Pub Date : 2025-12-10DOI: 10.1016/j.insmatheco.2025.103199
Ayse Arik , Allen Klein , Han Li
In this paper, we examine all-cause excess mortality due to the COVID-19 pandemic across 16 countries by age and sex. Utilising the Short-Term Fluctuations data series from the Human Mortality Database, we analyse various measures of excess mortality on weekly and yearly basis from 2020 through the end of 2023. We explore the strengths and limitations of different approaches to offer a comprehensive understanding of the pandemic’s impact on diverse nations. Specifically, we evaluate two methodologies employed by the UK’s Office for National Statistics, considering observed death counts both with and without adjusting for population sizes. We also apply a method based on annual mortality improvements and, as a final approach, implement a statistical model to weekly death counts. Each method defines excess mortality differently, allowing for comparison across alternative perspectives. Our analysis demonstrates largely consistent outcomes across different measures during the first two years of the pandemic, with significant variations in the last two years. These findings contribute to a nuanced understanding of various measures by highlighting their strengths and limitations.
{"title":"On measuring COVID-19 excess mortality: Insights and challenges","authors":"Ayse Arik , Allen Klein , Han Li","doi":"10.1016/j.insmatheco.2025.103199","DOIUrl":"10.1016/j.insmatheco.2025.103199","url":null,"abstract":"<div><div>In this paper, we examine all-cause excess mortality due to the COVID-19 pandemic across 16 countries by age and sex. Utilising the Short-Term Fluctuations data series from the Human Mortality Database, we analyse various measures of excess mortality on weekly and yearly basis from 2020 through the end of 2023. We explore the strengths and limitations of different approaches to offer a comprehensive understanding of the pandemic’s impact on diverse nations. Specifically, we evaluate two methodologies employed by the UK’s Office for National Statistics, considering observed death counts both with and without adjusting for population sizes. We also apply a method based on annual mortality improvements and, as a final approach, implement a statistical model to weekly death counts. Each method defines excess mortality differently, allowing for comparison across alternative perspectives. Our analysis demonstrates largely consistent outcomes across different measures during the first two years of the pandemic, with significant variations in the last two years. These findings contribute to a nuanced understanding of various measures by highlighting their strengths and limitations.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"126 ","pages":"Article 103199"},"PeriodicalIF":2.2,"publicationDate":"2025-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145789687","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 : 2025-12-08DOI: 10.1016/j.insmatheco.2025.103196
Martin Eling , Rustam Ibragimov , Dingchen Ning
Cyber risk poses severe challenges to the society and has become an important theme in risk management and insurance. Yet its statistical features and evolution over time are not sufficiently understood. This paper focuses on two key dimensions of cyber risk-loss severity and tail risk-using three different cyber loss databases. We first focus on the dynamics of loss severity, identifying structural shifts in distributions through a Fréchet-based change point detection method and applying inverse probability weighting to control for selection bias. Our results indicate an increase in the severity of malicious cyber losses since 2018, whereas negligent incidents do not follow the same trend. We then propose methods that combine tail index estimation and change point detection, finding that cyber loss distributions remain heavy-tailed over time, despite heterogeneity across different risk categories. Finally, we present a numerical analysis to illustrate how losses of a simulated cyber insurance portfolio evolve over time, emphasizing the importance of incorporating the dynamic properties of cyber risk into pricing strategies for insurance companies.
{"title":"The changing landscape of cyber risk: An empirical analysis of loss severity and tail dynamics","authors":"Martin Eling , Rustam Ibragimov , Dingchen Ning","doi":"10.1016/j.insmatheco.2025.103196","DOIUrl":"10.1016/j.insmatheco.2025.103196","url":null,"abstract":"<div><div>Cyber risk poses severe challenges to the society and has become an important theme in risk management and insurance. Yet its statistical features and evolution over time are not sufficiently understood. This paper focuses on two key dimensions of cyber risk-loss severity and tail risk-using three different cyber loss databases. We first focus on the dynamics of loss severity, identifying structural shifts in distributions through a Fréchet-based change point detection method and applying inverse probability weighting to control for selection bias. Our results indicate an increase in the severity of malicious cyber losses since 2018, whereas negligent incidents do not follow the same trend. We then propose methods that combine tail index estimation and change point detection, finding that cyber loss distributions remain heavy-tailed over time, despite heterogeneity across different risk categories. Finally, we present a numerical analysis to illustrate how losses of a simulated cyber insurance portfolio evolve over time, emphasizing the importance of incorporating the dynamic properties of cyber risk into pricing strategies for insurance companies.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"126 ","pages":"Article 103196"},"PeriodicalIF":2.2,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145789689","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 : 2025-11-24DOI: 10.1016/j.insmatheco.2025.103193
Lingfeng Lyu , Yang Shen , Michael Sherris , Jonathan Ziveyi
This paper addresses the critical funding challenge of long-term care in ageing societies by examining the role of home equity in supporting retiree welfare and complementing the fiscal. This paper focuses on how home equity can enhance retirement savings, enable bequests, support living arrangements, and mitigate aged care risks in the Australian context. A recursive utility framework incorporating housing-state-dependent consumption and wait times for means-tested aged care services is adopted. Numerical experiments reveal that retirees with low to moderate net wealth are less willing to enter residential aged care facilities (RACFs). This is due to home equity being perceived as a hedge against this risk, either through generating rental income for covering RACF fees (positive hedging) or acting as a fallback resource (negative hedging). Numerical illustrations reveal that when home care packages (HCPs) are underfunded and residential care is adequately resourced, wealthier retirees tend to draw more heavily on their home equity during the aged care phase. This behaviour effectively curtails overall expenditures. Furthermore, providing timely HCP access to individuals with lower wealth helps maintain retirees’ independence and pension eligibility, without significantly increasing overall government spending. These findings demonstrate the reciprocal relationship between retirees’ choices and government spending, underscoring the opportunity to incorporate both demand- and supply-side factors in policy design.
{"title":"Financing aged care with home equity allowing for government age pension and aged care support","authors":"Lingfeng Lyu , Yang Shen , Michael Sherris , Jonathan Ziveyi","doi":"10.1016/j.insmatheco.2025.103193","DOIUrl":"10.1016/j.insmatheco.2025.103193","url":null,"abstract":"<div><div>This paper addresses the critical funding challenge of long-term care in ageing societies by examining the role of home equity in supporting retiree welfare and complementing the fiscal. This paper focuses on how home equity can enhance retirement savings, enable bequests, support living arrangements, and mitigate aged care risks in the Australian context. A recursive utility framework incorporating housing-state-dependent consumption and wait times for means-tested aged care services is adopted. Numerical experiments reveal that retirees with low to moderate net wealth are less willing to enter residential aged care facilities (RACFs). This is due to home equity being perceived as a hedge against this risk, either through generating rental income for covering RACF fees (positive hedging) or acting as a fallback resource (negative hedging). Numerical illustrations reveal that when home care packages (HCPs) are underfunded and residential care is adequately resourced, wealthier retirees tend to draw more heavily on their home equity during the aged care phase. This behaviour effectively curtails overall expenditures. Furthermore, providing timely HCP access to individuals with lower wealth helps maintain retirees’ independence and pension eligibility, without significantly increasing overall government spending. These findings demonstrate the reciprocal relationship between retirees’ choices and government spending, underscoring the opportunity to incorporate both demand- and supply-side factors in policy design.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"126 ","pages":"Article 103193"},"PeriodicalIF":2.2,"publicationDate":"2025-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145684630","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 : 2025-11-24DOI: 10.1016/j.insmatheco.2025.103194
Rebecca Graziani , Andrea Nigri
Though pivotal in longevity studies, multi-outcome modelling is largely neglected in the associated statistical literature. Here, we focus on the case of compositional data, especially relevant in longevity analysis, where overall mortality can be described as the composition of several causes of death. We propose an age–period–cohort model within the Dirichlet framework with a specific interest in its use for modelling longevity with multiple causes of death. We introduce a flexible approach to incorporating the Dirichlet distribution into the age–period–cohort framework. Then, using US cause-specific mortality data, we provide a comprehensive discussion and comparison of alternative modelling approaches.
{"title":"An age–period–cohort model in a Dirichlet framework: A coherent causes of death estimation","authors":"Rebecca Graziani , Andrea Nigri","doi":"10.1016/j.insmatheco.2025.103194","DOIUrl":"10.1016/j.insmatheco.2025.103194","url":null,"abstract":"<div><div>Though pivotal in longevity studies, multi-outcome modelling is largely neglected in the associated statistical literature. Here, we focus on the case of compositional data, especially relevant in longevity analysis, where overall mortality can be described as the composition of several causes of death. We propose an age–period–cohort model within the Dirichlet framework with a specific interest in its use for modelling longevity with multiple causes of death. We introduce a flexible approach to incorporating the Dirichlet distribution into the age–period–cohort framework. Then, using US cause-specific mortality data, we provide a comprehensive discussion and comparison of alternative modelling approaches.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"126 ","pages":"Article 103194"},"PeriodicalIF":2.2,"publicationDate":"2025-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145737414","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 : 2025-11-24DOI: 10.1016/j.insmatheco.2025.103175
David Moriña , Amanda Fernández-Fontelo , Montserrat Guillén
A method based on Bayesian structural time series is proposed to predict healthcare usage trends and to test for changes in the series levels during or after an abnormal year, such as that of the 2020 COVID-19 pandemic. Our method can also serve to calculate correction factors for frequency count data that can be integrated in a preprocessing step before undertaking a cross-sectional statistical analysis, and, in this way, the impact of a shock can be eliminated. Here, adjustments are derived for a large private health insurer in Spain from estimates of average healthcare usage. Median claims rate levels in 2020 were 15 % down on 2019 figures, but rose in 2021 and 2022, when the rate was 11 % and 8 % higher than in 2019, respectively. Once the shock correction is incorporated in the preprocessing step, our approach is shown to outperform traditional time series techniques. Healthcare insurance usage in Spain did not fully go back to normal levels (assuming that pre-pandemic values represent normality) in 2022, with the exception of some patient groups and specific medical services. Our method can be implemented in other areas of risk analysis when frequency counts are exposed to shocks and it allows estimating the difference in claims volume between real figures and those estimated, had the shock not occurred.
{"title":"Back to normal? a method to test and correct a shock impact on healthcare usage frequency data","authors":"David Moriña , Amanda Fernández-Fontelo , Montserrat Guillén","doi":"10.1016/j.insmatheco.2025.103175","DOIUrl":"10.1016/j.insmatheco.2025.103175","url":null,"abstract":"<div><div>A method based on Bayesian structural time series is proposed to predict healthcare usage trends and to test for changes in the series levels during or after an abnormal year, such as that of the 2020 COVID-19 pandemic. Our method can also serve to calculate correction factors for frequency count data that can be integrated in a preprocessing step before undertaking a cross-sectional statistical analysis, and, in this way, the impact of a shock can be eliminated. Here, adjustments are derived for a large private health insurer in Spain from estimates of average healthcare usage. Median claims rate levels in 2020 were 15 % down on 2019 figures, but rose in 2021 and 2022, when the rate was 11 % and 8 % higher than in 2019, respectively. Once the shock correction is incorporated in the preprocessing step, our approach is shown to outperform traditional time series techniques. Healthcare insurance usage in Spain did not fully go back to normal levels (assuming that pre-pandemic values represent normality) in 2022, with the exception of some patient groups and specific medical services. Our method can be implemented in other areas of risk analysis when frequency counts are exposed to shocks and it allows estimating the difference in claims volume between real figures and those estimated, had the shock not occurred.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"126 ","pages":"Article 103175"},"PeriodicalIF":2.2,"publicationDate":"2025-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145618439","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 : 2025-11-21DOI: 10.1016/j.insmatheco.2025.103191
Jinggong Zhang , Xiaobai Zhu , Wei Wei
In this study, we investigate the optimal annuity divisor for a Notional Defined Contribution (NDC) pension scheme. Our analysis reveals that both the constant and actuarially fair annuity divisors, commonly used in practice, disproportionately benefit high-income individuals, resulting in an unintended wealth transfer from low-income to high-income groups. To address this issue, we employ an optimization framework based on a weighted social welfare function and derive the optimal annuity divisor using optimal control techniques. We present the explicit solution when the income distribution follows either Pareto or Pareto-lognormal and when the S-Gini function is adopted in prioritizing different income classes. Our findings suggest that excluding the low-income class from the NDC plan, as practiced in China, renders the NDC plan unnecessary unless the society is nearly inequality-neutral. By calibrating our model with Chinese data, we propose a progressive annuity divisor formula that adjusts for income inequality and mortality differentials, demonstrating its potential to enhance social welfare and achieve a more equitable pension system.
{"title":"Welfare-enhancing annuity divisor for notional defined contribution design","authors":"Jinggong Zhang , Xiaobai Zhu , Wei Wei","doi":"10.1016/j.insmatheco.2025.103191","DOIUrl":"10.1016/j.insmatheco.2025.103191","url":null,"abstract":"<div><div>In this study, we investigate the optimal annuity divisor for a Notional Defined Contribution (NDC) pension scheme. Our analysis reveals that both the constant and actuarially fair annuity divisors, commonly used in practice, disproportionately benefit high-income individuals, resulting in an unintended wealth transfer from low-income to high-income groups. To address this issue, we employ an optimization framework based on a weighted social welfare function and derive the optimal annuity divisor using optimal control techniques. We present the explicit solution when the income distribution follows either Pareto or Pareto-lognormal and when the S-Gini function is adopted in prioritizing different income classes. Our findings suggest that excluding the low-income class from the NDC plan, as practiced in China, renders the NDC plan unnecessary unless the society is nearly inequality-neutral. By calibrating our model with Chinese data, we propose a progressive annuity divisor formula that adjusts for income inequality and mortality differentials, demonstrating its potential to enhance social welfare and achieve a more equitable pension system.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"126 ","pages":"Article 103191"},"PeriodicalIF":2.2,"publicationDate":"2025-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145684631","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 : 2025-11-19DOI: 10.1016/j.insmatheco.2025.103181
Xiaobai Zhu , Kenneth Q. Zhou , Zijia Wang
Mortality modeling plays a central role in actuarial science, with applications ranging from life insurance valuation to optimal lifetime financial planning. Traditional approaches, such as mortality laws and factor-based models, often fall short in capturing the complexity and heterogeneity of mortality dynamics. This paper introduces a novel modeling framework based on the concept of vitality and its stochastic evolution over the life course. The framework consists of four components that account for initial health conditions, natural aging trends, stochastic fluctuations, and sudden accidental events. We explore how modeling mortality through vitality can replicate a wide class of existing mortality models and capture diverse features such as mortality plateaus and longevity trends. Through multiple applications, including optimal consumption planning and disability modeling, we show that the vitality-based framework is capable of providing tractable solutions and intuitive insights to a broad range of mortality-related problems. A numerical illustration using real-world mortality data further demonstrates the framework’s estimation procedure and modeling outcomes.
{"title":"Mortality modeling via vitality: Model constructions and actuarial applications","authors":"Xiaobai Zhu , Kenneth Q. Zhou , Zijia Wang","doi":"10.1016/j.insmatheco.2025.103181","DOIUrl":"10.1016/j.insmatheco.2025.103181","url":null,"abstract":"<div><div>Mortality modeling plays a central role in actuarial science, with applications ranging from life insurance valuation to optimal lifetime financial planning. Traditional approaches, such as mortality laws and factor-based models, often fall short in capturing the complexity and heterogeneity of mortality dynamics. This paper introduces a novel modeling framework based on the concept of vitality and its stochastic evolution over the life course. The framework consists of four components that account for initial health conditions, natural aging trends, stochastic fluctuations, and sudden accidental events. We explore how modeling mortality through vitality can replicate a wide class of existing mortality models and capture diverse features such as mortality plateaus and longevity trends. Through multiple applications, including optimal consumption planning and disability modeling, we show that the vitality-based framework is capable of providing tractable solutions and intuitive insights to a broad range of mortality-related problems. A numerical illustration using real-world mortality data further demonstrates the framework’s estimation procedure and modeling outcomes.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"126 ","pages":"Article 103181"},"PeriodicalIF":2.2,"publicationDate":"2025-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145618372","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 : 2025-11-16DOI: 10.1016/j.insmatheco.2025.103178
J. Chudziak, S. Wójcik
We introduce and investigate the zero utility principle in the Cumulative Prospect Theory under uncertainty. We prove the existence of the principle and characterize its important properties (comparability, equality, positive homogeneity, comonotonic additivity, and subadditivity). Moreover, we show that the zero utility principle under uncertainty can be uniquely extended from the family of binary risks onto the family of all risks.
{"title":"Zero utility principle under uncertainty","authors":"J. Chudziak, S. Wójcik","doi":"10.1016/j.insmatheco.2025.103178","DOIUrl":"10.1016/j.insmatheco.2025.103178","url":null,"abstract":"<div><div>We introduce and investigate the zero utility principle in the Cumulative Prospect Theory under uncertainty. We prove the existence of the principle and characterize its important properties (comparability, equality, positive homogeneity, comonotonic additivity, and subadditivity). Moreover, we show that the zero utility principle under uncertainty can be uniquely extended from the family of binary risks onto the family of all risks.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"126 ","pages":"Article 103178"},"PeriodicalIF":2.2,"publicationDate":"2025-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145618373","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 : 2025-11-15DOI: 10.1016/j.insmatheco.2025.103182
Harold A. Moreno-Franco , José-Luis Pérez
We study the optimal bailout dividend problem with transaction costs for an insurance company, where shareholder payouts are made at the arrival times of an independent Poisson process. In this scenario, the underlying risk model follows a spectrally negative Lévy process. Our analysis confirms the optimality of a periodic (b1, b2)-barrier policy with classical reflection at zero. This strategy involves reducing the surplus to b1 when it exceeds b2 at the Poisson arrival times and pushes the surplus to zero whenever it becomes negative.
{"title":"On the bailout dividend problem with periodic dividend payments and fixed transaction costs","authors":"Harold A. Moreno-Franco , José-Luis Pérez","doi":"10.1016/j.insmatheco.2025.103182","DOIUrl":"10.1016/j.insmatheco.2025.103182","url":null,"abstract":"<div><div>We study the optimal bailout dividend problem with transaction costs for an insurance company, where shareholder payouts are made at the arrival times of an independent Poisson process. In this scenario, the underlying risk model follows a spectrally negative Lévy process. Our analysis confirms the optimality of a periodic (<em>b</em><sub>1</sub>, <em>b</em><sub>2</sub>)-barrier policy with classical reflection at zero. This strategy involves reducing the surplus to <em>b</em><sub>1</sub> when it exceeds <em>b</em><sub>2</sub> at the Poisson arrival times and pushes the surplus to zero whenever it becomes negative.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"126 ","pages":"Article 103182"},"PeriodicalIF":2.2,"publicationDate":"2025-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145618371","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 : 2025-11-15DOI: 10.1016/j.insmatheco.2025.103177
Huifang Huang , Zhuo Jin , Pengbo Li , Fuke Wu , Hailiang Yang
This paper investigates a portfolio optimization problem for an investor on asset allocation among risk-free asset, risky asset, and surrender variable annuity contracts featuring guaranteed minimum death benefit and guaranteed minimum maturity benefit subject to mortality and surrender risk. The investor’s objective is to maximize the expected utility of the bequest at death or the expected utility of assets at contract maturity. On each trading day before the investor’s death, the investor can adjust the allocation between risk-free and risky assets, invest in a new surrender variable annuity product. Especially, the policyholder may exercise partial or full surrender options for any existing variable annuity contract. This dynamic adjustment creates a high-dimensional state and action space, making traditional optimization methods inadequate. To address this, we utilize the Lee-Carter model to analyze Australian demographic data, predict mortality risk, simulate surrender risk based on market changes, and estimate the fair pricing of variable annuity contracts in the portfolio. Subsequently, we introduce a deep reinforcement learning algorithm within a simulated trading environment that independently models the dynamic behavior of various assets and underlying indices. The algorithm utilizes neural networks to analyze high-dimensional state variables and leverages the interactive capabilities of the agent to flexibly adapt to asset fluctuations, dynamically optimizing investment allocation. Additionally, we prove the global convergence of the algorithm under standard assumptions and validate its effectiveness in managing the complexities of high-dimensional portfolios, particularly in capturing mortality, surrender, and financial risks. Numerical experiments further demonstrate the stability and robustness of the algorithm, showcasing its advantages in complex insurance and financial scenarios.
{"title":"Optimizing portfolios with surrender variable annuities: A deep reinforcement learning approach","authors":"Huifang Huang , Zhuo Jin , Pengbo Li , Fuke Wu , Hailiang Yang","doi":"10.1016/j.insmatheco.2025.103177","DOIUrl":"10.1016/j.insmatheco.2025.103177","url":null,"abstract":"<div><div>This paper investigates a portfolio optimization problem for an investor on asset allocation among risk-free asset, risky asset, and surrender variable annuity contracts featuring guaranteed minimum death benefit and guaranteed minimum maturity benefit subject to mortality and surrender risk. The investor’s objective is to maximize the expected utility of the bequest at death or the expected utility of assets at contract maturity. On each trading day before the investor’s death, the investor can adjust the allocation between risk-free and risky assets, invest in a new surrender variable annuity product. Especially, the policyholder may exercise partial or full surrender options for any existing variable annuity contract. This dynamic adjustment creates a high-dimensional state and action space, making traditional optimization methods inadequate. To address this, we utilize the Lee-Carter model to analyze Australian demographic data, predict mortality risk, simulate surrender risk based on market changes, and estimate the fair pricing of variable annuity contracts in the portfolio. Subsequently, we introduce a deep reinforcement learning algorithm within a simulated trading environment that independently models the dynamic behavior of various assets and underlying indices. The algorithm utilizes neural networks to analyze high-dimensional state variables and leverages the interactive capabilities of the agent to flexibly adapt to asset fluctuations, dynamically optimizing investment allocation. Additionally, we prove the global convergence of the algorithm under standard assumptions and validate its effectiveness in managing the complexities of high-dimensional portfolios, particularly in capturing mortality, surrender, and financial risks. Numerical experiments further demonstrate the stability and robustness of the algorithm, showcasing its advantages in complex insurance and financial scenarios.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"126 ","pages":"Article 103177"},"PeriodicalIF":2.2,"publicationDate":"2025-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145618374","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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