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Ordering higher risks in Yaari's dual theory 在Yaari的二元理论中，排序风险更高
IF 2.2 2区 经济学
Insurance Mathematics & Economics Pub Date : 2025-09-01 DOI: 10.1016/j.insmatheco.2025.103150
A. Castaño-Martínez, G. Pigueiras, C.D. Ramos, M.A. Sordo
{"title":"Ordering higher risks in Yaari's dual theory","authors":"A. Castaño-Martínez,&nbsp;G. Pigueiras,&nbsp;C.D. Ramos,&nbsp;M.A. Sordo","doi":"10.1016/j.insmatheco.2025.103150","DOIUrl":"10.1016/j.insmatheco.2025.103150","url":null,"abstract":"<div><div>In <span><span>Yaari</span></span>'s (<span><span>1987</span></span>) dual theory of choice under risk, risk preferences are based on a functional that incorporates a subjective distortion function. In the context of <span><span>Wang</span></span>'s (<span><span>1996</span></span>) premium principle, <span><span>Wang and Young (1998)</span></span> introduce a sequence of partial ordering classes for risk distributions which characterize the preferences of groups of risk-averse agents making decisions based on this functional. Under this framework, if one distribution is perceived as less risky than another, its mean is smaller than or equal to the latter's, which can make certain risk distributions non-comparable. In this paper, we investigate a sequence of partial orders for risk distributions, grounded in comparisons of successive integrals of TVaR curves, that capture the preferences of agents primarily concerned with large risks that exceed their expected values. The normative properties of these orders are explored through the <em>n</em>th-degree coefficient of dual risk aversion, which serves as the dual analog of the index of absolute risk aversion introduced by <span><span>Caballé and Pomansky (1996)</span></span> within the expected utility model.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"125 ","pages":"Article 103150"},"PeriodicalIF":2.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144931738","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 : 2025-08-25 DOI: 10.1016/j.insmatheco.2025.103151
Thomas Bernhardt
{"title":"A note on bequest preferences in utility maximisation for modern tontines","authors":"Thomas Bernhardt","doi":"10.1016/j.insmatheco.2025.103151","DOIUrl":"10.1016/j.insmatheco.2025.103151","url":null,"abstract":"<div><div>In this short note, we address two issues in the literature about modern tontines with bequest and utility maximisation: how to verify optimal controls and the decreasing allocation of funds in the tontine. We want to raise awareness about the dual approach to solve optimal control problems when working with power utilities in the actuarial community. Additionally, we highlight that bequest preferences should be time-dependent or otherwise yield unrealistic investment strategies. We base our attempt at modelling bequest preferences on rules like 100% payback upon death at the start that vanishes over time. Our modelling shows that the resulting investment strategy almost linearly adjusts the allocation in the tontine from 0% to 100% over time.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"125 ","pages":"Article 103151"},"PeriodicalIF":2.2,"publicationDate":"2025-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144906891","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
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 : 2025-08-25 DOI: 10.1016/j.insmatheco.2025.103152
Theis Bathke , Christian Furrer
{"title":"Non-parametric estimators of scaled cash flows","authors":"Theis Bathke ,&nbsp;Christian Furrer","doi":"10.1016/j.insmatheco.2025.103152","DOIUrl":"10.1016/j.insmatheco.2025.103152","url":null,"abstract":"<div><div>In multi-state life insurance, incidental policyholder behavior gives rise to expected cash flows that are not easily targeted by classic non-parametric estimators if data is subject to sampling effects. We introduce a scaled version of the classic Aalen–Johansen estimator that overcomes this challenge. Strong uniform consistency and asymptotic normality are established under entirely random right-censoring, subject to lax moment conditions on the multivariate counting process. In a simulation study, the estimator outperforms earlier proposals from the literature. Finally, we showcase the potential of the presented method to other areas of actuarial science.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"125 ","pages":"Article 103152"},"PeriodicalIF":2.2,"publicationDate":"2025-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145120297","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 : 2025-08-20 DOI: 10.1016/j.insmatheco.2025.103149
Jae Youn Ahn , Himchan Jeong , Yang Lu , Mario V. Wüthrich
{"title":"An observation-driven state-space count model for experience rating","authors":"Jae Youn Ahn ,&nbsp;Himchan Jeong ,&nbsp;Yang Lu ,&nbsp;Mario V. Wüthrich","doi":"10.1016/j.insmatheco.2025.103149","DOIUrl":"10.1016/j.insmatheco.2025.103149","url":null,"abstract":"<div><div>State-space models are widely used in applications, e.g., in economics, finance and actuarial science. In the domain of count data, one such example is the model proposed by <span><span>Harvey and Fernandes (1989)</span></span>. Unlike many of its parameter-driven alternatives, this model is observation-driven, and it leads to a closed-form expression for the predictive density. This predictive density takes into account past observations by assigning a seniority weighting to them. This feature makes this model very appealing for general insurance ratemaking. However, the model of <span><span>Harvey and Fernandes (1989)</span></span> has the property that the variance diverges in the long-run, which might be an undesirable model feature. In this paper, we extend the model of <span><span>Harvey and Fernandes (1989)</span></span> by allowing for flexible variance specifications including non-explosive ones, while keeping the model fully tractable.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"125 ","pages":"Article 103149"},"PeriodicalIF":2.2,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144890825","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 : 2025-08-19 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":"2025-08-19","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
Optimal life insurance and annuity decisions under money illusion 金钱错觉下的最优寿险和年金决策
IF 2.2 2区 经济学
Insurance Mathematics & Economics Pub Date : 2025-08-13 DOI: 10.1016/j.insmatheco.2025.103141
Wenyuan Li , Pengyu Wei
{"title":"Optimal life insurance and annuity decisions under money illusion","authors":"Wenyuan Li ,&nbsp;Pengyu Wei","doi":"10.1016/j.insmatheco.2025.103141","DOIUrl":"10.1016/j.insmatheco.2025.103141","url":null,"abstract":"<div><div>This paper investigates the optimal consumption, investment, and life insurance/annuity decisions for a family in an inflationary economy under money illusion. The family can invest in a financial market that consists of nominal bonds, inflation-linked bonds, and a stock index. The breadwinner can also purchase life insurance or annuities that are available continuously. The family's objective is to maximize the expected utility of a mixture of nominal and real consumption, as they partially overlook inflation and tend to think in terms of nominal rather than real monetary values. We formulate this life-cycle problem as a random horizon utility maximization problem and derive the optimal strategy. We calibrate our model to the U.S. data and demonstrate that money illusion increases life insurance demand for young adults and reduces annuity demand for retirees. Our findings indicate that the money illusion contributes to the annuity puzzle and highlight the role of financial literacy in an inflationary environment.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"125 ","pages":"Article 103141"},"PeriodicalIF":2.2,"publicationDate":"2025-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144863374","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
Uniform asymptotic estimates for ruin probabilities of a multidimensional risk model with càdlàg returns and multivariate heavy tailed claims 具有càdlàg收益和多变量重尾索赔的多维风险模型破产概率的一致渐近估计
IF 2.2 2区 经济学
Insurance Mathematics & Economics Pub Date : 2025-08-13 DOI: 10.1016/j.insmatheco.2025.103148
Dimitrios G. Konstantinides, Charalampos D. Passalidis
{"title":"Uniform asymptotic estimates for ruin probabilities of a multidimensional risk model with càdlàg returns and multivariate heavy tailed claims","authors":"Dimitrios G. Konstantinides,&nbsp;Charalampos D. Passalidis","doi":"10.1016/j.insmatheco.2025.103148","DOIUrl":"10.1016/j.insmatheco.2025.103148","url":null,"abstract":"<div><div>We study a multidimensional renewal risk model, with common counting process and càdlàg returns. Considering that the claim vectors have common distribution from some multivariate distribution class with heavy tail, are mutually weakly dependent, and each one has arbitrarily dependent components, we obtain uniformly asymptotic estimations for the probability of entrance of discounted aggregate claims into a some rare sets, over a finite time horizon. Direct consequence of the claim behavior is the estimation of the ruin probability of the model in some ruin sets. Further, restricting the distribution class of the claim vectors in the multivariate regular variation, the estimations still hold uniformly over the whole time horizon.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"125 ","pages":"Article 103148"},"PeriodicalIF":2.2,"publicationDate":"2025-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144903671","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
Equilibrium investment strategies for a defined contribution pension plan with random risk aversion 随机风险规避下固定缴款养老金计划的均衡投资策略
IF 2.2 2区 经济学
Insurance Mathematics & Economics Pub Date : 2025-08-07 DOI: 10.1016/j.insmatheco.2025.103140
Ling Wang , Bowen Jia
{"title":"Equilibrium investment strategies for a defined contribution pension plan with random risk aversion","authors":"Ling Wang ,&nbsp;Bowen Jia","doi":"10.1016/j.insmatheco.2025.103140","DOIUrl":"10.1016/j.insmatheco.2025.103140","url":null,"abstract":"<div><div>This paper investigates equilibrium investment strategies for a defined contribution (DC) pension plan member who faces random risk preferences. Downside protection for the pension plan and stochastic inflation are considered. The pension plan member is allowed to invest in cash, in an inflation-index bond, and in a stock in the financial market. Besides financial market risks, the wealth of the pension account is influenced by the stochastic contribution of the pension plan member. We adopt the framework proposed in <span><span>Desmettre and Steffensen (2023)</span></span> to tackle the time inconsistency issues arising from the incorporation of random risk aversion. The problem is first transformed into a self-financing investment problem and the semi-closed form of the equilibrium investment strategies is derived under the power utility function up to the solution of an ordinary differential equation (ODE) system. Our numerical analysis reveals that using expected risk aversion rather than random risk aversion results in a substantial welfare loss for the pension plan member.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"125 ","pages":"Article 103140"},"PeriodicalIF":2.2,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144810533","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
Portfolio selection and risk sharing via risk budgeting 通过风险预算进行投资组合选择和风险分担
IF 2.2 2区 经济学
Insurance Mathematics & Economics Pub Date : 2025-07-31 DOI: 10.1016/j.insmatheco.2025.103139
Vali Asimit , Wing Fung Chong , Radu Tunaru , Feng Zhou
{"title":"Portfolio selection and risk sharing via risk budgeting","authors":"Vali Asimit ,&nbsp;Wing Fung Chong ,&nbsp;Radu Tunaru ,&nbsp;Feng Zhou","doi":"10.1016/j.insmatheco.2025.103139","DOIUrl":"10.1016/j.insmatheco.2025.103139","url":null,"abstract":"<div><div>Risk budgeting is an effective risk management tool that a decision-maker uses to create a risk portfolio with a pre-determined risk profile. This paper provides a rich discussion about the theory and practice on how to construct risk budgeting portfolios in a variety of settings. We revisit the usual portfolio selection setting with and without clustered risk budgeting targets, and we then provide an approach on how to extend the usual setting to situations in which a non-hedgeable risk is present or fixed sub-portfolios are aimed by the decision-maker. Another study of this paper is how to include risk budgeting targets in risk sharing, which has not been discussed in the literature. Implementation issues are also discussed, and some bespoke algorithms are provided to identify such risk budgeting portfolios. Numerical experiments are performed for real-life financial data, and we explain the risk mitigation effect of our proposed portfolio. Specifically, financial risk budgeting portfolios with social responsibility targets are constructed.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"125 ","pages":"Article 103139"},"PeriodicalIF":2.2,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144781829","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
Co-opetition in reinsurance markets: When Pareto meets Stackelberg and Nash 再保险市场的合作竞争：当帕累托与Stackelberg和Nash相遇时
IF 2.2 2区 经济学
Insurance Mathematics & Economics Pub Date : 2025-07-31 DOI: 10.1016/j.insmatheco.2025.103133
Jingyi Cao , Dongchen Li , Virginia R. Young , Bin Zou
{"title":"Co-opetition in reinsurance markets: When Pareto meets Stackelberg and Nash","authors":"Jingyi Cao ,&nbsp;Dongchen Li ,&nbsp;Virginia R. Young ,&nbsp;Bin Zou","doi":"10.1016/j.insmatheco.2025.103133","DOIUrl":"10.1016/j.insmatheco.2025.103133","url":null,"abstract":"<div><div>We develop and solve a two-layer game to model co-opetition, a strategic combination of competition and cooperation, in a reinsurance market consisting of one primary insurer and two reinsurers, in which all players are equipped with mean-variance preferences and the reinsurance contracts are priced under the variance premium principle. The insurer negotiates reinsurance contracts with the two reinsurers simultaneously, modeled by two Stackelberg games, and the two reinsurers compete for business from the same insurer by setting their own pricing rules, modeled by a non-cooperative Nash game. The combined Stackelberg-Nash game constitutes the first layer of the game model and endogenously determines the risk assumed by each reinsurer. The two reinsurers, then, participate in a cooperative risk-sharing game, forming the second layer of the game model, and seek Pareto-optimal risk-sharing rules. We obtain equilibrium strategies in closed form for both layers. The equilibrium of the Stackelberg-Nash game consists of two proportional reinsurance contracts, with the more risk-averse reinsurer assuming a smaller portion of the insurer's total risk. The Pareto-optimal risk-sharing rules further dictate that the more risk-averse reinsurer transfers a portion of its assumed risk to the less risk-averse reinsurer, at the cost of a positive side payment.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"125 ","pages":"Article 103133"},"PeriodicalIF":2.2,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144781830","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
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