Pub Date : 2024-01-04DOI: 10.1017/s1748499523000258
Rong He, Zhuo Jin, Johnny Siu-Hang Li
This paper provides a review of cyber risk research accomplished in different disciplines, with a primary goal to aid researchers in the field of insurance and actuarial science in identifying potential research gaps as well as leveraging useful models and techniques that have been considered in the literature. We highlight the recent advancements in cyber risk prediction, modeling, management, and insurance achieved in different domains including computer engineering, actuarial science, and business studies. The surveyed works are classified according to their respective modeling approaches, allowing readers to more easily compare the technical aspects of the surveyed works and spot out research gaps based on the research tools of their liking. We conclude this paper with a summary of possible research directions that are identified from the review.
{"title":"Modeling and management of cyber risk: a cross-disciplinary review","authors":"Rong He, Zhuo Jin, Johnny Siu-Hang Li","doi":"10.1017/s1748499523000258","DOIUrl":"https://doi.org/10.1017/s1748499523000258","url":null,"abstract":"This paper provides a review of cyber risk research accomplished in different disciplines, with a primary goal to aid researchers in the field of insurance and actuarial science in identifying potential research gaps as well as leveraging useful models and techniques that have been considered in the literature. We highlight the recent advancements in cyber risk prediction, modeling, management, and insurance achieved in different domains including computer engineering, actuarial science, and business studies. The surveyed works are classified according to their respective modeling approaches, allowing readers to more easily compare the technical aspects of the surveyed works and spot out research gaps based on the research tools of their liking. We conclude this paper with a summary of possible research directions that are identified from the review.","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139373242","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 : 2023-11-28DOI: 10.1017/s1748499523000210
Daniel J. Crispin
Calculation of loss scenarios is a fundamental requirement of simulation-based capital models and these are commonly approximated. Within a life insurance setting, a loss scenario may involve an asset-liability optimization. When cashflows and asset values are dependent on only a small number of risk factor components, low-dimensional approximations may be used as inputs into the optimization and resulting in loss approximation. By considering these loss approximations as perturbations of linear optimization problems, approximation errors in loss scenarios can be bounded to first order and attributed to specific proxies. This attribution creates a mechanism for approximation improvements and for the eventual elimination of approximation errors in capital estimates through targeted exact computation. The results are demonstrated through a stylized worked example and corresponding numerical study. Advances in error analysis of proxy models enhance confidence in capital estimates. Beyond error analysis, the presented methods can be applied to general sensitivity analysis and the calculation of risk.
{"title":"Error propagation and attribution in simulation-based capital models","authors":"Daniel J. Crispin","doi":"10.1017/s1748499523000210","DOIUrl":"https://doi.org/10.1017/s1748499523000210","url":null,"abstract":"Calculation of loss scenarios is a fundamental requirement of simulation-based capital models and these are commonly approximated. Within a life insurance setting, a loss scenario may involve an asset-liability optimization. When cashflows and asset values are dependent on only a small number of risk factor components, low-dimensional approximations may be used as inputs into the optimization and resulting in loss approximation. By considering these loss approximations as perturbations of linear optimization problems, approximation errors in loss scenarios can be bounded to first order and attributed to specific proxies. This attribution creates a mechanism for approximation improvements and for the eventual elimination of approximation errors in capital estimates through targeted exact computation. The results are demonstrated through a stylized worked example and corresponding numerical study. Advances in error analysis of proxy models enhance confidence in capital estimates. Beyond error analysis, the presented methods can be applied to general sensitivity analysis and the calculation of risk.","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138509562","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 : 2023-10-31DOI: 10.1017/s1748499523000234
Stefano Cotticelli, Nino Savelli
Abstract For some time now, Solvency II requires that insurance companies calculate minimum capital requirements to face the risk of insolvency, either in accordance with the Standard Formula or using a full or partial Internal Model. An Internal Model must be based on a market-consistent valuation of assets and liabilities at a 1-year time span, where a real-world probabilistic structure is used for the first year of projection. In this paper, we describe the major risks of a non-life insurance company, i.e. the non-life underwriting risk and market risk, and their interactions, focusing on the non-life premium risk, equity risk, and interest rate risk. This analysis is made using some well-known stochastic models in the financial-actuarial literature and practical insurance business, i.e. the Collective Risk Model for non-life premium risk, the Geometric Brownian Motion for equity risk, and a real-world version of the G2++ Model for interest rate risk, where parameters are calibrated on current and real market data. Finally, we illustrate a case study on a single-line and a multi-line insurance company in order to see how the risk drivers behave in both a stand-alone and an aggregate framework.
{"title":"Capital requirement modeling for market and non-life premium risk in a dynamic insurance portfolio","authors":"Stefano Cotticelli, Nino Savelli","doi":"10.1017/s1748499523000234","DOIUrl":"https://doi.org/10.1017/s1748499523000234","url":null,"abstract":"Abstract For some time now, Solvency II requires that insurance companies calculate minimum capital requirements to face the risk of insolvency, either in accordance with the Standard Formula or using a full or partial Internal Model. An Internal Model must be based on a market-consistent valuation of assets and liabilities at a 1-year time span, where a real-world probabilistic structure is used for the first year of projection. In this paper, we describe the major risks of a non-life insurance company, i.e. the non-life underwriting risk and market risk, and their interactions, focusing on the non-life premium risk, equity risk, and interest rate risk. This analysis is made using some well-known stochastic models in the financial-actuarial literature and practical insurance business, i.e. the Collective Risk Model for non-life premium risk, the Geometric Brownian Motion for equity risk, and a real-world version of the G2++ Model for interest rate risk, where parameters are calibrated on current and real market data. Finally, we illustrate a case study on a single-line and a multi-line insurance company in order to see how the risk drivers behave in both a stand-alone and an aggregate framework.","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135871969","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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{"title":"A changing climate for actuarial science","authors":"Mathieu Boudreault, Iain Clacher, Johnny Siu-Hang Li, Catherine Pigott, Rui Zhou","doi":"10.1017/s1748499523000222","DOIUrl":"https://doi.org/10.1017/s1748499523000222","url":null,"abstract":"An abstract is not available for this content. As you have access to this content, full HTML content is provided on this page. A PDF of this content is also available in through the ‘Save PDF’ action button.","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135220382","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 : 2023-09-21DOI: 10.1017/s1748499523000192
Giovani Gracianti, Rui Zhou, Johnny Siu-Hang Li, Xueyuan Wu
Abstract Wind derivatives are financial instruments designed to mitigate losses caused by adverse wind conditions. With the rapid growth of wind power capacity due to efforts to reduce carbon emissions, the demand for wind derivatives to manage uncertainty in wind power production is expected to increase. However, existing wind derivative literature often assumes normally distributed wind speed, despite the presence of skewness and leptokurtosis in historical wind speed data. This paper investigates how the misspecification of wind speed models affects wind derivative prices and proposes the use of the generalized hyperbolic distribution to account for non-normality. The study develops risk-neutral approaches for pricing wind derivatives using the conditional Esscher transform, which can accommodate stochastic processes with any distribution, provided the moment-generating function exists. The analysis demonstrates that model risk varies depending on the choice of the underlying index and the derivative’s payoff structure. Therefore, caution should be exercised when choosing wind speed models. Essentially, model risk cannot be ignored in pricing wind speed derivatives.
{"title":"An assessment of model risk in pricing wind derivatives","authors":"Giovani Gracianti, Rui Zhou, Johnny Siu-Hang Li, Xueyuan Wu","doi":"10.1017/s1748499523000192","DOIUrl":"https://doi.org/10.1017/s1748499523000192","url":null,"abstract":"Abstract Wind derivatives are financial instruments designed to mitigate losses caused by adverse wind conditions. With the rapid growth of wind power capacity due to efforts to reduce carbon emissions, the demand for wind derivatives to manage uncertainty in wind power production is expected to increase. However, existing wind derivative literature often assumes normally distributed wind speed, despite the presence of skewness and leptokurtosis in historical wind speed data. This paper investigates how the misspecification of wind speed models affects wind derivative prices and proposes the use of the generalized hyperbolic distribution to account for non-normality. The study develops risk-neutral approaches for pricing wind derivatives using the conditional Esscher transform, which can accommodate stochastic processes with any distribution, provided the moment-generating function exists. The analysis demonstrates that model risk varies depending on the choice of the underlying index and the derivative’s payoff structure. Therefore, caution should be exercised when choosing wind speed models. Essentially, model risk cannot be ignored in pricing wind speed derivatives.","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136129646","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 : 2023-09-13DOI: 10.1017/s1748499523000209
Laura Francis, Mogens Steffensen
Abstract The coronavirus pandemic has created a new awareness of epidemics, and insurance companies have been reminded to consider the risk related to infectious diseases. This paper extends the traditional multi-state models to include epidemic effects. The main idea is to specify the transition intensities in a Markov model such that the impact of contagion is explicitly present in the same way as in epidemiological models. Since we can study the Markov model with contagious effects at an individual level, we consider individual risk and reserves relating to insurance products, conforming with the standard multi-state approach in life insurance mathematics. We compare our notions with other but related notions in the literature and perform numerical illustrations.
{"title":"Individual life insurance during epidemics","authors":"Laura Francis, Mogens Steffensen","doi":"10.1017/s1748499523000209","DOIUrl":"https://doi.org/10.1017/s1748499523000209","url":null,"abstract":"Abstract The coronavirus pandemic has created a new awareness of epidemics, and insurance companies have been reminded to consider the risk related to infectious diseases. This paper extends the traditional multi-state models to include epidemic effects. The main idea is to specify the transition intensities in a Markov model such that the impact of contagion is explicitly present in the same way as in epidemiological models. Since we can study the Markov model with contagious effects at an individual level, we consider individual risk and reserves relating to insurance products, conforming with the standard multi-state approach in life insurance mathematics. We compare our notions with other but related notions in the literature and perform numerical illustrations.","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135740470","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 : 2023-09-05DOI: 10.1017/s1748499523000179
Rüdiger Kiesel, Gerhard Stahl
Climate risks are systemic risks and may be clustered according to so-called volatilities, uncertainties, complexities, and ambiguities (VUCA) criteria. We analyze climate risk in the VUCA concept and provide a framework that allows to interpret systemic risks as model risk. As climate risks are characterized by deep uncertainties (unknown unknowns), we argue that precautionary and resilient principles should be applied instead of capital-based risk measures (reasonable for known unknows). A prominent example of the proposed principles is the precommitment approach (PCA). Within the PCA, subjective probabilities allow to discriminate between tolerable risks and acceptable ones. The amount of determined solvency capital for acceptable risks and estimations of model risk may be aggregated by means of a multiplier approach. This framework is in line with the three-pillar approach of Solvency II, especially with the recovery and resolution plan. Furthermore, it fits smoothly to a hybrid approach of micro- and macroprudential supervision.
{"title":"An uncertainty-based risk management framework for climate change risk","authors":"Rüdiger Kiesel, Gerhard Stahl","doi":"10.1017/s1748499523000179","DOIUrl":"https://doi.org/10.1017/s1748499523000179","url":null,"abstract":"\u0000 Climate risks are systemic risks and may be clustered according to so-called volatilities, uncertainties, complexities, and ambiguities (VUCA) criteria. We analyze climate risk in the VUCA concept and provide a framework that allows to interpret systemic risks as model risk. As climate risks are characterized by deep uncertainties (unknown unknowns), we argue that precautionary and resilient principles should be applied instead of capital-based risk measures (reasonable for known unknows). A prominent example of the proposed principles is the precommitment approach (PCA). Within the PCA, subjective probabilities allow to discriminate between tolerable risks and acceptable ones. The amount of determined solvency capital for acceptable risks and estimations of model risk may be aggregated by means of a multiplier approach. This framework is in line with the three-pillar approach of Solvency II, especially with the recovery and resolution plan. Furthermore, it fits smoothly to a hybrid approach of micro- and macroprudential supervision.","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48990961","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 : 2023-09-01DOI: 10.1017/s1748499523000180
Viviana G. R. Lobo, Thaís C. O. Fonseca, M. Alves
This paper focuses on modeling surrender time for policyholders in the context of life insurance. In this setup, a large lapse rate at the first months of a contract is often observed, with a decrease in this rate after some months. The modeling of the time to cancelation must account for this specific behavior. Another stylized fact is that policies which are not canceled in the study period are considered censored. To account for both censoring and heterogeneous lapse rates, this work assumes a Bayesian survival model with a mixture of regressions. The inference is based on data augmentation allowing for fast computations even for datasets of over millions of clients. Moreover, frequentist point estimation based on Expectation–Maximization algorithm is also presented. An illustrative example emulates a typical behavior for life insurance contracts, and a simulated study investigates the properties of the proposed model. A case study is considered and illustrates the flexibility of our proposed model allowing different specifications of mixture components. In particular, the observed censoring in the insurance context might be up to $50%$ of the data, which is very unusual for survival models in other fields such as epidemiology. This aspect is exploited in our simulated study.
{"title":"Lapse risk modeling in insurance: a Bayesian mixture approach","authors":"Viviana G. R. Lobo, Thaís C. O. Fonseca, M. Alves","doi":"10.1017/s1748499523000180","DOIUrl":"https://doi.org/10.1017/s1748499523000180","url":null,"abstract":"\u0000 This paper focuses on modeling surrender time for policyholders in the context of life insurance. In this setup, a large lapse rate at the first months of a contract is often observed, with a decrease in this rate after some months. The modeling of the time to cancelation must account for this specific behavior. Another stylized fact is that policies which are not canceled in the study period are considered censored. To account for both censoring and heterogeneous lapse rates, this work assumes a Bayesian survival model with a mixture of regressions. The inference is based on data augmentation allowing for fast computations even for datasets of over millions of clients. Moreover, frequentist point estimation based on Expectation–Maximization algorithm is also presented. An illustrative example emulates a typical behavior for life insurance contracts, and a simulated study investigates the properties of the proposed model. A case study is considered and illustrates the flexibility of our proposed model allowing different specifications of mixture components. In particular, the observed censoring in the insurance context might be up to \u0000 \u0000 \u0000 \u0000$50%$\u0000\u0000 \u0000 of the data, which is very unusual for survival models in other fields such as epidemiology. This aspect is exploited in our simulated study.","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49468786","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 : 2023-08-03DOI: 10.1017/s1748499523000167
Jing Zou, M. Odening, Ostap Okhrin
Given the assumption that weather risks affect crop yields, we designed a weather index insurance product for soybean producers in the US state of Illinois. By separating the entire vegetation cycle into four growth stages, we investigate whether the phase-division procedure contributes to weather–yield loss relation estimation and, hence, to basis risk mitigation. Concretely, supposing stage-variant interaction patterns between temperature-based weather index growing degree days and rainfall-based weather index cumulative rainfall, a nonparametric weather–yield loss relation is estimated by a generalized additive model. The model includes penalized B-spline (P-spline) approach based on nonlinear optimal indemnity solutions under the expected utility framework. The P-spline analysis of variance (PS-ANOVA) method is used for efficient estimation through mixed model re-parameterization. The results indicate that the phase-division models significantly outperform the benchmark whole-cycle ones either under quadratic utility or exponential utility, given different levels of risk aversions. Finally, regarding hedging effectiveness, the expected utility ratio between the phase-division contract and the whole-cycle contract, and the percentage changes of mean root square loss and variance of revenues support the proposed phase-division contract.
{"title":"Plant growth stages and weather index insurance design","authors":"Jing Zou, M. Odening, Ostap Okhrin","doi":"10.1017/s1748499523000167","DOIUrl":"https://doi.org/10.1017/s1748499523000167","url":null,"abstract":"\u0000 Given the assumption that weather risks affect crop yields, we designed a weather index insurance product for soybean producers in the US state of Illinois. By separating the entire vegetation cycle into four growth stages, we investigate whether the phase-division procedure contributes to weather–yield loss relation estimation and, hence, to basis risk mitigation. Concretely, supposing stage-variant interaction patterns between temperature-based weather index growing degree days and rainfall-based weather index cumulative rainfall, a nonparametric weather–yield loss relation is estimated by a generalized additive model. The model includes penalized B-spline (P-spline) approach based on nonlinear optimal indemnity solutions under the expected utility framework. The P-spline analysis of variance (PS-ANOVA) method is used for efficient estimation through mixed model re-parameterization. The results indicate that the phase-division models significantly outperform the benchmark whole-cycle ones either under quadratic utility or exponential utility, given different levels of risk aversions. Finally, regarding hedging effectiveness, the expected utility ratio between the phase-division contract and the whole-cycle contract, and the percentage changes of mean root square loss and variance of revenues support the proposed phase-division contract.","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42113444","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 : 2023-07-11DOI: 10.1017/s1748499523000143
Bao Doan, Jonathan J. Reeves, Michael Sherris
Insurers and pension funds face the challenges of historically low-interest rates and high volatility in equity markets, that have been accentuated due to the COVID-19 pandemic. Recent advances in equity portfolio management with a target volatility have been shown to deliver improved on average risk-adjusted return, after transaction costs. This paper studies these targeted volatility portfolios in applications to equity, balanced, and target-date funds with varying constraints on leverage. Conservative leverage constraints are particularly relevant to pension funds and insurance companies, with more aggressive leverage levels appropriate for alternative investments. We show substantial improvements in fund performance for differing leverage levels, and of most interest to insurers and pension funds, we show that the highest Sharpe ratios and smallest drawdowns are in targeted volatility-balanced portfolios with equity and bond allocations. Furthermore, we demonstrate the outperformance of targeted volatility portfolios during major stock market crashes, including the crash from the COVID-19 pandemic.
{"title":"Portfolio management for insurers and pension funds and COVID-19: targeting volatility for equity, balanced, and target-date funds with leverage constraints","authors":"Bao Doan, Jonathan J. Reeves, Michael Sherris","doi":"10.1017/s1748499523000143","DOIUrl":"https://doi.org/10.1017/s1748499523000143","url":null,"abstract":"Insurers and pension funds face the challenges of historically low-interest rates and high volatility in equity markets, that have been accentuated due to the COVID-19 pandemic. Recent advances in equity portfolio management with a target volatility have been shown to deliver improved on average risk-adjusted return, after transaction costs. This paper studies these targeted volatility portfolios in applications to equity, balanced, and target-date funds with varying constraints on leverage. Conservative leverage constraints are particularly relevant to pension funds and insurance companies, with more aggressive leverage levels appropriate for alternative investments. We show substantial improvements in fund performance for differing leverage levels, and of most interest to insurers and pension funds, we show that the highest Sharpe ratios and smallest drawdowns are in targeted volatility-balanced portfolios with equity and bond allocations. Furthermore, we demonstrate the outperformance of targeted volatility portfolios during major stock market crashes, including the crash from the COVID-19 pandemic.","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138509571","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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