driven state-space count model for experience rating 一种用于经验评级的观察驱动状态空间计数模型

IF 2.2 2区经济学

Insurance Mathematics & Economics Pub Date : 2025-11-01 Epub Date: 2025-08-20 DOI: 10.1016/j.insmatheco.2025.103149

Jae Youn Ahn , Himchan Jeong , Yang Lu , Mario V. Wüthrich

引用次数: 0

Non-parametric estimators of scaled cash flows 规模现金流量的非参数估计

IF 2.2 2区经济学

Insurance Mathematics & Economics Pub Date : 2025-11-01 Epub Date: 2025-08-25 DOI: 10.1016/j.insmatheco.2025.103152

Theis Bathke , Christian Furrer

引用次数: 0

Additive tree latent variable models with applications to insurance loss prediction 加性树隐变量模型及其在保险损失预测中的应用

IF 2.2 2区经济学

Insurance Mathematics & Economics Pub Date : 2025-11-01 Epub Date: 2025-10-25 DOI: 10.1016/j.insmatheco.2025.103168

Zhihao Wang , Yanlin Shi , Guangyuan Gao

{"title":"Additive tree latent variable models with applications to insurance loss prediction","authors":"Zhihao Wang , Yanlin Shi , Guangyuan Gao","doi":"10.1016/j.insmatheco.2025.103168","DOIUrl":"10.1016/j.insmatheco.2025.103168","url":null,"abstract":"<div><div>We consider a specific class of regression models with discrete latent variables, which are commonly used in actuarial science and other fields. When fitting these parametric regression models, regression functions are estimated for both the observed response variable and the latent variable, respectively. Feature engineering, variable selection and model selection become challenging due to the involvement of multiple regression functions and latent variable. To address these challenges, we propose additive tree latent variable models. To calibrate these models, we introduce an iteratively re-weighted gradient boosting (IRGB) algorithm that combines the EM algorithm with the gradient boosting. In each iteration, the IRGB algorithm trains only one weak learner in a stagewise manner. Theoretical analysis demonstrates the monotonic behavior of the likelihood in the IRGB algorithm. We further illustrate the advantages of the proposed nonparametric methods through an empirical example of motor insurance claim counts and a case study on French motor third-party liability insurance pure premiums.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"125 ","pages":"Article 103168"},"PeriodicalIF":2.2,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145424574","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0