Insurance Mathematics & Economics最新文献_第7页

Bowley-optimal convex-loaded premium principles bowley -最优凸负载溢价原理

IF 1.9 2区经济学

Insurance Mathematics & Economics Pub Date : 2025-01-27 DOI: 10.1016/j.insmatheco.2025.01.006

Mario Ghossoub, Bin Li, Benxuan Shi

{"title":"Bowley-optimal convex-loaded premium principles","authors":"Mario Ghossoub, Bin Li, Benxuan Shi","doi":"10.1016/j.insmatheco.2025.01.006","DOIUrl":"10.1016/j.insmatheco.2025.01.006","url":null,"abstract":"<div><div>This paper contributes to the literature on Stackelberg equilibria (Bowley optima) in monopolistic centralized sequential-move insurance markets in several ways. We consider a class of premium principles defined as expectations of increasing and convex functions of the indemnities. We refer to these as <em>convex-loaded premium principles</em>. Our analysis restricts the <em>ex ante</em> admissible class of indemnity functions to the two most popular and practically relevant classes: the deductible indemnities and the proportional indemnities, both of which satisfy the so-called no-sabotage condition. We study Bowley optimality of premium principles within the class of convex-loaded premium principles, when the indemnity functions are either of the deductible type or of the coinsurance type. Assuming that the policyholder is a risk-averse expected-utility maximizer, while the insurer is a risk-neutral expected-profit maximizer, we find that the <em>expected-value premium principle</em> is Bowley optimal for proportional indemnities, while the <em>stop-loss premium principle</em> is Bowley optimal for deductible indemnities under a mild condition. Methodologically, we introduce a novel <em>dual approach</em> to characterize Bowley optima.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"121 ","pages":"Pages 157-180"},"PeriodicalIF":1.9,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143144366","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Axiomatic risk sharing and capital allocation 公理化的风险分担和资本配置

IF 1.9 2区经济学

Insurance Mathematics & Economics Pub Date : 2025-01-23 DOI: 10.1016/j.insmatheco.2025.01.005

Tim J. Boonen , Maurice Koster

引用次数: 0

Innovative combo product design embedding variable annuity and long-term care insurance contracts 创新组合产品设计，嵌入可变年金和长期护理保险合同

IF 1.9 2区经济学

Insurance Mathematics & Economics Pub Date : 2025-01-17 DOI: 10.1016/j.insmatheco.2025.01.004

Yang Shen, Michael Sherris, Yawei Wang, Jonathan Ziveyi

{"title":"Innovative combo product design embedding variable annuity and long-term care insurance contracts","authors":"Yang Shen, Michael Sherris, Yawei Wang, Jonathan Ziveyi","doi":"10.1016/j.insmatheco.2025.01.004","DOIUrl":"10.1016/j.insmatheco.2025.01.004","url":null,"abstract":"<div><div>This paper presents a novel combo insurance product design consisting of a variable annuity contract embedded with guaranteed minimum income benefit and long-term care insurance riders. This combo product provides enhanced benefits when the policyholder is functionally disabled. The policyholder and provider's joint optimal decision is formulated as a Nash equilibrium of a two-stage non-zero sum game. The provider aims to offer the optimal insurance product that minimises solvency capital requirement (SCR) per unit premium under Solvency II in the first stage. The policyholder aims to purchase the optimal amount of insurance that maximises lifetime utility in the second stage. The Hamiltonian Monte Carlo (HMC) simulation technique is utilised for numerically valuing the combo product whose underlying fund is proportionally invested in multiple asset classes. Due to the natural hedging effect between longevity and disability risks and the option payoff structure, the combo product is a win-win solution for providers and policyholders compared with an LTC annuity or an LTC insurance and a variable annuity with guaranteed minimum income benefit. From the policyholder's perspective, we quantify the extent to which the combo product costs less premium and the policyholder gains more lifetime utility. From the provider's perspective, we show that the combo product requires less SCR per initial unit premium. Product features including the elimination period and the maximum benefit period, are examined, and we show that they can effectively reduce the product premium. We perform fee sensitivity tests on model parameters to reveal insights regarding risk management from the provider's perspective.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"121 ","pages":"Pages 79-99"},"PeriodicalIF":1.9,"publicationDate":"2025-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143144370","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Designing and valuing new equity-linked insurance products for couples 为夫妻设计和评估新的股票挂钩保险产品

IF 1.9 2区经济学

Insurance Mathematics & Economics Pub Date : 2025-01-14 DOI: 10.1016/j.insmatheco.2025.01.003

Kelvin Tang, Eric C.K. Cheung, Jae-Kyung Woo

{"title":"Designing and valuing new equity-linked insurance products for couples","authors":"Kelvin Tang, Eric C.K. Cheung, Jae-Kyung Woo","doi":"10.1016/j.insmatheco.2025.01.003","DOIUrl":"10.1016/j.insmatheco.2025.01.003","url":null,"abstract":"<div><div>Equity-linked insurance products have gained popularity in recent years as retirement products with investment benefits. However, the design and pricing of these products for couples have been overlooked despite empirical evidence showing positive dependence in a couple's lifetimes. In this paper, we propose some suitable products for couples where the benefits depend on the death times of both lives, and perform valuation using the discounted density approach while allowing the lifetimes to be dependent. By modeling the lifetimes with a bivariate mixed Erlang distribution, closed-form pricing formulas are developed for a variety of benefit types such as income protection for the last survivor (possibly with roll-up guarantee or benefit indexation) and dynamic fund protection/withdrawals. Fitting of bivariate lifetime data is also discussed in relation to bivariate Laguerre series. The impact of dependence on the prices of these products is demonstrated via numerical examples. In particular, our results suggest that incorrectly assuming independence between lifetimes would overprice these products compared to the actual situation of positive dependence, thereby making the products less attractive.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"121 ","pages":"Pages 111-132"},"PeriodicalIF":1.9,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143144372","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Optimal investment and benefit strategies for a target benefit pension plan where the risky assets are jump diffusion processes 风险资产跳跃扩散过程下目标收益养老金计划的最优投资与收益策略

IF 1.9 2区经济学

Insurance Mathematics & Economics Pub Date : 2025-01-09 DOI: 10.1016/j.insmatheco.2025.01.002

Ricardo Josa-Fombellida, Paula López-Casado

引用次数: 0

Estimating the impact of COVID-19 on mortality using granular data 利用颗粒数据估计COVID-19对死亡率的影响

IF 1.9 2区经济学

Insurance Mathematics & Economics Pub Date : 2025-01-09 DOI: 10.1016/j.insmatheco.2025.01.001

Frank van Berkum , Bertrand Melenberg , Michel Vellekoop

{"title":"Estimating the impact of COVID-19 on mortality using granular data","authors":"Frank van Berkum , Bertrand Melenberg , Michel Vellekoop","doi":"10.1016/j.insmatheco.2025.01.001","DOIUrl":"10.1016/j.insmatheco.2025.01.001","url":null,"abstract":"<div><div>We present an extension of the Li and Lee model to quantify mortality in five European countries during the COVID-19 pandemic. The first two layers specify pre-COVID mortality, with the first one modeling the common trend and the second one the country-specific deviation from the common trend. We calibrate this part of the model using annual data from 1970 to 2019 and then add a third layer to capture the country-specific impact of COVID-19 in 2020 and 2021. The calibration of the added layer is based on data with a higher granularity in time, since we analyze weekly instead of annual data. We also investigate whether estimates improve if we increase the granularity over the ages, utilizing data we obtained for single ages instead of the usual aggregated age groups. We complement our analysis by presenting mortality forecasts based on different possible scenarios for the future course of the pandemic and a backtest in which we compare predictions of Dutch mortality improvements from 2021 to 2022 against their realizations. The results from this backtest can be used to update mortality forecasts as new observations become available.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"121 ","pages":"Pages 144-156"},"PeriodicalIF":1.9,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143144368","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Uncertainty in heteroscedastic Bayesian model averaging 异方差贝叶斯模型平均的不确定性

IF 1.9 2区经济学

Insurance Mathematics & Economics Pub Date : 2025-01-03 DOI: 10.1016/j.insmatheco.2024.12.008

Sébastien Jessup , Mélina Mailhot , Mathieu Pigeon

引用次数: 0

Insurance loss modeling with gradient tree-boosted mixture models 梯度树增强混合模型的保险损失建模

IF 1.9 2区经济学

Insurance Mathematics & Economics Pub Date : 2025-01-03 DOI: 10.1016/j.insmatheco.2024.12.007

Yanxi Hou , Jiahong Li , Guangyuan Gao

{"title":"Insurance loss modeling with gradient tree-boosted mixture models","authors":"Yanxi Hou , Jiahong Li , Guangyuan Gao","doi":"10.1016/j.insmatheco.2024.12.007","DOIUrl":"10.1016/j.insmatheco.2024.12.007","url":null,"abstract":"<div><div>In actuarial practice, finite mixture model is one widely applied statistical method to model the insurance loss. Although the Expectation-Maximization (EM) algorithm usually plays an essential tool for the parameter estimation of mixture models, it suffers from other issues which cause unstable predictions. For example, feature engineering and variable selection are two crucial modeling issues that are challenging for mixture models as they involve several component models. Avoiding overfitting is another technical concern of the modeling method for the prediction of future losses. To address those issues, we propose an Expectation-Boosting (EB) algorithm, which implements the gradient boosting decision trees to adaptively increase the likelihood in the second step. Our proposed EB algorithm can estimate both the mixing probabilities and the component parameters non-parametrically and overfitting-sensitively, and further perform automated feature engineering, model fitting, and variable selection simultaneously, which fully explores the predictive power of feature space. Moreover, the proposed algorithm can be combined with parallel computation methods to improve computation efficiency. Finally, we conduct two simulation studies to show the good performance of the proposed algorithm and an empirical analysis of the claim amounts for illustration.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"121 ","pages":"Pages 45-62"},"PeriodicalIF":1.9,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143144746","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

Robust Nash equilibrium for defined contribution pension games with delay under multivariate stochastic covariance models 多元随机协方差模型下具有延迟的固定缴费养老金博弈的鲁棒纳什均衡

IF 1.9 2区经济学

Insurance Mathematics & Economics Pub Date : 2025-01-01 DOI: 10.1016/j.insmatheco.2024.12.002

Huainian Zhu , Yumo Zhang

{"title":"Robust Nash equilibrium for defined contribution pension games with delay under multivariate stochastic covariance models","authors":"Huainian Zhu , Yumo Zhang","doi":"10.1016/j.insmatheco.2024.12.002","DOIUrl":"10.1016/j.insmatheco.2024.12.002","url":null,"abstract":"<div><div>This paper explores a stochastic differential investment game problem with delay among <em>n</em> defined contribution pension fund managers. These managers are concerned with relative performance and model ambiguity and participate in an incomplete financial market comprising a risk-free asset, a market index, and a stock. The market index and stock are described by a class of potentially non-Markovian multivariate stochastic covariance models, with the market prices of risks dependent on a multivariate affine-diffusion factor process. Managers' wealth processes are modeled by stochastic differential delay equations, considering performance-related capital inflow and outflow. Each manager aims to maximize the expected exponential utility of his terminal wealth with delay relative to the averages among his competitors under the worst-case scenario of the alternative measures and seek a robust investment strategy. By employing a backward stochastic differential equation approach to address this robust non-Markovian control problem, we derive, in closed form, the robust Nash equilibrium investment strategies, the probability perturbation processes under the well-defined worst-case scenarios, and the corresponding value functions. The admissibility of robust equilibrium policies is confirmed under specific technical conditions. Finally, we conduct numerical examples to demonstrate the impact of model parameters on robust investment policies and derive economic interpretations from the results.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"120 ","pages":"Pages 236-268"},"PeriodicalIF":1.9,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143133329","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

Valuation of variable annuity portfolios using finite and infinite width neural networks 基于有限和无限宽度神经网络的可变年金组合估值

IF 1.9 2区经济学

Insurance Mathematics & Economics Pub Date : 2025-01-01 DOI: 10.1016/j.insmatheco.2024.12.005

Hong Beng Lim , Nariankadu D. Shyamalkumar , Siyang Tao

{"title":"Valuation of variable annuity portfolios using finite and infinite width neural networks","authors":"Hong Beng Lim , Nariankadu D. Shyamalkumar , Siyang Tao","doi":"10.1016/j.insmatheco.2024.12.005","DOIUrl":"10.1016/j.insmatheco.2024.12.005","url":null,"abstract":"<div><div>Direct valuation of variable annuity guarantees relies on nested simulation, which is computationally costly. One way of feasibly valuing large portfolios relies on a two-step process in which such computationally intensive valuations are only performed on a set of carefully chosen representative policies. These values are then used to train a predictive model to obtain those for the remainder of the portfolio. This is known as the metamodeling framework. We empirically demonstrate that, when used as the predictive model, neural networks outperform state-of-the-art tree-based methods in terms of valuation accuracy. Further, we introduce Neural Tangent Kernel (NTK) regression as an easier-to-use and better-performing alternative to standard neural networks. NTK regression is equivalent to fitting the corresponding neural network with layers of infinite width, sidestepping the need to specify the number of nodes. As a kernel regression method, it is also easier to optimize, simplifying greatly the tuning process. We demonstrate that, in the setting of variable annuity valuation, NTK regression delivers significantly better empirical performance compared to finite-width networks.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"120 ","pages":"Pages 269-284"},"PeriodicalIF":1.9,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143133330","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