Insurance Mathematics & Economics最新文献

英文中文

Performance-based variable premium scheme and reinsurance design 基于绩效的可变保费方案与再保险设计

IF 2.2 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2025-10-22 DOI: 10.1016/j.insmatheco.2025.103169

Ziyue Shi , David Landriault , Fangda Liu

In the literature, insurance and reinsurance pricing is typically determined by a premium principle, characterized by a risk measure that reflects the policy seller’s risk attitude. Building on the work of Meyers (1980) and Chen et al. (2016), we propose a new performance-based variable premium scheme for reinsurance policies, where the premium depends on both the distribution of the ceded loss and the actual realized loss. Under this scheme, the insurer and the reinsurer face a random premium at the beginning of the policy period. Based on the realized loss, the premium is adjusted into either a “reward” or “penalty” scenario, resulting in a discount or surcharge at the end of the policy period. We characterize the optimal reinsurance policy from the insurer’s perspective under this new variable premium scheme. In addition, we formulate a Bowley optimization problem between the insurer and the monopoly reinsurer. Numerical examples demonstrate that, compared to the expected-value premium principle, the reinsurer prefers the variable premium scheme as it reduces the reinsurer’s total risk exposure.

在文献中，保险和再保险定价通常由保费原则决定，其特征是反映保单卖方风险态度的风险度量。在Meyers（1980）和Chen等人（2016）的研究基础上，我们提出了一种新的基于绩效的再保险保单可变保费方案，其中保费取决于已让与损失的分配和实际已实现损失。在此计划下，保险公司和再保险公司在保单期开始时面临随机保费。根据已实现的损失，保费被调整为“奖励”或“惩罚”方案，从而在保单期结束时产生折扣或附加费。我们从保险人的角度刻画了这种新的可变保费方案下的最优再保险政策。此外，我们还建立了保险公司与垄断再保险公司之间的Bowley优化问题。数值算例表明，与期望值保费原则相比，再保险人更倾向于采用可变保费方案，因为它可以减少再保险人的总风险暴露。

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引用次数: 0

Optimal consumption-leisure-investment and retirement choices with nonconcave aspirational utility 具有非凹期望效用的最优消费-休闲-投资与退休选择

IF 2.2 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2025-10-10 DOI: 10.1016/j.insmatheco.2025.103165

Shuang Li , Hui Meng , Ming Zhou

This paper investigates the optimal strategies for investment, consumption, leisure, and voluntary retirement in a continuous-time framework. Beyond standard consumption, we incorporate aspirational consumption which involves a constant and costly expenditure while generating surges in utility, leading to a two-dimensional nonconcave utility function for consumption and leisure. Using the martingale duality method and concavification principle, we classify individuals into “leisure-seekers”, “aspiration-seekers”, and “centrists” based on the prioritization of aspirational consumption versus maximum leisure, and derive semi-closed solutions for the optimal strategies. Through model calibration, we explore the impact of aspiration on optimal policies, finding that the aspiration postpones retirement, strengthens the incentive to invest, and shrinks both leisure and consumption until the aspiration is fulfilled.

本文在连续时间框架下研究了投资、消费、休闲和自愿退休的最优策略。在标准消费之外，我们纳入了期望消费，这涉及到持续和昂贵的支出，同时产生效用激增，导致消费和休闲的二维非凹效用函数。利用鞅对偶方法和凹化原理，基于期望消费与最大休闲的优先性，将个体划分为“休闲寻求者”、“渴望寻求者”和“中间派”，并推导出最优策略的半封闭解。通过模型校准，我们探索了愿望对最优政策的影响，发现愿望推迟了退休时间，增强了投资激励，收缩了休闲和消费，直到愿望得到满足。

引用次数: 0

Numerical methods for computing risk measures of variable annuities under exponential Lévy models 指数lsamvy模型下可变年金风险测度的数值计算方法

IF 2.2 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2025-10-10 DOI: 10.1016/j.insmatheco.2025.103166

Oleg Kudryavtsev , Xiao Wei

We propose an efficient numerical method to calculate the Value-at-Risk and Conditional Tail Expectation for variable annuities under exponential Lévy models. In the proposed approach, the probability density of the net liabilities, expressed in terms of the final position and integral of the exponential Lévy process, is approximated using frame theory and Riesz bases using 3rd order B-splines. The key element of the numerical method is a new algorithm for calculating the integral of the exponential Lévy process, approximated by a discrete sum whose expectation coincides with the expected value of the desired integral. In the main part of our numerical algorithm, to find Value-at-Risk as a quantile of the loss distribution, we numerically solve the equation for the corresponding cumulative distribution function using Newton's method adapted to the probability density approximation by B-splines. Once the Value-at-Risk is found, we calculate the Conditional Tail Expectation using integration by parts, again taking advantage of the properties of cubic B-splines. Numerical experiments on the application of the developed method for the Black-Scholes and CGMY models clearly demonstrate its high accuracy and speed.

我们提出了一种有效的数值方法来计算指数lsamvy模型下可变年金的风险值和条件尾期望。在提出的方法中，净负债的概率密度，以最终位置和指数lsamvy过程的积分表示，使用框架理论和Riesz基使用三阶b样条近似。数值方法的关键是一种新的计算指数型lsamvy过程积分的算法，该算法近似为一个离散和，其期望与期望积分的期望值一致。在我们的数值算法的主要部分，为了找到损失分布的分位数值，我们使用适用于b样条概率密度近似的牛顿方法对相应的累积分布函数的方程进行了数值求解。一旦发现风险值，我们使用分部积分法计算条件尾期望，再次利用三次b样条的性质。将该方法应用于Black-Scholes和CGMY模型的数值实验表明，该方法具有较高的精度和速度。

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引用次数: 0

Robust parameter estimation for the Lee-Carter family: A probabilistic principal component approach 李-卡特族的鲁棒参数估计：一种概率主成分方法

IF 2.2 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2025-10-01 DOI: 10.1016/j.insmatheco.2025.103164

Yiping Guo , Johnny Siu-Hang Li

Although the impact of outliers on stochastic mortality modelling has been examined, previous studies on this topic focus on how outliers in the estimated time-varying indexes may be detected and/or modelled, with little attention being paid to the adverse effects of outliers on estimation robustness, particularly that pertaining to age-specific parameters. In this paper, we propose a robust estimation method for the Lee-Carter model, through a reformulation of the model into a probabilistic principal component analysis with multivariate t-distributions and an efficient expectation-maximization algorithm for implementation. The proposed method yields significantly more robust parameter estimates, while preserving the fundamental interpretation for the bilinear term in the model as the first principal component and the flexibility of pairing the estimated time-varying parameters with any appropriate time-series process. We also extend the proposed method for use with multi-population generalizations of the Lee-Carter model, allowing for a wider range of applications such as quantification of population basis risk in index-based longevity hedges. Using a combination of real and pseudo datasets, we demonstrate the superiority of the proposed method relative to conventional estimation approaches such as singular value decomposition and maximum likelihood.

虽然已经研究了异常值对随机死亡率建模的影响，但先前关于这一主题的研究主要集中在如何检测和/或建模估计时变指数中的异常值，很少关注异常值对估计稳健性的不利影响，特别是与特定年龄参数有关的不利影响。在本文中，我们通过将Lee-Carter模型重新表述为具有多元t分布的概率主成分分析和有效的期望最大化算法来提出一种稳健的估计方法。该方法显著提高了参数估计的鲁棒性，同时保留了对模型中双线性项作为第一主成分的基本解释，以及将估计的时变参数与任何适当的时间序列过程配对的灵活性。我们还扩展了所提出的方法，用于Lee-Carter模型的多种群推广，允许更广泛的应用，例如基于指数的长寿对冲中种群基础风险的量化。使用真实和伪数据集的组合，我们证明了该方法相对于传统的估计方法（如奇异值分解和最大似然）的优越性。

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引用次数: 0

Individual survivor fund account: The impact of bequest motives on tontine participation 个人遗属基金账户：遗赠动机对长期参与的影响

IF 2.2 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2025-10-01 DOI: 10.1016/j.insmatheco.2025.103161

Tak Wa Ng, Thai Nguyen

We introduce a new model for individual survivor fund account with bequest that allows the tontine's participants to leave inheritances to their heirs. Two proposed designs, constant and variable participation, are examined through the lens of an individual account, addressing optimal investment and bequest proportions. Our formulation captures two types of bequest motives: the relative concern between terminal benefit and premature bequest and the intention to smooth the bequest plan. Our numerical illustrations show that the individual's willingness to participate in the longevity risk pool will decrease with these two bequest motive levels and address the question of when and with what motive level the individual will join the pool. Furthermore, we incorporate labor income and consumption in the participant's optimization problem and perform a welfare analysis thereon.

我们引入了一个新的模式，个人遗赠基金账户，允许tontine的参与者留下遗产给他们的继承人。两种提议的设计，恒定和可变参与，通过个人账户的镜头进行检查，解决最佳投资和遗产比例。我们的公式抓住了两种类型的遗赠动机：对临终利益和过早遗赠的相对关注，以及使遗赠计划顺利进行的意图。我们的数值实例表明，在这两种动机水平下，个人参与长寿风险池的意愿会降低，并解决了个人何时以及以何种动机水平加入风险池的问题。在此基础上，我们将劳动收入和消费纳入到参与者的优化问题中，并对其进行福利分析。

引用次数: 0

Modelling seasonal mortality: An age–period–cohort approach 季节性死亡率建模：一种年龄时期队列方法

IF 2.2 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2025-09-30 DOI: 10.1016/j.insmatheco.2025.103162

Jean-François Bégin , Mathieu Boudreault , Thomas Landry

Age–period–cohort (APC) mortality models have become the standard approach in actuarial science to project mortality improvements for uses such as pricing annuities and setting contributions in pension plans. Annual mortality rates are sufficient for such long-term applications; yet, for understanding excess mortality due to, e.g., epidemics and heat waves, annual observations have important limitations, and high-frequency data need to be used. This study introduces a seasonal overlay that can be used in the context of APC models. Based on a periodic spline, this extra layer allows the model to capture seasonal features parsimoniously. In an empirical application, we fit a CBDX variant of the APC family to daily mortality data from the province of Quebec in Canada. Our dataset covers over 3.6 million individuals aged at least 60 between 1996 and 2019. Our results show significant seasonal patterns consistent with the flu season, which are similar between males and females. We also test different parametric models and find that the shape of seasonality remained constant over time for most age groups. As part of a sensitivity analysis, we investigate intra-annual mortality patterns between subgroups and report that the local climate, scheme of urbanization, and individual socio-economic status do not affect seasonal patterns. Excess mortality during 2020–2022 is also explored using our modelling framework.

年龄-时期-队列（APC）死亡率模型已成为精算科学中预测死亡率改善的标准方法，用于诸如定价年金和确定养恤金计划的缴款。年死亡率足以满足这种长期应用；然而，为了了解由于流行病和热浪等原因造成的死亡率过高，年度观测有很大的局限性，需要使用高频数据。本研究引入了一种可用于APC模型的季节性叠加。基于周期性样条，这个额外的层使模型能够简洁地捕捉季节特征。在实证应用中，我们拟合了APC家族的CBDX变体与加拿大魁北克省的每日死亡率数据。我们的数据集涵盖了1996年至2019年间超过360万60岁以上的人。我们的研究结果显示了与流感季节一致的显著季节性模式，这在男性和女性之间是相似的。我们还测试了不同的参数模型，发现季节性的形状随着时间的推移对大多数年龄组保持不变。作为敏感性分析的一部分，我们调查了亚组之间的年度内死亡率模式，并报告了当地气候、城市化方案和个人社会经济地位不影响季节模式。还使用我们的建模框架探讨了2020-2022年期间的超额死亡率。

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引用次数: 0

Dynamic investment-driven insurance pricing and optimal regulation 动态投资驱动的保险定价与最优监管

IF 2.2 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2025-09-29 DOI: 10.1016/j.insmatheco.2025.103160

Bingzheng Chen , Zongxia Liang , Shunzhi Pang

This paper analyzes the competitive equilibrium of insurance market in a dynamic setting, focusing on the interaction between insurers' underwriting and investment strategies. Three possible equilibrium outcomes are identified: a positive insurance market, a zero insurance market, and market failure. Our findings reveal why insurers may rationally accept underwriting losses by setting a negative safety loading while relying on investment profits, particularly when there is a negative correlation between insurance gains and financial returns. Such losses can still occur even when the insurance market is monopolistic. Additionally, we explore the impact of regulatory frictions, showing that while imposing a cost on investment can enhance social welfare under certain conditions, it may not always be necessary.

本文分析了动态环境下保险市场的竞争均衡，重点研究了保险公司承保与投资策略之间的相互作用。本文确定了三种可能的均衡结果：正保险市场、零保险市场和市场失灵。我们的研究结果揭示了为什么保险公司在依赖投资利润的同时，通过设定负安全负荷来理性地接受承保损失，特别是当保险收益与财务回报之间存在负相关时。即使在保险市场是垄断的情况下，这种损失仍可能发生。此外，我们探讨了监管摩擦的影响，表明虽然在某些条件下对投资施加成本可以提高社会福利，但它可能并不总是必要的。

引用次数: 0

Transformers-based least square Monte Carlo for solvency calculation in life insurance 基于变压器的寿险偿付能力最小二乘蒙特卡罗计算

IF 2.2 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2025-09-29 DOI: 10.1016/j.insmatheco.2025.103163

Francesca Perla , Salvatore Scognamiglio , Andrea Spadaro , Paolo Zanetti

The Solvency Capital Requirement (SCR), mandated by Solvency II, represents the capital insurers must hold to ensure solvency, calculated as the Value-at-Risk of the Net Asset Value at a 99.5% confidence level over a one-year period. While Nested Monte Carlo simulations are the gold standard for SCR calculation, they are highly resource-intensive. The Least Squares Monte Carlo (LSMC) method provides a more efficient alternative but faces challenges with high-dimensional data due to the curse of dimensionality. We introduce a novel extension of LSMC, incorporating advanced deep learning models, specifically Transformer models, which enhance traditional machine learning methods. This approach significantly improves the accuracy of approximating the complex relationship between insurance liabilities and risk factors, leading to a more accurate SCR calculation. Our extensive experiments on two insurance portfolios demonstrate the effectiveness of this transformer-based LSMC approach. Additionally, we show that Shapley values can be applied to achieve model explainability, which is crucial for regulatory compliance and for fostering the adoption of deep learning in the highly regulated insurance sector.

偿付能力资本要求（SCR），由偿付能力II授权，代表保险公司必须持有以确保偿付能力的资本，计算为净资产价值的风险价值，在一年的时间内以99.5%的置信度计算。虽然嵌套蒙特卡罗模拟是SCR计算的黄金标准，但它们是高度资源密集型的。最小二乘蒙特卡罗（LSMC）方法提供了一种更有效的替代方法，但由于维度的限制，它在处理高维数据时面临挑战。我们引入了LSMC的新扩展，结合了先进的深度学习模型，特别是Transformer模型，它增强了传统的机器学习方法。该方法显著提高了近似保险责任与风险因素之间复杂关系的准确性，从而使SCR的计算更加准确。我们在两个保险组合上的大量实验证明了这种基于变压器的LSMC方法的有效性。此外，我们表明Shapley值可以应用于实现模型的可解释性，这对于法规遵从性和促进在高度监管的保险行业采用深度学习至关重要。

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引用次数: 0

Dynamic derivative-based pension investment with stochastic volatility: A behavioral perspective 基于动态衍生品的随机波动养老金投资：行为视角

IF 2.2 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2025-09-18 DOI: 10.1016/j.insmatheco.2025.103158

Zheng Chen , Zhongfei Li , Yan Zeng , Yang Shen

We study a derivative-based optimal investment strategy for a defined contribution (DC) pension plan under the Heston stochastic volatility model. The investor's preferences are described by an S-shaped utility that combines risk-seeking and loss-averse behaviors, benchmarked to a reference point of retirement savings. By the martingale approach and the inverse Fourier transform method, we obtain a semi-analytical form for the optimal investment strategy. We investigate the distinct roles of various factors, such as preferences, wealth goals, market conditions, in the investor's optimal decision, and clarify the dynamic relationship between these factors and derivatives trading. We also provide comprehensive comparisons between the results derived under prospect theory and expected utility theory. A portfolio decomposition validates that the optimal derivatives trading strategy is influenced by both psychological and risk-averse factors. Numerical illustrations are provided to further elaborate our results.

研究了在赫斯顿随机波动率模型下，基于衍生工具的养老金计划最优投资策略。投资者的偏好由一个s型效用来描述，它结合了寻求风险和规避损失的行为，以退休储蓄为基准。利用鞅方法和傅里叶反变换方法，得到了最优投资策略的半解析形式。我们研究了偏好、财富目标、市场条件等因素在投资者最优决策中的不同作用，并阐明了这些因素与衍生品交易之间的动态关系。我们还对前景理论和期望效用理论的结果进行了全面的比较。组合分解验证了最优衍生品交易策略受到心理因素和风险厌恶因素的影响。数值说明进一步阐述了我们的结果。

引用次数: 0

Robust time-consistent Stackelberg differential game for insurance with stochastic interest rates and 4/2 stochastic volatility 具有随机利率和4/2随机波动率的保险稳健时一致Stackelberg微分对策

IF 2.2 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2025-09-18 DOI: 10.1016/j.insmatheco.2025.103159

Hao Chang, Xiao-Jia Li

This paper studies the robust time-consistent investment-reinsurance problem for an insurer and a reinsurer under the framework of the Stackelberg stochastic differential game, in which the reinsurer is the leader and the insurer is the follower. The insurer hedges the claim risk by purchasing proportional reinsurance, and both the insurer and reinsurer can invest in a financial market consisting of a risk-free asset, a stock, and a rolling bond to manage risk. The interest rates and the volatility of stock price are assumed to obey the affine term-structure model and the 4/2 stochastic volatility model, respectively. Assume that both the insurer and the reinsurer are ambiguity-averse, and we establish the robust optimal control problem for an insurer and a reinsurer under the mean-variance criterion, respectively. Robust time-consistent investment and reinsurance strategies are determined by the Stackelberg equilibrium of the game, which considers the interests of both the insurer and the reinsurer and reflects the information asymmetry between the two parties. By employing the stochastic optimal control theory, we derive the robust time-consistent Stackelberg strategies. Finally, some sensitivity analysis and comparative analysis are presented to illustrate the results obtained.

本文研究了在Stackelberg随机微分对策框架下，再保险人是领导者，保险人是跟随者的保险人和再保险人的稳健时间一致投资再保险问题。保险公司通过购买比例再保险来对冲理赔风险，保险公司和再保险公司都可以投资于由无风险资产、股票和滚动债券组成的金融市场来管理风险。假设利率和股价波动分别服从仿射期限结构模型和4/2随机波动模型。假设保险人和再保险人都是歧义厌恶者，分别在均值-方差准则下建立了保险人和再保险人的鲁棒最优控制问题。稳健的时间一致性投资和再保险策略由博弈的Stackelberg均衡决定，该博弈考虑了保险人和再保险人双方的利益，反映了双方的信息不对称。利用随机最优控制理论，导出了鲁棒时一致Stackelberg策略。最后，对所得结果进行了敏感性分析和对比分析。

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