Pub Date : 2023-12-19DOI: 10.1007/s13385-023-00374-0
Abstract
We consider an empirical backtesting for the Solvency Capital Required (SCR) under Solvency II. Based on empirical facts that the Basic own Funds (BoF) can be assumed to evolve log-normally and have a much lower volatility than the corresponding equity for our test data, we make a proposal based on Earnings at Risk (EaR) that can be used to reduce the biases from overshooting SCR estimates in a prudential way.
摘要 我们考虑对偿付能力 II 要求的偿付能力资本（SCR）进行实证回溯测试。在我们的测试数据中，基本自有资金（BoF）可被假定为对数正态分布，其波动性远低于相应的权益，基于这一经验事实，我们提出了一项基于风险收益（EaR）的建议，该建议可用于以审慎的方式减少超调 SCR 估计值所产生的偏差。
{"title":"A first look back: model performance under Solvency II","authors":"","doi":"10.1007/s13385-023-00374-0","DOIUrl":"https://doi.org/10.1007/s13385-023-00374-0","url":null,"abstract":"<h3>Abstract</h3> <p>We consider an empirical backtesting for the Solvency Capital Required (SCR) under Solvency II. Based on empirical facts that the Basic own Funds (BoF) can be assumed to evolve log-normally and have a much lower volatility than the corresponding equity for our test data, we make a proposal based on Earnings at Risk (EaR) that can be used to reduce the biases from overshooting SCR estimates in a prudential way.</p>","PeriodicalId":44305,"journal":{"name":"European Actuarial Journal","volume":"1 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138741318","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-07DOI: 10.1007/s13385-023-00371-3
Moritz Hanika
COVID-19 has affected mortality rates and financial markets worldwide. Against this background, we perform a COVID-19 stress test for life insurance, considering a joint financial and mortality shock, to evaluate the effectiveness of different risk mitigation strategies. Specifically, we conduct a model-based simulation analysis of a life insurer selling annuities and term life insurances. The analysis includes stress scenarios that are calibrated to observations during the first year of the COVID-19 pandemic. We also consider new business and study the risk situation under three different risk mitigation strategies observed in practice as an immediate response to the pandemic: stopping sales, increasing premiums, or adjusting investment strategies. Results show that a life insurer’s risk situation is mainly affected in the short term, selling annuities (in addition to term life insurance) immunizes against the mortality shock, and the immediate use of risk mitigation strategies can help reduce the negative impact.
{"title":"A COVID-19 stress test for life insurance: insights into the effectiveness of different risk mitigation strategies","authors":"Moritz Hanika","doi":"10.1007/s13385-023-00371-3","DOIUrl":"https://doi.org/10.1007/s13385-023-00371-3","url":null,"abstract":"<p>COVID-19 has affected mortality rates and financial markets worldwide. Against this background, we perform a COVID-19 stress test for life insurance, considering a joint financial and mortality shock, to evaluate the effectiveness of different risk mitigation strategies. Specifically, we conduct a model-based simulation analysis of a life insurer selling annuities and term life insurances. The analysis includes stress scenarios that are calibrated to observations during the first year of the COVID-19 pandemic. We also consider new business and study the risk situation under three different risk mitigation strategies observed in practice as an immediate response to the pandemic: stopping sales, increasing premiums, or adjusting investment strategies. Results show that a life insurer’s risk situation is mainly affected in the short term, selling annuities (in addition to term life insurance) immunizes against the mortality shock, and the immediate use of risk mitigation strategies can help reduce the negative impact.</p>","PeriodicalId":44305,"journal":{"name":"European Actuarial Journal","volume":"283 1 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138579318","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-14DOI: 10.1007/s13385-023-00369-x
Matthias Reitzner
Abstract In Germany, a trend for decreasing mortality probabilities has been observed in the last 50 years, yielding an increasing life expectancy. The German Actuarial Association DAV offers a standard method for modeling this longevity trend in calculations concerning life insurance by using the life table DAV 2004R. In this note it is investigated, whether or to which extent the longevity function of the DAV 2004R can be used for calculating the expected total number of deaths in Germany.
{"title":"Longevity trend in Germany","authors":"Matthias Reitzner","doi":"10.1007/s13385-023-00369-x","DOIUrl":"https://doi.org/10.1007/s13385-023-00369-x","url":null,"abstract":"Abstract In Germany, a trend for decreasing mortality probabilities has been observed in the last 50 years, yielding an increasing life expectancy. The German Actuarial Association DAV offers a standard method for modeling this longevity trend in calculations concerning life insurance by using the life table DAV 2004R. In this note it is investigated, whether or to which extent the longevity function of the DAV 2004R can be used for calculating the expected total number of deaths in Germany.","PeriodicalId":44305,"journal":{"name":"European Actuarial Journal","volume":"42 12","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134954586","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-08DOI: 10.1007/s13385-023-00370-4
Jean-François Bégin, Nikhil Kapoor, Barbara Sanders
{"title":"A new approximation of annuity prices for age–period–cohort models","authors":"Jean-François Bégin, Nikhil Kapoor, Barbara Sanders","doi":"10.1007/s13385-023-00370-4","DOIUrl":"https://doi.org/10.1007/s13385-023-00370-4","url":null,"abstract":"","PeriodicalId":44305,"journal":{"name":"European Actuarial Journal","volume":"62 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135341911","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-08DOI: 10.1007/s13385-023-00367-z
Mathias Lindholm, Ronald Richman, Andreas Tsanakas, Mario V. Wüthrich
Abstract In applications of predictive modeling, such as insurance pricing, indirect or proxy discrimination is an issue of major concern. Namely, there exists the possibility that protected policyholder characteristics are implicitly inferred from non-protected ones by predictive models and are thus having an undesirable (and possibly illegal) impact on prices. A technical solution to this problem relies on building a best-estimate model using all policyholder characteristics (including protected ones) and then averaging out the protected characteristics for calculating individual prices. However, such an approach requires full knowledge of policyholders’ protected characteristics, which may in itself be problematic. Here, we address this issue by using a multi-task neural network architecture for claim predictions, which can be trained using only partial information on protected characteristics and produces prices that are free from proxy discrimination. We demonstrate the proposed method on both synthetic data and a real-world motor claims dataset, in which proxy discrimination can be observed. In both examples we find that the predictive accuracy of the multi-task network is comparable to a conventional feed-forward neural network, when the protected information is available for at least half of the insurance policies. However, the multi-task network has superior performance in the case when the protected information is known for less than half of the insurance policyholders.
{"title":"A multi-task network approach for calculating discrimination-free insurance prices","authors":"Mathias Lindholm, Ronald Richman, Andreas Tsanakas, Mario V. Wüthrich","doi":"10.1007/s13385-023-00367-z","DOIUrl":"https://doi.org/10.1007/s13385-023-00367-z","url":null,"abstract":"Abstract In applications of predictive modeling, such as insurance pricing, indirect or proxy discrimination is an issue of major concern. Namely, there exists the possibility that protected policyholder characteristics are implicitly inferred from non-protected ones by predictive models and are thus having an undesirable (and possibly illegal) impact on prices. A technical solution to this problem relies on building a best-estimate model using all policyholder characteristics (including protected ones) and then averaging out the protected characteristics for calculating individual prices. However, such an approach requires full knowledge of policyholders’ protected characteristics, which may in itself be problematic. Here, we address this issue by using a multi-task neural network architecture for claim predictions, which can be trained using only partial information on protected characteristics and produces prices that are free from proxy discrimination. We demonstrate the proposed method on both synthetic data and a real-world motor claims dataset, in which proxy discrimination can be observed. In both examples we find that the predictive accuracy of the multi-task network is comparable to a conventional feed-forward neural network, when the protected information is available for at least half of the insurance policies. However, the multi-task network has superior performance in the case when the protected information is known for less than half of the insurance policyholders.","PeriodicalId":44305,"journal":{"name":"European Actuarial Journal","volume":" 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135340772","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-01DOI: 10.1007/s13385-023-00362-4
Yevhen Havrylenko, Julia Heger
Abstract The quality of generalized linear models (GLMs), frequently used by insurance companies, depends on the choice of interacting variables. The search for interactions is time-consuming, especially for data sets with a large number of variables, depends much on expert judgement of actuaries, and often relies on visual performance indicators. Therefore, we present an approach to automating the process of finding interactions that should be added to GLMs to improve their predictive power. Our approach relies on neural networks and a model-specific interaction detection method, which is computationally faster than the traditionally used methods like Friedman’s H-Statistic or SHAP values. In numerical studies, we provide the results of our approach on artificially generated data as well as open-source data.
{"title":"Detection of interacting variables for generalized linear models via neural networks","authors":"Yevhen Havrylenko, Julia Heger","doi":"10.1007/s13385-023-00362-4","DOIUrl":"https://doi.org/10.1007/s13385-023-00362-4","url":null,"abstract":"Abstract The quality of generalized linear models (GLMs), frequently used by insurance companies, depends on the choice of interacting variables. The search for interactions is time-consuming, especially for data sets with a large number of variables, depends much on expert judgement of actuaries, and often relies on visual performance indicators. Therefore, we present an approach to automating the process of finding interactions that should be added to GLMs to improve their predictive power. Our approach relies on neural networks and a model-specific interaction detection method, which is computationally faster than the traditionally used methods like Friedman’s H-Statistic or SHAP values. In numerical studies, we provide the results of our approach on artificially generated data as well as open-source data.","PeriodicalId":44305,"journal":{"name":"European Actuarial Journal","volume":"41 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135325630","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-29DOI: 10.1007/s13385-023-00365-1
Matteo Cattaneo, Ron S. Kenett, Elisa Luciano
{"title":"Adversarial AI in insurance: an overview","authors":"Matteo Cattaneo, Ron S. Kenett, Elisa Luciano","doi":"10.1007/s13385-023-00365-1","DOIUrl":"https://doi.org/10.1007/s13385-023-00365-1","url":null,"abstract":"","PeriodicalId":44305,"journal":{"name":"European Actuarial Journal","volume":"109 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136134588","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-20DOI: 10.1007/s13385-023-00364-2
Nadine Gatzert, Onur Özdil
Abstract The aim of this paper is to examine the impact of dependencies between climate transition and physical risks on the default probability and profitability of a non-life insurer focusing on the scenario of a delayed and sudden transition. Toward this end, we suggest a simplified modeling approach for scenario analyses for climate risks affecting assets and liabilities, taking into account potential nonlinear dependence structures. Our results show that dependencies on the liability side and between assets and liabilities in the context of physical-transition scenarios can have a significant impact, particularly on the default risk of a non-life insurer. We additionally analyze the mitigating effects of stop loss reinsurance and risk-adjusted pricing, which—if implementable—seem to be an effective risk management measure against physical climate risks in particular.
{"title":"The impact of dependencies between climate risks on the asset and liability side of non-life insurers","authors":"Nadine Gatzert, Onur Özdil","doi":"10.1007/s13385-023-00364-2","DOIUrl":"https://doi.org/10.1007/s13385-023-00364-2","url":null,"abstract":"Abstract The aim of this paper is to examine the impact of dependencies between climate transition and physical risks on the default probability and profitability of a non-life insurer focusing on the scenario of a delayed and sudden transition. Toward this end, we suggest a simplified modeling approach for scenario analyses for climate risks affecting assets and liabilities, taking into account potential nonlinear dependence structures. Our results show that dependencies on the liability side and between assets and liabilities in the context of physical-transition scenarios can have a significant impact, particularly on the default risk of a non-life insurer. We additionally analyze the mitigating effects of stop loss reinsurance and risk-adjusted pricing, which—if implementable—seem to be an effective risk management measure against physical climate risks in particular.","PeriodicalId":44305,"journal":{"name":"European Actuarial Journal","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135571215","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-07DOI: 10.1007/s13385-023-00363-3
Theis Bathke, Marcus C. Christiansen
Abstract Forward transition rates were originally introduced with the aim to evaluate life insurance liabilities market-consistently. While this idea turned out to have its limitations, recent literature repurposes forward transition rates as a tool for avoiding Markov assumptions in the calculation of life insurance reserves. While life insurance reserves are some form of conditional first-order moments, the calculation of conditional second-order moments needs an extension of the forward transition rate concept from one dimension to two dimensions. Two-dimensional forward transition rates are also needed for the calculation of path-dependent life insurance cash-flows as they occur upon contract modifications. Forward transition rates are designed for doing prospective calculations, and by a time-symmetric definition of so-called backward transition rates one can do retrospective calculations.
{"title":"Two-dimensional forward and backward transition rates","authors":"Theis Bathke, Marcus C. Christiansen","doi":"10.1007/s13385-023-00363-3","DOIUrl":"https://doi.org/10.1007/s13385-023-00363-3","url":null,"abstract":"Abstract Forward transition rates were originally introduced with the aim to evaluate life insurance liabilities market-consistently. While this idea turned out to have its limitations, recent literature repurposes forward transition rates as a tool for avoiding Markov assumptions in the calculation of life insurance reserves. While life insurance reserves are some form of conditional first-order moments, the calculation of conditional second-order moments needs an extension of the forward transition rate concept from one dimension to two dimensions. Two-dimensional forward transition rates are also needed for the calculation of path-dependent life insurance cash-flows as they occur upon contract modifications. Forward transition rates are designed for doing prospective calculations, and by a time-symmetric definition of so-called backward transition rates one can do retrospective calculations.","PeriodicalId":44305,"journal":{"name":"European Actuarial Journal","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135254751","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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