Pub Date : 2023-09-07DOI: 10.1080/03461238.2023.2255399
Jingyi Cao, Dongchen Li, Virginia R. Young, Bin Zou
{"title":"Stackelberg reinsurance chain under model ambiguity","authors":"Jingyi Cao, Dongchen Li, Virginia R. Young, Bin Zou","doi":"10.1080/03461238.2023.2255399","DOIUrl":"https://doi.org/10.1080/03461238.2023.2255399","url":null,"abstract":"","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78516253","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}
Pub Date : 2023-08-17DOI: 10.1080/03461238.2023.2246743
Mario V. Wüthrich, Johanna Ziegel
Insurance pricing systems should fulfill the auto-calibration property to ensure that there is no systematic cross-financing between different price cohorts. Often, regression models are not auto-calibrated. We propose to apply isotonic recalibration to a given regression model to restore auto-calibration. Our main result proves that under a low signal-to-noise ratio, this isotonic recalibration step leads to an explainable pricing system because the resulting isotonically recalibrated regression function has a low complexity.
{"title":"Isotonic recalibration under a low signal-to-noise ratio","authors":"Mario V. Wüthrich, Johanna Ziegel","doi":"10.1080/03461238.2023.2246743","DOIUrl":"https://doi.org/10.1080/03461238.2023.2246743","url":null,"abstract":"Insurance pricing systems should fulfill the auto-calibration property to ensure that there is no systematic cross-financing between different price cohorts. Often, regression models are not auto-calibrated. We propose to apply isotonic recalibration to a given regression model to restore auto-calibration. Our main result proves that under a low signal-to-noise ratio, this isotonic recalibration step leads to an explainable pricing system because the resulting isotonically recalibrated regression function has a low complexity.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136337408","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}
Pub Date : 2023-08-09DOI: 10.1080/03461238.2022.2145233
Jingyi Cao, Dongchen Li, V. Young, B. Zou
We solve a Stackelberg differential game between a buyer and a seller of insurance policies, in which both parties are ambiguous about the insurable loss. Both the buyer and seller maximize their expected wealth, plus a penalty term that reflects ambiguity, over an exogenous random horizon. Under a mean-variance premium principle and a general divergence that measures the players' ambiguity, we obtain the Stackelberg equilibrium semi-explicitly. Our main results are that the optimal variance loading equals zero and that the seller's robust optimal premium rule equals the net premium under the buyer's optimally distorted probability. Both of these important results generalize those we obtained in [Cao, J., Li, D., Young, V. R. & Zou, B. (2022). Stackelberg differential game for insurance under model ambiguity. Insurance: Mathematics and Economics, 106, 128–145.] under squared-error divergence.
本文解决了保险买卖双方对保险损失不明确的Stackelberg微分博弈问题。在外生随机视界上，买卖双方都最大化了他们的预期财富，加上一个反映模糊性的惩罚条款。在平均方差溢价原则和衡量参与者模糊性的一般散度下，我们得到了半显式的Stackelberg均衡。我们的主要结果是最优方差负荷等于零，卖方的鲁棒最优溢价规则等于买方最优扭曲概率下的净溢价。这两个重要的结果推广了我们在[Cao, J.， Li, D.， Young, V. R. & Zou, B.(2022)]中得到的结果。模型模糊下保险的Stackelberg微分对策。保险:数学与经济，106,128-145。在平方误差散度下。
{"title":"Stackelberg differential game for insurance under model ambiguity: general divergence","authors":"Jingyi Cao, Dongchen Li, V. Young, B. Zou","doi":"10.1080/03461238.2022.2145233","DOIUrl":"https://doi.org/10.1080/03461238.2022.2145233","url":null,"abstract":"We solve a Stackelberg differential game between a buyer and a seller of insurance policies, in which both parties are ambiguous about the insurable loss. Both the buyer and seller maximize their expected wealth, plus a penalty term that reflects ambiguity, over an exogenous random horizon. Under a mean-variance premium principle and a general divergence that measures the players' ambiguity, we obtain the Stackelberg equilibrium semi-explicitly. Our main results are that the optimal variance loading equals zero and that the seller's robust optimal premium rule equals the net premium under the buyer's optimally distorted probability. Both of these important results generalize those we obtained in [Cao, J., Li, D., Young, V. R. & Zou, B. (2022). Stackelberg differential game for insurance under model ambiguity. Insurance: Mathematics and Economics, 106, 128–145.] under squared-error divergence.","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73176778","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}
Pub Date : 2023-07-26DOI: 10.1080/03461238.2023.2239533
Oma Coke, Mario Ghossoub, Mi Zhu
{"title":"Pareto-optimal insurance with an upper limit on the insurer's exposure","authors":"Oma Coke, Mario Ghossoub, Mi Zhu","doi":"10.1080/03461238.2023.2239533","DOIUrl":"https://doi.org/10.1080/03461238.2023.2239533","url":null,"abstract":"","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81855767","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}
Pub Date : 2023-07-13DOI: 10.1080/03461238.2023.2234914
Tsz Chai Fung, Himchan Jeong, George Tzougas
Considerations of both the heavy-tail phenomenon and multi-modality of a claim severity distribution have been challenging in the actuarial literature and practices. In this article, we develop a novel class of soft splicing models that bridges the gap between pre-existing methods for handling the issues above. The proposed method is flexible enough to incorporate tail-heaviness and multi-modality with computational efficiency and nests finite mixture models and splicing models as its special and/or limiting cases. The soft splicing model is also more robust in extrapolating the tail-heaviness of distribution subject to model contamination. According to simulation studies and real insurance claim data analyses, it is shown that the proposed soft splicing model provides superior goodness-of-fit and more accurate estimates of tail risk measures than both finite mixture and composite models.
{"title":"Soft splicing model: bridging the gap between composite model and finite mixture model","authors":"Tsz Chai Fung, Himchan Jeong, George Tzougas","doi":"10.1080/03461238.2023.2234914","DOIUrl":"https://doi.org/10.1080/03461238.2023.2234914","url":null,"abstract":"<p>Considerations of both the heavy-tail phenomenon and multi-modality of a claim severity distribution have been challenging in the actuarial literature and practices. In this article, we develop a novel class of soft splicing models that bridges the gap between pre-existing methods for handling the issues above. The proposed method is flexible enough to incorporate tail-heaviness and multi-modality with computational efficiency and nests finite mixture models and splicing models as its special and/or limiting cases. The soft splicing model is also more robust in extrapolating the tail-heaviness of distribution subject to model contamination. According to simulation studies and real insurance claim data analyses, it is shown that the proposed soft splicing model provides superior goodness-of-fit and more accurate estimates of tail risk measures than both finite mixture and composite models.</p>","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138528630","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}
Pub Date : 2023-07-12DOI: 10.1080/03461238.2023.2232816
Jackie Li
{"title":"Bayesian joint modelling of life expectancy and healthy life expectancy and valuation of retirement village contract","authors":"Jackie Li","doi":"10.1080/03461238.2023.2232816","DOIUrl":"https://doi.org/10.1080/03461238.2023.2232816","url":null,"abstract":"","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73997702","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}
Pub Date : 2023-06-07DOI: 10.1080/03461238.2023.2220219
Xia Han, D. Landriault, Danping Li
{"title":"Optimal reinsurance contract in a Stackelberg game framework: a view of social planner","authors":"Xia Han, D. Landriault, Danping Li","doi":"10.1080/03461238.2023.2220219","DOIUrl":"https://doi.org/10.1080/03461238.2023.2220219","url":null,"abstract":"","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78981965","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}
Pub Date : 2023-05-12DOI: 10.1080/03461238.2023.2209858
Yichun Chi, Yuxia Huang, K. S. Tan
{"title":"An insurer's optimal strategy towards a new independent business","authors":"Yichun Chi, Yuxia Huang, K. S. Tan","doi":"10.1080/03461238.2023.2209858","DOIUrl":"https://doi.org/10.1080/03461238.2023.2209858","url":null,"abstract":"","PeriodicalId":49572,"journal":{"name":"Scandinavian Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72540471","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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