Insurance Mathematics & Economics最新文献

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Optimal reinsurance design under convex premium principles and distortion risk measures 凸保费原则和失真风险措施下的最优再保险设计

IF 2.2 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2026-01-01 DOI: 10.1016/j.insmatheco.2025.103202

Yiying Zhang , Wenjun Jiang

This paper studies an optimal reinsurance problem from an insurer’s perspective under convex premium principles. The insurer’s preference is assumed to be dictated by the distortion risk measure. When doing business with only one reinsurer, the general form of the optimal indemnity function for the insurer is derived by jointly applying the calculation of variation and marginal indemnification function approaches. We demonstrate that the optimal indemnity function for the insurer takes the form of a limited stop-loss when the insurer adopts a Range Value-at-Risk preference. In contrast, when the insurer applies strictly convex distortion risk measures, we show that, under mild conditions, the optimal indemnity function may include a co-insurance component. We also extend the results to the case of multiple reinsurers through a representative reinsurer lens, and present a sufficient condition under which the representative reinsurer’s premium principle is of the same mathematical form of the convex premium principle studied in this paper. We also show the connection between the optimal reinsurance problems under the certainty-equivalent premium principle and under the convex premium principle. Some interesting results are presented for the problem between one insurer and multiple reinsurers when each reinsurer applies an ith-moment premium principle.

本文从保险人的角度研究凸保费原则下的最优再保险问题。假设保险人的偏好是由扭曲风险度量决定的。在只有一家再保险公司的情况下，通过联合应用变异计算和边际赔偿函数方法，推导出保险人最优赔偿函数的一般形式。我们证明了当保险人采用范围风险价值偏好时，保险人的最优赔偿函数采用有限止损的形式。相反，当保险人严格采用凸扭曲风险度量时，我们表明，在温和条件下，最优赔偿函数可能包括共同保险成分。我们还通过代表性再保险人的视角将结果推广到多再保险人的情况，并给出了代表性再保险人的保费原则与本文研究的凸保费原则具有相同数学形式的充分条件。同时，给出了确定等价保费原则下的最优再保险问题与凸保费原则下的最优再保险问题的联系。当每个再保险人应用第i时刻保费原则时，对一个保险人和多个再保险人之间的问题提出了一些有趣的结果。

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引用次数: 0

Dynamic reinsurance design with heterogeneous beliefs under the mean-variance framework 均值-方差框架下异质信念的动态再保险设计

IF 2.2 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2025-12-30 DOI: 10.1016/j.insmatheco.2025.103207

Junyi Guo , Xia Han , Hao Wang

This paper investigates the dynamic reinsurance design problem under the mean-variance criterion, incorporating heterogeneous beliefs between the insurer and the reinsurer, and introducing an incentive compatibility constraint to address moral hazard. The insurer’s surplus process is modeled using the classical Cramér-Lundberg risk model, with the option to invest in a risk-free asset. To solve the extended Hamilton-Jacobi-Bellman (HJB) system, we apply the partitioned domain optimization technique, transforming the infinite-dimensional optimization problem into a finite-dimensional one determined by several key parameters. The resulting optimal reinsurance contracts are more complex than the standard proportional and excess-of-loss contracts commonly studied in the mean-variance literature with homogeneous beliefs. By further assuming specific forms of belief heterogeneity, we derive the parametric solutions and obtain a clear optimal equilibrium solution. Finally, we compare our results with models where the insurer and reinsurer share identical beliefs or where the incentive compatibility constraint is relaxed. Numerical examples are provided to illustrate the impacts of belief heterogeneity and the incentive compatibility constraint on optimal reinsurance strategies.

本文研究了均值方差准则下的动态再保险设计问题，考虑了保险人和再保险人之间的异质信念，并引入了激励相容约束来解决道德风险。保险公司的盈余过程使用经典的cram - lundberg风险模型建模，并选择投资于无风险资产。为了求解扩展Hamilton-Jacobi-Bellman （HJB）系统，我们采用了分域优化技术，将无限维优化问题转化为由几个关键参数决定的有限维优化问题。所得到的最优再保险合同比具有齐次信念的均值-方差文献中通常研究的标准比例合同和超额损失合同更为复杂。通过进一步假设信念异质性的具体形式，导出了参数解，得到了一个清晰的最优均衡解。最后，我们将我们的结果与保险人和再保险人拥有相同信念或激励兼容性约束放松的模型进行比较。通过数值算例说明了信念异质性和激励相容约束对最优再保险策略的影响。

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引用次数: 0

Generalized expected-shortfalls based on distortion risk measures 基于失真风险度量的广义预期缺陷

IF 2.2 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2025-12-30 DOI: 10.1016/j.insmatheco.2025.103206

Shuyu Gong , Zhenfeng Zou , Meng Guan , Taizhong Hu

This paper establishes explicit representations of generalized Expected-Shortfall (ES) based on a distortion risk measure with arbitrary (possibly non-differentiable) distortion function. We further derive a novel reverse generalized-ES optimization formula, which enables one to obtain closed-form solutions for the supremum value of a stop-loss random variable’s distortion risk measure over a Wasserstein-2 uncertainty set constrained by the first two moments, and exact characterization of the extremal distribution attaining this bound. The method is validated through an insurance data case study, demonstrating its applicability in risk management scenarios with distributional ambiguity.

本文建立了基于任意（可能不可微）失真函数的失真风险测度的广义期望缺陷（ES）的显式表示。我们进一步推导了一种新的反向广义es优化公式，该公式可以得到受前两个矩约束的Wasserstein-2不确定性集上的止损随机变量失真风险测度的最大值的封闭解，以及得到该界的极值分布的精确表征。通过一个保险数据的案例研究，验证了该方法在具有分布模糊性的风险管理场景中的适用性。

引用次数: 0

A complete proof of the De Vylder and Goovaerts conjecture for homogeneous risk models 齐次风险模型的De Vylder和Goovaerts猜想的完整证明

IF 2.2 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2025-12-25 DOI: 10.1016/j.insmatheco.2025.103205

Bara Kim , Jeongsim Kim , Jerim Kim

De Vylder and Goovaerts (2000) conjectured that the finite-time ruin probability in a homogeneous risk model is greater than or equal to the corresponding ruin probability in an associated model with equalized claim amounts. This conjecture holds provided that the conjecture asserting that the same inequality holds for the conditional finite-time ruin probabilities, conditioned on n claims occurring during the finite time, for all n ≥ 1, is true. They proved the conjecture for

n = 1

and

n = 2

, but left the case n ≥ 3 as an open problem. Kim et al. (2021) resolved the case

n = 3

. In this paper, we completely resolve the conjecture for all n.

De Vylder和Goovaerts（2000）推测齐次风险模型的有限时间破产概率大于或等于索赔金额相等的关联模型的相应破产概率。这个猜想成立，前提是断言相同的不等式对有限时间破产概率成立的猜想成立，条件是在有限时间内发生的n个索赔，对于所有n ≥ 1，是成立的。他们证明了n=1和n=2的猜想，但将n ≥ 3的情况留作开放问题。Kim et al.（2021）解决了该病例n=3。在本文中，我们完全解决了所有n的猜想。

引用次数: 0

Mortality risks, survival pessimism, and subjective well-Being: Evidence from the health and retirement study 死亡风险、生存悲观主义和主观幸福感：来自健康和退休研究的证据

IF 2.2 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2025-12-25 DOI: 10.1016/j.insmatheco.2025.103204

Lisa Posey , Sharon Tennyson , Nan Zhu

The positive relationship between an individual’s subjective well-being (SWB) and their future survival prospects has been well documented. Using data from the Health and Retirement Study (HRS), we present empirical evidence of how this relationship operates through various channels. We use a two-stage approach where objective survival probability estimates derived from our first-stage Cox model are used to construct the survival bias employed as the dependent variable in the second stage, with SWB and other demographic and health-related variables being covariates in both stages. Our findings reveal that even after controlling for objective health-related factors and potential private information on health and mortality, individuals’ SWB remains as a significant factor to their objective mortality. Moreover, respondents’ SWB also affects the bias in the survival estimation—measured as the disparity between their subjective and objective survival probabilities. In particular, a higher SWB is correlated with a reduction in survival pessimism. We provide new evidence that bias in survival estimates can distort consumption and saving decisions, and provide estimates of its impact on welfare across different levels of SWB.

一个人的主观幸福感（SWB）与他们未来的生存前景之间的正相关关系已经得到了很好的证明。利用健康与退休研究（HRS）的数据，我们提出了这种关系如何通过各种渠道运作的经验证据。我们采用两阶段方法，其中使用第一阶段Cox模型得出的客观生存概率估计来构建生存偏差，作为第二阶段的因变量，SWB和其他人口统计学和健康相关变量作为两阶段的协变量。我们的研究结果表明，即使在控制了客观健康相关因素和潜在的健康和死亡率私人信息之后，个人的主观幸福感仍然是其客观死亡率的重要因素。此外，受访者的主观幸福感也会影响生存估计的偏差——以主观和客观生存概率之间的差异来衡量。特别是，较高的主观幸福感与生存悲观情绪的减少相关。我们提供了新的证据，证明生存估计的偏差会扭曲消费和储蓄决策，并提供了其对不同SWB水平的福利影响的估计。

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引用次数: 0

Iterated poisson processes for catastrophic risk modeling in ruin theory 破产理论中灾难性风险建模的迭代泊松过程

IF 2.2 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2025-12-20 DOI: 10.1016/j.insmatheco.2025.103200

Dongdong Hu , Svetlozar T. Rachev , Hasanjan Sayit , Hailiang Yang , Yildiray Yildirim

This paper studies the properties of the Multiple Iterated Poisson Process (MIPP), a stochastic process constructed by repeatedly time-changing a Poisson process, and its applications in ruin theory. Like standard Poisson processes, MIPPs have exponentially distributed sojourn times (waiting times between jumps). We explicitly derive the probabilities of all possible jump sizes at the first jump and obtain the Laplace transform of the joint distribution of the first jump time and its corresponding jump size. In ruin theory, the classical Cramér–Lundberg model assumes that claims arrive independently according to a Poisson process. In contrast, our model employs an MIPP to allow for clustered arrivals, reflecting real-world scenarios, such as catastrophic events. Under this new framework, we derive the corresponding scale function in closed form, facilitating accurate calculations of the probability of ruin in the presence of clustered claims. These results improve the modeling of extreme risks and have practical implications for insurance solvency assessments, pricing reinsurance, and the estimation of capital reserves.

本文研究了多重迭代泊松过程（Multiple Iterated Poisson Process， MIPP）的性质及其在破产理论中的应用。与标准泊松过程一样，MIPPs具有指数分布的逗留时间（跳跃之间的等待时间）。我们显式地导出了第一次跳跃时所有可能的跳跃大小的概率，并得到了第一次跳跃时间及其相应的跳跃大小的联合分布的拉普拉斯变换。在破产理论中，经典的cram - lundberg模型假设索赔是根据泊松过程独立产生的。相比之下，我们的模型采用MIPP来考虑集群到达，反映现实世界的场景，如灾难性事件。在这个新框架下，我们以封闭形式推导出相应的比例函数，便于准确计算聚集索赔时的破产概率。这些结果改进了极端风险的建模，并对保险偿付能力评估、再保险定价和资本准备金估计具有实际意义。

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引用次数: 0

Optimal periodic strategies with dividends payable from gains only 仅从收益中支付股息的最优周期性策略

IF 2.2 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2025-12-18 DOI: 10.1016/j.insmatheco.2025.103203

Eric C.K. Cheung , Guo Liu , Jae-Kyung Woo , Jiannan Zhang , Dan Zhu

In this paper, we consider the compound Poisson insurance risk model and analyze the optimal dividend strategy (that maximizes the expected present value of dividend payments until ruin) when dividends can only be paid periodically as lump sums. If one makes the usual assumption that dividends can be paid from the available surplus, then the optimal strategies are often of band or barrier type, resulting in a ruin probability of one (e.g. Albrecher et al. (2011a)). As opposed to such an assumption, we propose that dividends can only be paid from a certain fraction of the gains (i.e. positive increment of the process between successive dividend decision times), and such a constraint allows the surplus process to have a positive survival probability. Some theoretical properties of the value function and the optimal strategy are derived in connection to the Bellman equation. These properties suggest that a bang-bang type of control can be a candidate for the optimal strategy, where dividend is paid at the highest possible amount as long as the surplus is high enough. The dividend function under the candidate strategy is subsequently derived under exponential inter-observation times and claims with a rational Laplace transform, and we also provide specific numerical examples with (mixed) exponential claims where the proposed strategy is optimal in such cases.

本文考虑复合泊松保险风险模型，分析了当股利只能定期一次性支付时的最优股利策略（即股利支付的预期现值最大化直至破产）。如果人们通常假设可以从可用盈余中支付股息，那么最优策略通常是波段或障碍型，导致破产概率为1（例如Albrecher等人（2011a））。与这种假设相反，我们提出股息只能从收益的一定比例中支付（即连续股息决策时间之间的过程正增量），并且这种约束允许盈余过程具有正的生存概率。结合Bellman方程，导出了价值函数和最优策略的一些理论性质。这些性质表明，bang-bang类型的控制可以作为最优策略的候选，只要盈余足够高，就以尽可能高的金额支付股息。候选策略下的红利函数随后在指数间观测时间和有理拉普拉斯变换下得到，我们还提供了（混合）指数声明的具体数值示例，其中所提出的策略在这种情况下是最优的。

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引用次数: 0

No-sabotage under conditional mean risk sharing of dependent-by-mixture insurance losses 有条件无破坏意味着混合依赖保险损失的风险共担

IF 2.2 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2025-12-12 DOI: 10.1016/j.insmatheco.2025.103195

Michel Denuit , Patricia Ortega-Jimenez , Christian Y. Robert

Conditional mean risk sharing defines an allocation rule to distribute total losses among participants in an insurance pool. Under this risk-sharing scheme, the no-sabotage condition holds when conditional expectations of individual losses given their sum are comonotonic. This property has been widely studied considering independent risks, often assuming that they possess log-concave densities. This paper considers the no-sabotage condition for dependent-by-mixture risks which do not necessarily obey log-concave distributions. Sufficient conditions derived from three different approaches are proposed in order to fulfill the no-sabotage requirement. Several examples are given to illustrate the applicability of the results.

条件平均风险分担定义了一种分配规则，在保险池的参与者之间分配总损失。在这种风险分担方案下，当个人损失的条件期望给定其总和是单调的时，无破坏条件成立。考虑到独立风险，通常假设它们具有对数凹密度，这一性质已被广泛研究。本文研究了不一定服从对数凹分布的混合依赖风险的无破坏条件。通过三种不同的方法，提出了满足无破坏要求的充分条件。给出了几个例子来说明结果的适用性。

引用次数: 0

Asymptotics of systemic risk in a renewal model with multiple business lines and heterogeneous claims 具有多条业务线和异质索赔的更新模型中系统风险的渐近性

IF 2.2 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2025-12-11 DOI: 10.1016/j.insmatheco.2025.103197

Bingzhen Geng , Yang Liu , Hongfu Wan

Systemic risk is receiving increasing attention in the insurance industry. In this paper, we propose a multi-dimensional Lévy process-based renewal risk model with heterogeneous insurance claims, where every dimension indicates a business line of an insurer. We use the systemic expected shortfall (SES) and marginal expected shortfall (MES) defined with a Value-at-Risk (VaR) target level as the measurement of systemic risk. Assuming that all the claim sizes are pairwise asymptotically independent (PAI), we derive asymptotic formulas for the tail probabilities of discounted aggregate claims and the total loss, which hold uniformly for all time horizons. We further obtain the asymptotics of the above systemic risk measures. The main technical issues involve the treatment of uniform convergence in the dynamic time setting. Finally, we perform a detailed Monte Carlo study to validate our asymptotics and analyze the impact and sensitivity of key parameters in the asymptotic expressions both analytically and numerically.

系统性风险在保险业受到越来越多的关注。在本文中，我们提出了一个具有异构保险理赔的基于lsamvy流程的多维续保风险模型，其中每个维度表示保险公司的一条业务线。我们使用系统预期缺口（SES）和边际预期缺口（MES）定义了风险价值（VaR）目标水平作为系统风险的度量。假设所有索赔规模都是两两渐近独立的（PAI），我们导出了贴现总索赔和总损失尾部概率的渐近公式，这些公式在所有时间范围内都是一致的。进一步得到了上述系统风险测度的渐近性。主要的技术问题涉及到动态时间设定中一致收敛的处理。最后，我们进行了详细的蒙特卡罗研究来验证我们的渐近性，并分析了渐近表达式中关键参数的影响和灵敏度。

引用次数: 0

Prolonging life by vitagions: Modelling of mortality improvement shocks 延长寿命：死亡率改善冲击的模型

IF 2.2 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2025-12-11 DOI: 10.1016/j.insmatheco.2025.103198

Maria Carannante , Valeria D’Amato , Cinzia Di Palo

Changes in life expectancy are commonly used to track shifts in mortality dynamics, yet they are hard to interpret, especially during so-called mortality shocks that arrive suddenly, are temporary, and run counter to the long-run trend. Purely extrapolative models cannot capture such changes. Therefore, we propose a forward-looking extension of the Lee-Carter framework, which integrates mortality improvements due to ‘vitagions’. Vitagions are individual sources of mortality improvement, and projects how these might unfold in the future. To model mortality increases related to medical innovation, we consider extending the Lee-Carter model to capture heterogeneity in morality (i.e. fraity-based model) and include a jump diffusion process estimated as a function of the relationship between medical progress and mortality trends to improve mortality projections.

预期寿命的变化通常被用来追踪死亡率动态的变化，但它们很难解释，特别是在所谓的死亡率冲击突然到来、是暂时的、与长期趋势背道而驰的情况下。纯粹的外推模型无法捕捉到这些变化。因此，我们提出了李-卡特框架的前瞻性扩展，其中整合了由于“迁移”导致的死亡率改善。Vitagions是死亡率改善的个别来源，并预测这些可能在未来展开。为了模拟与医疗创新相关的死亡率增加，我们考虑扩展Lee-Carter模型以捕捉道德的异质性（即基于真实性的模型），并包括一个跳跃扩散过程，估计作为医疗进步和死亡率趋势之间关系的函数，以改善死亡率预测。

引用次数: 0

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