Insurance Mathematics & Economics最新文献

英文中文

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 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2025-04-02 DOI: 10.1016/j.insmatheco.2025.03.008

Lv Chen , Danping Li , Yumin Wang , Xiaobai Zhu

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.

在本文中，我们开发了一个风险分担养老金设计的目标福利养老金计划，以最小化所有未来退休人员的收入不稳定性在布莱克-斯科尔斯市场设置和稳定的人口。与现有文献相比，我们明确考虑了个体和代际贴现函数之间的差异。由于不同世代的个人时间偏好和社会偏好根本不同，这种区别导致了养老金保荐人的时间偏好不一致。通过将收益结构作为控制变量，求解扩展Hamilton-Jacobi-Bellman方程组，我们推导出了代际纳什均衡设计，该设计隐含地平衡了不同代之间的收益-风险。与几种传统设计相比，我们发现均衡设计对代际权重和时间偏好的选择具有更强的鲁棒性。因此，它在风险分担结构中促进更强的代际团结，加强养恤金计划的稳定性和连续性。另外还进行了敏感性测试，包括不同的个体和代际贴现函数以及动态投资策略。

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引用次数: 0

Forecasting age distribution of deaths: Cumulative distribution function transformation 预测死亡年龄分布：累积分布函数变换

IF 1.9 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2025-03-31 DOI: 10.1016/j.insmatheco.2025.03.007

Han Lin Shang , Steven Haberman

Like density functions, period life-table death counts are nonnegative and have a constrained integral, and thus live in a constrained nonlinear space. Implementing established modelling and forecasting methods without obeying these constraints can be problematic for such nonlinear data. We introduce cumulative distribution function transformation to forecast the life-table death counts. Using the Japanese life-table death counts obtained from the Japanese Mortality Database (2024), we evaluate the point and interval forecast accuracies of the proposed approach, which compares favourably to an existing compositional data analytic approach. The improved forecast accuracy of life-table death counts is of great interest to demographers for estimating age-specific survival probabilities and life expectancy and actuaries for determining temporary annuity prices for different ages and maturities.

与密度函数一样，周期生命表死亡计数是非负的，并且具有约束积分，因此存在于约束的非线性空间中。对于这样的非线性数据，在不遵守这些约束的情况下实施既定的建模和预测方法可能会有问题。我们引入累积分布函数变换来预测生命表死亡人数。使用从日本死亡率数据库（2024）获得的日本生命表死亡计数，我们评估了所提出方法的点和区间预测精度，该方法与现有的成分数据分析方法相比具有优势。提高生命表死亡计数的预测准确性对人口统计学家估计特定年龄的生存概率和预期寿命以及精算师确定不同年龄和期限的临时年金价格具有极大的兴趣。

引用次数: 0

Length of stay in residential aged care: Patterns and determinants from a population-based cohort study 老年护理住院时间：基于人群的队列研究的模式和决定因素

IF 1.9 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2025-03-24 DOI: 10.1016/j.insmatheco.2025.03.006

Mengyi Xu , Gaoyun Yan

The length of stay in permanent residential care is a crucial metric for evaluating the utilization of institutional care and informing sustainable aged care policies. Understanding this metric is especially relevant in Australia, where the decision on how to pay the substantial nursing home accommodation costs must be made shortly after admission and is heavily influenced by the expected duration of stay. We investigate the length of stay in long-term institutional care by analyzing a cohort of older Australians first admitted to permanent residential care in 2008. By employing survival analysis that captures time-varying covariates, we find that, in addition to demographic factors like age and gender, the organization type of nursing homes and their service size significantly influence the length of stay. Failing to account for potential changes due to transfers between nursing homes can lead to a significant underestimation of the impact of organization type and service size.

永久住宿护理的停留时间是评估机构护理利用和为可持续老年护理政策提供信息的关键指标。了解这一指标在澳大利亚尤为重要，因为在澳大利亚，必须在入院后不久就决定如何支付养老院的大量住宿费用，这在很大程度上受到预期住院时间的影响。我们通过分析2008年首次入住永久住宿护理的澳大利亚老年人队列来调查长期机构护理的停留时间。通过采用捕获时变协变量的生存分析，我们发现，除了年龄和性别等人口统计学因素外，养老院的组织类型及其服务规模显著影响住院时间。未能考虑到养老院之间转移的潜在变化可能导致对组织类型和服务规模的影响的严重低估。

引用次数: 0

Mean-variance optimization for participating life insurance contracts 参与式寿险合同的均值方差优化

IF 1.9 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2025-03-17 DOI: 10.1016/j.insmatheco.2025.03.005

Felix Fießinger, Mitja Stadje

This paper studies the equity holders' mean-variance optimal portfolio choice problem for (non-)protected participating life insurance contracts. We derive explicit formulas for the optimal terminal wealth and the optimal strategy in the multi-dimensional Black-Scholes model, showing the existence of all necessary parameters. Moreover, we provide a numerical analysis of the Black-Scholes market. The equity holders on average increase their investment into the risky asset in bad economic states and decrease their investment over time.

本文研究了（非）受保护参与式人寿保险合同中权益持有人的均值方差最优投资组合选择问题。导出了多维Black-Scholes模型的最优终端财富和最优策略的显式公式，证明了所有必要参数的存在性。此外，我们还提供了布莱克-斯科尔斯市场的数值分析。在经济不景气的情况下，股权持有者平均会增加对风险资产的投资，并随着时间的推移减少投资。

引用次数: 0

Optimal reinsurance from an optimal transport perspective 最优运输视角下的最优再保险

IF 1.9 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2025-03-12 DOI: 10.1016/j.insmatheco.2025.03.004

Beatrice Acciaio , Hansjörg Albrecher , Brandon García Flores

We use the randomization idea and proof techniques from optimal transport to study optimal reinsurance problems. We start by providing conditions for a class of problems that allow us to characterize the support of optimal treaties, and show how this can be used to deduce the shape of the optimal contract, reducing the task to an optimization problem with finitely many constraints, for which standard techniques can be applied. For a more general class of problems, we regard the optimal reinsurance problem as an iterated optimal transport problem between a (known) initial risk exposure of the insurer and an (unknown) resulting risk exposure of the reinsurer. The proposed approach provides a general framework that encompasses many reinsurance problems, which we illustrate in several concrete examples, providing alternative proofs to classical optimal reinsurance results, as well as establishing new optimality results, some of which contain optimal treaties that involve external randomness.

我们利用随机化思想和最优运输的证明技术来研究最优再保险问题。我们首先提供了一类问题的条件，这些条件使我们能够描述最优协议的支持，并展示了如何使用这些条件来推断最优协议的形状，将任务简化为具有有限多个约束的优化问题，可以应用标准技术。对于更一般的一类问题，我们将最优再保险问题视为保险人（已知）初始风险暴露与再保险人（未知）最终风险暴露之间的迭代最优运输问题。本文提出的方法提供了一个涵盖许多再保险问题的总体框架，我们用几个具体的例子来说明，提供了经典最优再保险结果的替代证明，并建立了新的最优性结果，其中一些结果包含涉及外部随机性的最优条约。

引用次数: 0

A generalized tail mean-variance model for optimal capital allocation 最优资本配置的广义尾均值-方差模型

IF 1.9 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2025-03-07 DOI: 10.1016/j.insmatheco.2025.03.003

Yang Yang , Guojing Wang , Jing Yao , Hengyue Xie

Capital allocation is a core task in financial and actuarial risk management. Some well-known capital allocation principles, such as the “Euler principle” and the “haircut principle”, have been widely used in the banking and insurance industry. The partitions of allocated capital not only serve as a buffer against potential losses but also provide certain risk pricing and performance measurement to the underlying risks. Dhaene et al. (2012) proposed a unified distance-minimizing capital allocation framework. Their objective function in the optimization only considers the magnitude of the loss function but not the variability. In this paper, we propose a general tail mean-variance (GTMV) model, which employs the Bregman divergences to construct distance-minimizing functions, and takes both the magnitude and the variability into account. We prove the existence and uniqueness of the optimal allocation and provide the general system of equations that characterizes the optimal solution. In this context, we further introduce the Mahalanobis tail mean-variance (MTMV) model and provide explicit distribution-free optimal allocation formulas, which cover many existing results as special cases. In particular, we derive the parametric analytical solutions for multivariate generalized hyperbolic distributed risks. For multivariate log-generalized hyperbolic distributed non-negative risks, we use the convex approximation method to obtain explicit solutions. We present two numerical examples showing the good performance of our optimal capital allocation rules. The first one analyzes the market risk of S&P 500 industry sector indices. We show that our optimal capital allocation framework is applicable to various scenario analyses and provides a performance measure for the indices and the financial market. The other example is based on insurance claims from an Australian insurance company, showing our approximate formulas are both robust and accurate.

资本配置是金融精算风险管理的核心任务。一些著名的资本配置原则，如“欧拉原则”和“理发原则”，已被广泛应用于银行和保险业。分配资本的分割不仅可以作为潜在损失的缓冲，还可以为潜在风险提供一定的风险定价和绩效衡量。Dhaene et al.（2012）提出了统一的距离最小化资本配置框架。他们在优化中的目标函数只考虑损失函数的大小而不考虑可变性。在本文中，我们提出了一个通用的尾部均值方差（GTMV）模型，该模型采用Bregman散度构造距离最小化函数，同时考虑了幅度和可变性。我们证明了最优分配的存在唯一性，并给出了表征最优解的一般方程组。在此背景下，我们进一步引入了马氏尾均值方差（MTMV）模型，并提供了明确的无分布最优分配公式，作为特例涵盖了许多已有的结果。特别地，我们导出了多元广义双曲分布风险的参数解析解。对于多元对数-广义双曲分布非负风险，我们使用凸逼近方法得到显式解。我们给出了两个数值例子，证明了我们的最优资本配置规则的良好性能。第一部分分析了标普500行业板块指数的市场风险。我们的研究表明，我们的最优资本配置框架适用于各种情景分析，并为指数和金融市场提供了一个绩效衡量指标。另一个例子是基于一家澳大利亚保险公司的保险索赔，表明我们的近似公式既稳健又准确。

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引用次数: 0

Pricing insurance contracts with an existing portfolio as background risk 以现有投资组合作为背景风险为保险合同定价

IF 1.9 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2025-03-07 DOI: 10.1016/j.insmatheco.2025.03.001

Corrado De Vecchi , Matthias Scherer

We develop and investigate a premium principle that explicitly takes into account the impact of a new risk on some insurer's existing portfolio. Specifically, we propose the notion of an indifference premium for a new risk conditioned on an existing portfolio acting as background risk. The resulting premium rule, which in our case depends on the joint distribution of the new risk and the existing portfolio, is analyzed in detail with respect to its mathematical properties. In order to underline the differences between our approach and the literature on law-invariant premium rules, special attention is given to the indifference premium behaviour with respect to some well-known dependence concepts. Axiomatic and continuity properties of the proposed indifference premium rule are also investigated. To demonstrate the practical relevance of our approach, we consider a portfolio of exchangeable risks and investigate the role of the portfolio's dimension on the price of a risk to be added. This illustrates the (limits of) diversification benefits under the flexible exchangeability assumption on the joint distribution of a sequence of risks.

我们开发并研究了一项保费原则，该原则明确考虑了新风险对某些保险公司现有投资组合的影响。具体来说，我们提出了以现有投资组合作为背景风险为条件的新风险的无差异溢价的概念。由此产生的溢价规则，在我们的例子中取决于新风险和现有投资组合的联合分布，我们对其数学性质进行了详细分析。为了强调我们的方法与关于定律不变保费规则的文献之间的差异，我们特别关注了一些众所周知的依赖概念的无差异保费行为。研究了所提出的无差异溢价规则的公理化性质和连续性性质。为了证明我们方法的实际相关性，我们考虑了一个可交换风险的投资组合，并研究了投资组合的维度对要增加的风险价格的作用。这说明了在一系列风险共同分布的弹性可交换性假设下，多元化收益的局限性。

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引用次数: 0

The impact of intermediaries on insurance demand and pricing 中介机构对保险需求和定价的影响

IF 1.9 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2025-03-05 DOI: 10.1016/j.insmatheco.2025.03.002

Dongchen Li , Yan Zeng , Yixing Zhao

We study the impact of an independent insurance intermediary on insurance demand and pricing. The intermediary holds a fiduciary duty to an unsophisticated insurance buyer and adopts two remuneration systems: a fee-for-advice system and a commission system. Insurance contracting between the buyer (via the intermediary) and the insurer is formulated as a Stackelberg insurance game. Our analysis yields closed-form expressions for the buyer's equilibrium indemnity and the insurer's equilibrium premium loading. Subsequently, we explore the effects of fiduciary duty and remuneration arrangements on equilibrium strategies and stakeholder welfare, unraveling several economic implications. We find that the phenomenon of over-insuring at high premiums attributes to the deterioration of fiduciary duty. Additionally, our results point to the potential presence of tacit collusion between the intermediary and insurer. Moreover, we observe that there is no consensus among stakeholders regarding the most favored remuneration system in the market.

我们研究了独立保险中介对保险需求和定价的影响。中介人对没有经验的保险买家负有信义责任，并采用两种报酬制度：咨询收费制度和佣金制度。买方（通过中介）与保险人之间的保险契约被表述为一个Stackelberg保险博弈。我们的分析得到了买方均衡赔偿和保险人均衡保费负担的封闭表达式。随后，我们探讨了受托责任和报酬安排对均衡策略和利益相关者福利的影响，揭示了几个经济含义。我们发现，高保费的过度保险现象是信义义务恶化的结果。此外，我们的结果指出中介和保险公司之间存在潜在的默契勾结。此外，我们观察到利益相关者对市场上最受青睐的薪酬制度没有达成共识。

引用次数: 0

Self-protection under Nth-degree risk increase of random unit cost 随机单位成本n度风险增加下的自我保护

IF 1.9 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2025-02-28 DOI: 10.1016/j.insmatheco.2025.02.004

Yongjin Yin, Shengwang Meng

Cost risk, as a type of multiplicative risk, should be given more attention in decision-making issues. Crainich and Menegatti (2021) have studied the effects of introducing random unit cost in self-protection under the four standard self-protection model frameworks. They focus on the case where the unit cost of effort in self-protection changes from certainty (denoted as

c

) to randomness (denoted as

\tilde{c}

) with

E [\tilde{c}] = c

, which represents second-degree risk increase in Ekern (1980). In this paper, we generalize the concept of second-degree risk increase to Nth-degree risk increase and provide sufficient conditions for increasing or decreasing effort in self-protection, which are closely related to the parity of the order of the risk change and decision-maker's higher-order risk attitudes. We use the multiplicative effect and apportionment effect to explain the decision-maker's preference conditions.

成本风险作为一种乘数风险，在决策问题中应受到重视。Crainich和Menegatti（2021）研究了在四种标准自我保护模型框架下引入随机单位成本对自我保护的影响。他们关注的是自我保护的单位努力成本从确定性（表示为c）变为随机性（表示为c ~），其中E[c ~]=c，这在Ekern（1980）中表示二级风险增加。本文将二度风险增加的概念推广到n度风险增加，并提供了增加或减少自我保护努力的充分条件，这与风险变化顺序的宇称性和决策者的高阶风险态度密切相关。我们利用乘数效应和分配效应来解释决策者的偏好条件。

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引用次数: 0

Efficient evaluation of risk allocations 风险分配的有效评估

IF 1.9 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics

Pub Date : 2025-02-27 DOI: 10.1016/j.insmatheco.2025.02.006

Christopher Blier-Wong , Hélène Cossette , Etienne Marceau

Expectations of marginals conditional on the total risk of a portfolio are crucial in risk-sharing and allocation. However, computing these conditional expectations may be challenging, especially in critical cases where the marginal risks have compound distributions or when the risks are dependent. We introduce a generating function method to compute these conditional expectations. We provide efficient algorithms to compute the conditional expectations of marginals given the total risk for a portfolio of risks with lattice-type support. We show that the ordinary generating function of unconditional expected allocations is a function of the multivariate probability generating function of the portfolio. The generating function method allows us to develop recursive and transform-based techniques to compute the unconditional expected allocations. We illustrate our method to large-scale risk-sharing and risk allocation problems, including cases where the marginal risks have compound distributions, where the portfolio is composed of dependent risks, and where the risks have heavy tails, leading in some cases to computational gains of several orders of magnitude. Our approach is useful for risk-sharing in peer-to-peer insurance and risk allocation based on Euler's rule.

以投资组合的总风险为条件的边际预期在风险分担和分配中至关重要。然而，计算这些条件期望可能具有挑战性，特别是在边际风险具有复合分布或风险依赖的关键情况下。我们引入了一种生成函数的方法来计算这些条件期望。我们提供了有效的算法来计算边际的条件期望给定风险组合的总风险与格型支持。我们证明了无条件期望配置的普通生成函数是投资组合的多元概率生成函数的函数。生成函数方法允许我们开发递归和基于转换的技术来计算无条件预期分配。我们将我们的方法用于大规模风险分担和风险分配问题，包括边际风险具有复合分布的情况，其中投资组合由依赖风险组成，以及风险具有重尾的情况，在某些情况下导致几个数量级的计算收益。该方法可用于p2p保险的风险分担和基于欧拉规则的风险分配。

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