Pub Date : 2025-09-15DOI: 10.1016/j.insmatheco.2025.103157
Martin Bladt, Christoffer Øhlenschlæger
This paper establishes the functional convergence of the Extreme Nelson–Aalen and Extreme Kaplan–Meier estimators, which are designed to capture the heavy-tailed behavior of censored losses. The resulting limit representations can be used to obtain the distributions of functionals with respect to the so-called tail process. For instance, we may recover the convergence of a censored Hill estimator, and we further investigate two goodness-of-fit statistics for the tail of the loss distribution. Using the latter limit theorems, we propose two rules for selecting a suitable number of order statistics, both based on test statistics derived from the functional convergence results. The effectiveness of these selection rules is investigated through simulations and an application to a real dataset comprised of French motor insurance claim sizes.
{"title":"Censored and extreme losses: Functional convergence and applications to tail goodness-of-fit","authors":"Martin Bladt, Christoffer Øhlenschlæger","doi":"10.1016/j.insmatheco.2025.103157","DOIUrl":"10.1016/j.insmatheco.2025.103157","url":null,"abstract":"<div><div>This paper establishes the functional convergence of the Extreme Nelson–Aalen and Extreme Kaplan–Meier estimators, which are designed to capture the heavy-tailed behavior of censored losses. The resulting limit representations can be used to obtain the distributions of functionals with respect to the so-called tail process. For instance, we may recover the convergence of a censored Hill estimator, and we further investigate two goodness-of-fit statistics for the tail of the loss distribution. Using the latter limit theorems, we propose two rules for selecting a suitable number of order statistics, both based on test statistics derived from the functional convergence results. The effectiveness of these selection rules is investigated through simulations and an application to a real dataset comprised of French motor insurance claim sizes.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"125 ","pages":"Article 103157"},"PeriodicalIF":2.2,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145105073","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}
There are two main practical questions in the context of multivariate risk transfers. First, non-intragroup risk transfers raise the question of whether to purchase (re)insurance coverage for the aggregate risk or separately for each risk. Second, intragroup risk transfers are always challenged by regulators on whether there is a commercial purpose in such transactions, and therefore, insurance buyers must commercially validate their decisions. This paper investigates the diversification effect from the buyer's and the seller's perspectives. Our analysis for insurance buyers is based on the ratio between the optimal reinsurance risk margin cost for the total sum of losses and the sum of the individual optimal risk margin costs for each loss type. Because analytical comparison is infeasible, we develop a statistical inference method for this ratio and evaluate its finite sample performance through simulation. The seller's perspective is modeled via a new measure to assess the relative profitability of offering joint versus separate risk transfer contracts. The combined use of these measures enables both buyers and sellers to identify optimal risk transfer decisions that are commercially viable for both parties. Finally, we apply the proposed inference methods to the widely studied Danish fire loss dataset, illustrating the practical implications of our findings that equally apply to an intragroup or non-intragroup risk transfer.
{"title":"Diversification effect in multivariate optimal risk transfer","authors":"Vali Asimit , Tsz Chai Fung , Liang Peng , Fang Yang","doi":"10.1016/j.insmatheco.2025.103156","DOIUrl":"10.1016/j.insmatheco.2025.103156","url":null,"abstract":"<div><div>There are two main practical questions in the context of multivariate risk transfers. First, non-intragroup risk transfers raise the question of whether to purchase (re)insurance coverage for the aggregate risk or separately for each risk. Second, intragroup risk transfers are always challenged by regulators on whether there is a commercial purpose in such transactions, and therefore, insurance buyers must commercially validate their decisions. This paper investigates the diversification effect from the buyer's and the seller's perspectives. Our analysis for insurance buyers is based on the ratio between the optimal reinsurance risk margin cost for the total sum of losses and the sum of the individual optimal risk margin costs for each loss type. Because analytical comparison is infeasible, we develop a statistical inference method for this ratio and evaluate its finite sample performance through simulation. The seller's perspective is modeled via a new measure to assess the relative profitability of offering joint versus separate risk transfer contracts. The combined use of these measures enables both buyers and sellers to identify optimal risk transfer decisions that are commercially viable for both parties. Finally, we apply the proposed inference methods to the widely studied Danish fire loss dataset, illustrating the practical implications of our findings that equally apply to an intragroup or non-intragroup risk transfer.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"125 ","pages":"Article 103156"},"PeriodicalIF":2.2,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145105072","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}
Pub Date : 2025-09-09DOI: 10.1016/j.insmatheco.2025.103155
Laura Iveth Aburto Barrera , Anna Nicolet , Christophe Bagnoud , Joachim Marti , Joël Wagner
Multimorbidity, multiple long-term health conditions co-occurring in one individual, is a complex challenge that affects individuals, healthcare systems, and society. People with multimorbidity have a lower quality of life, higher mortality, and more complex needs and holistic treatments, resulting in higher health insurance and overall healthcare costs. Our study aims to investigate the progression of multimorbidity by identifying the main disease patterns in the adult population. Using an extensive dataset of health insurance claims from one of the largest Swiss health insurance companies, we categorize chronic long-term diseases into different pharmacy cost groups based on a medical classification system to assess the morbidity status of insureds. Developing on a competing risks framework, we use subdistribution hazard models adjusted for age effects to model key multimorbidity patterns, considering the most prevalent chronic diseases in the population. Our analysis focuses on estimating cumulative incidence functions for gender-specific trajectories. By shedding light on these patterns, our study contributes to a deeper understanding of multimorbidity dynamics and potential patient pathways. It provides information for decision-makers, financial planners, and healthcare professionals to enable optimal resource allocation and facilitate prevention and interventions tailored to the needs of various morbidity groups to reduce the disease burden and economic impact.
{"title":"Development of multimorbidity patterns in older adults in Switzerland: A competing risks modeling approach","authors":"Laura Iveth Aburto Barrera , Anna Nicolet , Christophe Bagnoud , Joachim Marti , Joël Wagner","doi":"10.1016/j.insmatheco.2025.103155","DOIUrl":"10.1016/j.insmatheco.2025.103155","url":null,"abstract":"<div><div>Multimorbidity, multiple long-term health conditions co-occurring in one individual, is a complex challenge that affects individuals, healthcare systems, and society. People with multimorbidity have a lower quality of life, higher mortality, and more complex needs and holistic treatments, resulting in higher health insurance and overall healthcare costs. Our study aims to investigate the progression of multimorbidity by identifying the main disease patterns in the adult population. Using an extensive dataset of health insurance claims from one of the largest Swiss health insurance companies, we categorize chronic long-term diseases into different pharmacy cost groups based on a medical classification system to assess the morbidity status of insureds. Developing on a competing risks framework, we use subdistribution hazard models adjusted for age effects to model key multimorbidity patterns, considering the most prevalent chronic diseases in the population. Our analysis focuses on estimating cumulative incidence functions for gender-specific trajectories. By shedding light on these patterns, our study contributes to a deeper understanding of multimorbidity dynamics and potential patient pathways. It provides information for decision-makers, financial planners, and healthcare professionals to enable optimal resource allocation and facilitate prevention and interventions tailored to the needs of various morbidity groups to reduce the disease burden and economic impact.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"125 ","pages":"Article 103155"},"PeriodicalIF":2.2,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145026607","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}
Pub Date : 2025-09-02DOI: 10.1016/j.insmatheco.2025.103154
Mark Kelbert, Harold A. Moreno-Franco
We study the problem of optimal risk policies and dividend strategies for an insurance company operating under the constraint that the timing of shareholder payouts is governed by the arrival times of a Poisson process. Concurrently, risk control is continuously managed through proportional reinsurance. Our analysis confirms the optimality of a periodic-classical barrier strategy for maximizing the expected net present value until the first instance of bankruptcy across all admissible periodic-classical strategies.
{"title":"An optimal periodic dividend and risk control problem for an insurance company","authors":"Mark Kelbert, Harold A. Moreno-Franco","doi":"10.1016/j.insmatheco.2025.103154","DOIUrl":"10.1016/j.insmatheco.2025.103154","url":null,"abstract":"<div><div>We study the problem of optimal risk policies and dividend strategies for an insurance company operating under the constraint that the timing of shareholder payouts is governed by the arrival times of a Poisson process. Concurrently, risk control is continuously managed through proportional reinsurance. Our analysis confirms the optimality of a periodic-classical barrier strategy for maximizing the expected net present value until the first instance of bankruptcy across all admissible periodic-classical strategies.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"125 ","pages":"Article 103154"},"PeriodicalIF":2.2,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144988501","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}
Pub Date : 2025-09-01DOI: 10.1016/j.insmatheco.2025.103150
A. Castaño-Martínez, G. Pigueiras, C.D. Ramos, M.A. Sordo
In Yaari's (1987) dual theory of choice under risk, risk preferences are based on a functional that incorporates a subjective distortion function. In the context of Wang's (1996) premium principle, Wang and Young (1998) 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 nth-degree coefficient of dual risk aversion, which serves as the dual analog of the index of absolute risk aversion introduced by Caballé and Pomansky (1996) within the expected utility model.
{"title":"Ordering higher risks in Yaari's dual theory","authors":"A. Castaño-Martínez, G. Pigueiras, C.D. Ramos, 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}
Pub Date : 2025-08-25DOI: 10.1016/j.insmatheco.2025.103151
Thomas Bernhardt
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.
{"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}
Pub Date : 2025-08-25DOI: 10.1016/j.insmatheco.2025.103152
Theis Bathke , Christian Furrer
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.
{"title":"Non-parametric estimators of scaled cash flows","authors":"Theis Bathke , 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}
Pub Date : 2025-08-20DOI: 10.1016/j.insmatheco.2025.103149
Jae Youn Ahn , Himchan Jeong , Yang Lu , Mario V. Wüthrich
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 Harvey and Fernandes (1989). 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 Harvey and Fernandes (1989) 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 Harvey and Fernandes (1989) by allowing for flexible variance specifications including non-explosive ones, while keeping the model fully tractable.
状态空间模型广泛应用于经济学、金融学和精算科学等领域。在计数数据领域，Harvey和Fernandes（1989）提出的模型就是这样一个例子。与许多参数驱动的替代方案不同，该模型是观测驱动的，它导致预测密度的封闭形式表达式。这种预测密度通过分配资历权重来考虑过去的观察结果。这一特性使得该模型对一般保险费率制定非常有吸引力。然而，Harvey and Fernandes（1989）的模型具有方差在长期内发散的性质，这可能是一个不受欢迎的模型特征。在本文中，我们扩展了Harvey和Fernandes（1989）的模型，允许灵活的方差规范，包括非爆炸性的，同时保持模型完全可处理。
{"title":"An observation-driven state-space count model for experience rating","authors":"Jae Youn Ahn , Himchan Jeong , Yang Lu , 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}
Pub Date : 2025-08-19DOI: 10.1016/j.insmatheco.2025.103153
Guy Coughlan
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.
{"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}
Pub Date : 2025-08-13DOI: 10.1016/j.insmatheco.2025.103141
Wenyuan Li , Pengyu Wei
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.
{"title":"Optimal life insurance and annuity decisions under money illusion","authors":"Wenyuan Li , 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}
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