Mathilde Bourget, Mathieu Boudreault, D. Carozza, Jérémie Boudreault, Sébastien Raymond
There is mounting pressure on (re)insurers to quantify the impacts of climate change, notably on the frequency and severity of claims due to weather events such as flooding. This is however a very challenging task for (re)insurers as it requires modeling at the scale of a portfolio and at a high enough spatial resolution to incorporate local climate change effects. In this paper, we introduce a data science approach to climate change risk assessment of pluvial flooding for insurance portfolios over Canada and the United States (US). The underlying flood occurrence model quantifies the financial impacts of short-term (12–48 h) precipitation dynamics over the present (2010–2030) and future climate (2040–2060) by leveraging statistical/machine learning and regional climate models. The flood occurrence model is designed for applications that do not require street-level precision as is often the case for scenario and trend analyses. It is applied at the full scale of Canada and the US over 10–25 km grids. Our analyses show that climate change and urbanization will typically increase losses over Canada and the US, while impacts are strongly heterogeneous from one state or province to another, or even within a territory. Portfolio applications highlight the importance for a (re)insurer to differentiate between future changes in hazard and exposure, as the latter may magnify or attenuate the impacts of climate change on losses.
{"title":"A data science approach to climate change risk assessment applied to pluvial flood occurrences for the United States and Canada","authors":"Mathilde Bourget, Mathieu Boudreault, D. Carozza, Jérémie Boudreault, Sébastien Raymond","doi":"10.1017/asb.2024.19","DOIUrl":"https://doi.org/10.1017/asb.2024.19","url":null,"abstract":"\u0000 There is mounting pressure on (re)insurers to quantify the impacts of climate change, notably on the frequency and severity of claims due to weather events such as flooding. This is however a very challenging task for (re)insurers as it requires modeling at the scale of a portfolio and at a high enough spatial resolution to incorporate local climate change effects. In this paper, we introduce a data science approach to climate change risk assessment of pluvial flooding for insurance portfolios over Canada and the United States (US). The underlying flood occurrence model quantifies the financial impacts of short-term (12–48 h) precipitation dynamics over the present (2010–2030) and future climate (2040–2060) by leveraging statistical/machine learning and regional climate models. The flood occurrence model is designed for applications that do not require street-level precision as is often the case for scenario and trend analyses. It is applied at the full scale of Canada and the US over 10–25 km grids. Our analyses show that climate change and urbanization will typically increase losses over Canada and the US, while impacts are strongly heterogeneous from one state or province to another, or even within a territory. Portfolio applications highlight the importance for a (re)insurer to differentiate between future changes in hazard and exposure, as the latter may magnify or attenuate the impacts of climate change on losses.","PeriodicalId":8617,"journal":{"name":"ASTIN Bulletin","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141115062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The theory of utility is a well-known method of constructing insurance premiums (see e.g., Newton et al. (1986) Actuarial Mathematics. Itasca, Illinois: The Society of Actuaries.). Furman and Zitikis ((2008) Insurance: Mathematics and Economics, 42, 459–465.) proposed an alternative method using the mean value of a weighted random variable. According to this approach, for various choices of weighting, popular premiums such as net premium, modified variance premium, Esscher premium, and Kamps premium are obtained. On the other hand, some premiums cannot be obtained with this method, such as the premium of the exponential principle. In this paper, we provide a complementary theory by introducing a family of unimodal weighted distributions for which the mode is a premium principle.
效用理论是一种著名的保险费计算方法（参见 Newton 等人 (1986) Actuarial Mathematics.伊利诺斯州伊塔斯卡市：The Society of Actuaries.）。Furman 和 Zitikis（（2008 年）《保险：数学与经济学》，42，459-465）提出了一种使用加权随机变量平均值的替代方法。根据这种方法，对于不同的权重选择，可以得到常用的保费，如净保费、修正方差保费、埃舍尔保费和坎普斯保费。另一方面，有些溢价无法用这种方法求得，如指数原理溢价。在本文中，我们引入了一个单模态加权分布族，为其提供了一种补充理论，该分布族的模态是溢价原理。
{"title":"Calculating premium principles from the mode of a unimodal weighted distribution","authors":"Georgios Psarrakos","doi":"10.1017/asb.2024.18","DOIUrl":"https://doi.org/10.1017/asb.2024.18","url":null,"abstract":"\u0000 The theory of utility is a well-known method of constructing insurance premiums (see e.g., Newton et al. (1986) Actuarial Mathematics. Itasca, Illinois: The Society of Actuaries.). Furman and Zitikis ((2008) Insurance: Mathematics and Economics, 42, 459–465.) proposed an alternative method using the mean value of a weighted random variable. According to this approach, for various choices of weighting, popular premiums such as net premium, modified variance premium, Esscher premium, and Kamps premium are obtained. On the other hand, some premiums cannot be obtained with this method, such as the premium of the exponential principle. In this paper, we provide a complementary theory by introducing a family of unimodal weighted distributions for which the mode is a premium principle.","PeriodicalId":8617,"journal":{"name":"ASTIN Bulletin","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140973910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Arianna Vallarino, Giovanni Rabitti, Amir Khorrami Chokami
Abstract The ratemaking process is a key issue in insurance pricing. It consists in pooling together policyholders with similar risk profiles into rating classes and assigning the same premium for policyholders in the same class. In actuarial practice, rating systems are typically not based on all risk factors but rather only some of factors are selected to construct the rating classes. The objective of this study is to investigate the selection of risk factors in order to construct rating classes that exhibit maximum internal homogeneity. For this selection, we adopt the Shapley effects from global sensitivity analysis. While these sensitivity indices are used for model interpretability, we apply them to construct rating classes. We provide a new strategy to estimate them, and we connect them to the intra-class variability and heterogeneity of the rating classes. To verify the appropriateness of our procedure, we introduce a measure of heterogeneity specifically designed to compare rating systems with a different number of classes. Using a well-known car insurance dataset, we show that the rating system constructed with the Shapley effects is the one minimizing this heterogeneity measure.
{"title":"Construction of rating systems using global sensitivity analysis: A numerical investigation","authors":"Arianna Vallarino, Giovanni Rabitti, Amir Khorrami Chokami","doi":"10.1017/asb.2023.34","DOIUrl":"https://doi.org/10.1017/asb.2023.34","url":null,"abstract":"Abstract The ratemaking process is a key issue in insurance pricing. It consists in pooling together policyholders with similar risk profiles into rating classes and assigning the same premium for policyholders in the same class. In actuarial practice, rating systems are typically not based on all risk factors but rather only some of factors are selected to construct the rating classes. The objective of this study is to investigate the selection of risk factors in order to construct rating classes that exhibit maximum internal homogeneity. For this selection, we adopt the Shapley effects from global sensitivity analysis. While these sensitivity indices are used for model interpretability, we apply them to construct rating classes. We provide a new strategy to estimate them, and we connect them to the intra-class variability and heterogeneity of the rating classes. To verify the appropriateness of our procedure, we introduce a measure of heterogeneity specifically designed to compare rating systems with a different number of classes. Using a well-known car insurance dataset, we show that the rating system constructed with the Shapley effects is the one minimizing this heterogeneity measure.","PeriodicalId":8617,"journal":{"name":"ASTIN Bulletin","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135730870","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this paper, we study the optimal VIX-linked target benefit (TB) pension design. By applying the dynamic programming approach, we show the optimal risk-sharing structure for the benefit payment exhibits a linear form that consists of three components: (1) a model-robust performance adjustment, (2) a counter-cyclical volatility adjustment that depends on the VIX index, and (3) a TB level that is partially indexed to the cost-of-living adjustment. Differences between our results and the previous literature are highlighted via both theoretical derivations and numerical illustrations.
{"title":"Optimal VIX-linked structure for the target benefit pension plan","authors":"Lv Chen, Danping Li, Yumin Wang, Xiaobai Zhu","doi":"10.1017/asb.2023.33","DOIUrl":"https://doi.org/10.1017/asb.2023.33","url":null,"abstract":"Abstract In this paper, we study the optimal VIX-linked target benefit (TB) pension design. By applying the dynamic programming approach, we show the optimal risk-sharing structure for the benefit payment exhibits a linear form that consists of three components: (1) a model-robust performance adjustment, (2) a counter-cyclical volatility adjustment that depends on the VIX index, and (3) a TB level that is partially indexed to the cost-of-living adjustment. Differences between our results and the previous literature are highlighted via both theoretical derivations and numerical illustrations.","PeriodicalId":8617,"journal":{"name":"ASTIN Bulletin","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135883626","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We study the optimal investment-reinsurance problem in the context of equity-linked insurance products. Such products often have a capital guarantee, which can motivate insurers to purchase reinsurance. Since a reinsurance contract implies an interaction between the insurer and the reinsurer, we model the optimization problem as a Stackelberg game. The reinsurer is the leader in the game and maximizes its expected utility by selecting its optimal investment strategy and a safety loading in the reinsurance contract it offers to the insurer. The reinsurer can assess how the insurer will rationally react on each action of the reinsurer. The insurance company is the follower and maximizes its expected utility by choosing its investment strategy and the amount of reinsurance the company purchases at the price offered by the reinsurer. In this game, we derive the Stackelberg equilibrium for general utility functions. For power utility functions, we calculate the equilibrium explicitly and find that the reinsurer selects the largest reinsurance premium such that the insurer may still buy the maximal amount of reinsurance. Since in the equilibrium the insurer is indifferent in the amount of reinsurance, in practice, the reinsurer should consider charging a smaller reinsurance premium than the equilibrium one. Therefore, we propose several criteria for choosing such a discount rate and investigate its wealth-equivalent impact on the expected utility of each party.
{"title":"Risk sharing in equity-linked insurance products: Stackelberg equilibrium between an insurer and a reinsurer","authors":"Yevhen Havrylenko, Maria Hinken, Rudi Zagst","doi":"10.1017/asb.2023.32","DOIUrl":"https://doi.org/10.1017/asb.2023.32","url":null,"abstract":"Abstract We study the optimal investment-reinsurance problem in the context of equity-linked insurance products. Such products often have a capital guarantee, which can motivate insurers to purchase reinsurance. Since a reinsurance contract implies an interaction between the insurer and the reinsurer, we model the optimization problem as a Stackelberg game. The reinsurer is the leader in the game and maximizes its expected utility by selecting its optimal investment strategy and a safety loading in the reinsurance contract it offers to the insurer. The reinsurer can assess how the insurer will rationally react on each action of the reinsurer. The insurance company is the follower and maximizes its expected utility by choosing its investment strategy and the amount of reinsurance the company purchases at the price offered by the reinsurer. In this game, we derive the Stackelberg equilibrium for general utility functions. For power utility functions, we calculate the equilibrium explicitly and find that the reinsurer selects the largest reinsurance premium such that the insurer may still buy the maximal amount of reinsurance. Since in the equilibrium the insurer is indifferent in the amount of reinsurance, in practice, the reinsurer should consider charging a smaller reinsurance premium than the equilibrium one. Therefore, we propose several criteria for choosing such a discount rate and investigate its wealth-equivalent impact on the expected utility of each party.","PeriodicalId":8617,"journal":{"name":"ASTIN Bulletin","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135885032","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
{"title":"ASB volume 53 issue 3 Cover and Front matter","authors":"","doi":"10.1017/asb.2023.30","DOIUrl":"https://doi.org/10.1017/asb.2023.30","url":null,"abstract":"An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.","PeriodicalId":8617,"journal":{"name":"ASTIN Bulletin","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135304915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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