Insurance Mathematics & Economics最新文献

Optimal valuation of variable annuity guaranteed lifetime withdrawal benefits with embedded top-up option 最优估值可变年金保证终身提取利益与嵌入式充值选项

IF 1.9 2区经济学

Insurance Mathematics & Economics Pub Date : 2025-05-28 DOI: 10.1016/j.insmatheco.2025.103117

Budhi Arta Surya, Wawan Hafid Syaifudin

{"title":"Optimal valuation of variable annuity guaranteed lifetime withdrawal benefits with embedded top-up option","authors":"Budhi Arta Surya, Wawan Hafid Syaifudin","doi":"10.1016/j.insmatheco.2025.103117","DOIUrl":"10.1016/j.insmatheco.2025.103117","url":null,"abstract":"<div><div>This paper generalizes earlier works on the variable annuity guaranteed lifetime withdrawal benefits (VAGLWB) by introducing an embedded top-up option to the contract. This new feature/rider gives the policyholder an option to top-up the existing contract to a new one with larger withdrawal rate and reduced premium rate subject to paying a cost proportional to the current account value. The option is of American type which can be exercised at anytime prior to the maturity of the contract. In this work, we provide an analytical solution to the risk-neutral valuation for the VAGLWB with embedded top-up option from both policyholder's and insurer's perspective. From the perspective of policyholder, the valuation is formulated in terms of an optimal stopping problem of finding an exercise time of the option and the optimal account level at which the monetary value of the contract is maximized. The optimal solution to the stopping problem is derived under geometric Brownian motion dynamics of the equity price, the underlying investment vehicle of VAGLWB. The optimal value function (early exercise premium of the option) is given explicitly in terms of the confluent hypergeometric function satisfying both continuous and smooth pasting conditions. Furthermore, majorant and (super) harmonic properties of the value function are established to show the optimality of the solution. In the absence of top-up option, i.e., the new contract has equal withdrawal and premium rates with that of the existing contract, the results reduce to that of <span><span>Feng and Jing (2017)</span></span>. Valuation from the insurer's perspective is discussed using equivalence principle between insurer's liabilities and fee incomes to find the fair value of the new premium rate. Finally, numerical examples are provided to exemplify the main results.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"124 ","pages":"Article 103117"},"PeriodicalIF":1.9,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144169222","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

Efficient hedging of life insurance portfolio for loss-averse insurers 规避损失保险公司寿险投资组合的有效套期保值

IF 1.9 2区经济学

Insurance Mathematics & Economics Pub Date : 2025-05-23 DOI: 10.1016/j.insmatheco.2025.103116

Edouard Motte, Donatien Hainaut

{"title":"Efficient hedging of life insurance portfolio for loss-averse insurers","authors":"Edouard Motte, Donatien Hainaut","doi":"10.1016/j.insmatheco.2025.103116","DOIUrl":"10.1016/j.insmatheco.2025.103116","url":null,"abstract":"<div><div>This paper investigates the hedging of equity-linked life insurance portfolio for loss-averse insurers. We consider a general arbitrage-free financial market and an actuarial market composed of <em>n</em>-independent policyholders. As the combined market is incomplete, perfect hedging of any actuarial-financial payoff is not possible. Instead, we study the efficient hedging of <em>n</em>-size equity-linked life insurance portfolio for insurers who are only concerned with their losses. To this end, we consider stochastic control problems (under the real-world measure) in order to determine the optimal hedging strategies that either maximize the probability of successful hedge (called quantile hedging) or minimize the expectation for a class of shortfall loss functions (called shortfall hedging). Based on the super-replication theory and a duality approach, we show that the optimal strategies depend both on actuarial and financial risks. Moreover, these strategies adapt not only to the size of the insurance portfolio but also to the risk-aversion of the insurer. The numerical results show that, for loss-averse insurers, the strategies outperform the mean-variance hedging strategy, demonstrating the relevance of adopting the right strategy according to the insurers' risk aversion and portfolio size.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"123 ","pages":"Article 103116"},"PeriodicalIF":1.9,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144138149","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 insurance contract under mean-variance preference with value at risk constraint 风险约束下均值-方差偏好下的最优保险契约

IF 1.9 2区经济学

Insurance Mathematics & Economics Pub Date : 2025-05-23 DOI: 10.1016/j.insmatheco.2025.103115

Zixuan Li , Hui Meng , Ming Zhou

{"title":"Optimal insurance contract under mean-variance preference with value at risk constraint","authors":"Zixuan Li , Hui Meng , Ming Zhou","doi":"10.1016/j.insmatheco.2025.103115","DOIUrl":"10.1016/j.insmatheco.2025.103115","url":null,"abstract":"<div><div>In this paper, we investigate the optimal insurance arrangement for an agent who exhibits a mean-variance preference. For the purpose of risk management, the agent's terminal wealth is constrained via a Value at Risk condition. As for the admissible indemnity functions, we suppose that they are subjected to principle of indemnity, incentive compatibility condition, and a so-called Vajda condition as well. The Vajda condition stipulates that within an insurance contract, the proportion of the loss borne by the insurance company should be non-decreasing as the total loss amount increases. By employing a non-decreasing rearrangement technique and a modification approach, our results show that the optimal insurance is either a pure deductible insurance or a mixed proportional insurance with a deductible under expected value premium principle. As by-products, we also obtain the optimal insurance policies under preferences of mean-variance, mean-VaR, and mean-variance with a portfolio insurance constraint, respectively. Finally, we present numerical studies to provide economic insights into these findings.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"123 ","pages":"Article 103115"},"PeriodicalIF":1.9,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144138148","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

Learning from COVID-19: A catastrophe mortality bond solution in the post-pandemic era 从COVID-19吸取教训：大流行后时代的巨灾死亡率债券解决方案

IF 1.9 2区经济学

Insurance Mathematics & Economics Pub Date : 2025-05-21 DOI: 10.1016/j.insmatheco.2025.103113

Ze Chen , Hong Li , Yu Mao , Kenneth Q. Zhou

引用次数: 0

Pricing and hedging of variable annuities with path-dependent guarantee in Wishart stochastic volatility models Wishart随机波动率模型中路径相关担保的可变年金定价与套期保值

IF 1.9 2区经济学

Insurance Mathematics & Economics Pub Date : 2025-05-20 DOI: 10.1016/j.insmatheco.2025.103114

José Da Fonseca , Patrick Wong

引用次数: 0

Improving detections of serial dynamics for longitudinal actuarial data with underwriting-controlled testing 利用承保控制测试改进纵向精算数据的连续动态检测

IF 1.9 2区经济学

Insurance Mathematics & Economics Pub Date : 2025-04-16 DOI: 10.1016/j.insmatheco.2025.103111

Tsz Chai Fung

{"title":"Improving detections of serial dynamics for longitudinal actuarial data with underwriting-controlled testing","authors":"Tsz Chai Fung","doi":"10.1016/j.insmatheco.2025.103111","DOIUrl":"10.1016/j.insmatheco.2025.103111","url":null,"abstract":"<div><div>Longitudinal actuarial data, where policyholders' claims are recorded over multiple years, offer valuable insights for pricing and reserving. However, standard modeling approaches typically assume no serial dynamics in conditional claim distributions over time. Such an assumption is difficult to validate given that most non-life insurance products are short-term, yielding data from only a few years. Recent diagnostic methods can detect serial dynamics but do not distinguish between changes induced by endogenous underwriting standards (e.g., renewal and pricing policies favoring low-risk policyholders) and genuine, exogenous temporal shifts (e.g., evolving socioeconomic environment). In this paper, we develop underwriting-controlled serial dynamic tests for longitudinal actuarial data. By applying an inverse-probability-weighted estimation approach, we adjust for underwriting effects and thus detect the true underlying serial dynamics. We propose tests based on three metrics, parameter difference, prediction bias, and prediction loss, enabling both statistical and economic interpretations of dynamic changes. Simulation studies show that our tests avoid false detections caused by underwriting effects. An analysis using European automobile insurance data illustrates how our approach offers deeper insights into when and why serial dynamics emerge.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"123 ","pages":"Article 103111"},"PeriodicalIF":1.9,"publicationDate":"2025-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143855796","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

Approximations of multi-period liability values by simple formulas 用简单公式近似计算多期负债值

IF 1.9 2区经济学

Insurance Mathematics & Economics Pub Date : 2025-04-15 DOI: 10.1016/j.insmatheco.2025.103112

Nils Engler, Filip Lindskog

引用次数: 0

Portfolio benchmarks in defined contribution pension plan management 固定缴费养老金计划管理中的投资组合基准

IF 1.9 2区经济学

Insurance Mathematics & Economics Pub Date : 2025-04-08 DOI: 10.1016/j.insmatheco.2025.04.002

Daxin Huang , Yang Liu

{"title":"Portfolio benchmarks in defined contribution pension plan management","authors":"Daxin Huang , Yang Liu","doi":"10.1016/j.insmatheco.2025.04.002","DOIUrl":"10.1016/j.insmatheco.2025.04.002","url":null,"abstract":"<div><div>In financial practice, a portfolio benchmark is of importance as it characterizes the fluctuation of the market and better evaluates the performance of the fund manager. We study the optimal investment problem of Defined Contribution (DC) pension plan management with portfolio benchmarks. As such, three technical difficulties arise, and we overcome them accordingly. First, the classic Legendre transformation cannot handle the stochastic nature of the portfolio benchmark. We introduce a parameterized Legendre transformation technique and conduct it to obtain closed-form optimal control strategies. Second, we discover that the optimal solution is not unique when the drift parameter of the benchmark is exactly Merton's constant. We employ a risk management criterion minimizing the liquidation probability to further select a “best” control strategy among the optimums. Third, the Lagrange multiplier cannot be directly solved from the budget constraint. We propose a new numerical technique called the Monte Carlo bisection method to solve it. Therefore, we can analyze the optimal strategies with asymptotic analysis and demonstrate financial insights. We find that when the benchmark is deterministic or its drift is low, the optimal investment aligns with the literature, while the high-drift benchmarks lead to an opposite risk behavior. Finally, empirical validation using the US and Chinese market data shows that our strategy is more effective in a lower risk-premium market.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"123 ","pages":"Article 103110"},"PeriodicalIF":1.9,"publicationDate":"2025-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143834319","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Bayesian adaptive portfolio optimization for DC pension plans 固定缴费养老金计划的贝叶斯自适应投资组合优化

IF 1.9 2区经济学

Insurance Mathematics & Economics Pub Date : 2025-04-03 DOI: 10.1016/j.insmatheco.2025.04.001

Shuping Gao , Junyi Guo , Xiaoqing Liang

{"title":"Bayesian adaptive portfolio optimization for DC pension plans","authors":"Shuping Gao , Junyi Guo , Xiaoqing Liang","doi":"10.1016/j.insmatheco.2025.04.001","DOIUrl":"10.1016/j.insmatheco.2025.04.001","url":null,"abstract":"<div><div>This paper investigates an optimally defined contribution (DC) pension fund problem with partial information. The fund manager invests his wealth in a financial market consisting of a risk-free asset, a stock, and an index bond. He aims to maximize the expected utility of the terminal wealth minus the minimum guarantee. The drift terms of the stock and the index bond are represented by unobservable random variables and the market price of risk follows a prior probability distribution. Using the Bayesian approach and filtering theory, we first transform the original unobservable optimization problem into one with full information. After that, we introduce an auxiliary process to convert the full information problem into an equivalent unconstrained self-financing optimization problem. We then solve the problem and obtain an explicit expression for the optimal investment strategy by using the martingale approach. To compare the results, we also derive the optimal investment strategy for the DC pension model under constant relative risk aversion (CRRA) utility in which the financial market is fully observable.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"122 ","pages":"Pages 262-274"},"PeriodicalIF":1.9,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143785289","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 intergenerational risk-sharing design for a target benefit pension plan 目标收益养老金计划的均衡代际风险分担设计

IF 1.9 2区经济学

Insurance Mathematics & Economics Pub Date : 2025-04-02 DOI: 10.1016/j.insmatheco.2025.03.008

Lv Chen , Danping Li , Yumin Wang , Xiaobai Zhu

{"title":"Equilibrium intergenerational risk-sharing design for a target benefit pension plan","authors":"Lv Chen , Danping Li , Yumin Wang , Xiaobai Zhu","doi":"10.1016/j.insmatheco.2025.03.008","DOIUrl":"10.1016/j.insmatheco.2025.03.008","url":null,"abstract":"<div><div>In this paper, we develop a risk-sharing pension design for a target benefit pension plan to minimize the income instability for all future retirees within a Black-Scholes market setting and a stable population. In contrast to the existing literature, we explicitly consider the difference between individual and intergenerational discount functions. This distinction, motivated by the fact that individual time preferences and societal preferences for different generations are fundamentally different, leads to time-inconsistent preferences for pension sponsors. By using the benefit structure as a control variable and solving a system of extended Hamilton-Jacobi-Bellman equations, we derive an intergenerational Nash equilibrium design that implicitly balances the benefit-risk across different generations. Compared to several conventional designs, we find that the equilibrium design is more robust to the choices of generational weights and time preferences. Consequently, it fosters stronger intergenerational solidarity in the risk-sharing structure, enhancing the stability and continuity of the pension plan. Additional sensitivity tests, including different individual and generational discount functions as well as dynamic investment strategies, are performed.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"122 ","pages":"Pages 275-299"},"PeriodicalIF":1.9,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143785196","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