Pub Date : 2022-03-03DOI: 10.1080/10920277.2021.2022498
Tzuling Lin, Cary Chi‐liang Tsai, Hung-Wen Cheng
In this article, we propose to attach a mortality index to a conventional bond, called a survival–mortality (SM) bond. Its cash flow pattern is like a conventional bond but it can be separated into a survival (S) part and a mortality (M) part; the cash flow pattern in the former is like an annuity or a longevity bond and that in the latter is like a mortality–catastrophe bond. We further propose to split it into S, M, and SM zero-coupon STRIPS (Separate Trading Registered Interest and Principal Securities). We apply these S, M, and SM issues to hedging longevity risk and interest rate risk of 1-year and multiple-year annuity exposures for the asset liability management of an annuity provider by adopting mortality, interest, mortality–interest duration, and convexity matching strategies. Numerical illustrations show that using SM STRIPS rather than S STRIPS can be sufficient to hedge the risks embedded in 1-year annuity exposures, whereas for multiple-year annuity exposures using S issues is more effective to reduce longevity risk and interest rate risk than using SM issues. We can infer that mortality-linked bonds play an essential role in asset liability management; the proposed survival–mortality bonds will be a feasible way to develop an efficient market for longevity risk.
{"title":"Asset Liability Management of Longevity and Interest Rate Risks: Using Survival–Mortality Bonds","authors":"Tzuling Lin, Cary Chi‐liang Tsai, Hung-Wen Cheng","doi":"10.1080/10920277.2021.2022498","DOIUrl":"https://doi.org/10.1080/10920277.2021.2022498","url":null,"abstract":"In this article, we propose to attach a mortality index to a conventional bond, called a survival–mortality (SM) bond. Its cash flow pattern is like a conventional bond but it can be separated into a survival (S) part and a mortality (M) part; the cash flow pattern in the former is like an annuity or a longevity bond and that in the latter is like a mortality–catastrophe bond. We further propose to split it into S, M, and SM zero-coupon STRIPS (Separate Trading Registered Interest and Principal Securities). We apply these S, M, and SM issues to hedging longevity risk and interest rate risk of 1-year and multiple-year annuity exposures for the asset liability management of an annuity provider by adopting mortality, interest, mortality–interest duration, and convexity matching strategies. Numerical illustrations show that using SM STRIPS rather than S STRIPS can be sufficient to hedge the risks embedded in 1-year annuity exposures, whereas for multiple-year annuity exposures using S issues is more effective to reduce longevity risk and interest rate risk than using SM issues. We can infer that mortality-linked bonds play an essential role in asset liability management; the proposed survival–mortality bonds will be a feasible way to develop an efficient market for longevity risk.","PeriodicalId":46812,"journal":{"name":"North American Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47278926","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 : 2022-03-03DOI: 10.1080/10920277.2022.2026229
G. P. Clemente, N. Savelli, G. Spedicato, D. Zappa
Monitoring general practitioner prescribing costs is an important topic in order to efficiently allocate National Health Insurance resources. Using generalized additive models for location, scale, and shape with random effects, we investigate how second-order variables, related to patients, contribute to estimating the frequency, severity, and hence the total amount of costs. The total cost of prescriptions associated with a general practitioner is then derived following a collective risk theory approach by aggregating cumulants of patient cost distributions. By means of the fourth-order Cornish-Fisher expansion series of quantiles of the aggregate cost distribution of general practitioners, we construct a confidence interval for each doctor, which is used to select a subset of doctors that should be monitored to identify potential inefficiencies. A case study is developed by using structured data regarding the number and cost of prescriptions of about 900,000 patients linked to corresponding general practitioners. The prescription costs considered are only those paid fully by the national health coverage.
{"title":"Modeling General Practitioners’ Total Drug Costs through GAMLSS and Collective Risk Models","authors":"G. P. Clemente, N. Savelli, G. Spedicato, D. Zappa","doi":"10.1080/10920277.2022.2026229","DOIUrl":"https://doi.org/10.1080/10920277.2022.2026229","url":null,"abstract":"Monitoring general practitioner prescribing costs is an important topic in order to efficiently allocate National Health Insurance resources. Using generalized additive models for location, scale, and shape with random effects, we investigate how second-order variables, related to patients, contribute to estimating the frequency, severity, and hence the total amount of costs. The total cost of prescriptions associated with a general practitioner is then derived following a collective risk theory approach by aggregating cumulants of patient cost distributions. By means of the fourth-order Cornish-Fisher expansion series of quantiles of the aggregate cost distribution of general practitioners, we construct a confidence interval for each doctor, which is used to select a subset of doctors that should be monitored to identify potential inefficiencies. A case study is developed by using structured data regarding the number and cost of prescriptions of about 900,000 patients linked to corresponding general practitioners. The prescription costs considered are only those paid fully by the national health coverage.","PeriodicalId":46812,"journal":{"name":"North American Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41950241","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 : 2022-03-02DOI: 10.1080/10920277.2022.2036197
Daniel M. Abramson
Correct pricing of nonproportional (primary or excess of loss) insurance for construction risks must consider not only how the insured property values build up over time, but also how the probable maximum loss (PML) changes. Conventional pricing methods for static property risks cannot be employed for construction risks, since the latter are characterized by PML patterns that change over time, as well as evolving loss exposures and perils arising from the various phases of the construction project. A further complication arises when delay in startup (DSU) is covered, because a DSU loss is triggered by a property damage loss and both losses contribute jointly to the erosion of an excess layer. This article describes a pricing method with analysis of specific cases of interest, including guidelines for creating practical excess of loss rating models.
{"title":"A Nonproportional Premium Rating Method for Construction Risks","authors":"Daniel M. Abramson","doi":"10.1080/10920277.2022.2036197","DOIUrl":"https://doi.org/10.1080/10920277.2022.2036197","url":null,"abstract":"Correct pricing of nonproportional (primary or excess of loss) insurance for construction risks must consider not only how the insured property values build up over time, but also how the probable maximum loss (PML) changes. Conventional pricing methods for static property risks cannot be employed for construction risks, since the latter are characterized by PML patterns that change over time, as well as evolving loss exposures and perils arising from the various phases of the construction project. A further complication arises when delay in startup (DSU) is covered, because a DSU loss is triggered by a property damage loss and both losses contribute jointly to the erosion of an excess layer. This article describes a pricing method with analysis of specific cases of interest, including guidelines for creating practical excess of loss rating models.","PeriodicalId":46812,"journal":{"name":"North American Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44728415","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 : 2022-02-10DOI: 10.1080/10920277.2021.2018614
Le Chang, Yanlin Shi
Accurate forecasts and analyses of mortality rates are essential to many practical issues, such as population projections and the design of pension schemes. Recent studies have considered a spatial–temporal autoregressive (STAR) model, in which the mortality rates of each age depend on their own historical values (temporality) and the neighboring cohort ages (spatiality). Despite the realization of age coherence and improved forecasting accuracy over the famous Lee-Carter (LC) model, the assumption of STAR that only the effects of the same and the neighboring cohorts exist can be too restrictive. In this study, we adopt a data-driven principle, as in a sparse vector autoregressive (SVAR) model, to improve the flexibility of the parametric structure of STAR and develop a constrained SVAR (CSVAR) model. To solve its objective function consisting of non-standard L2 and L1 penalties subject to constraints, we develop a new algorithm and prove the existence of the desirable age-coherence in CSVAR. Using empirical data from the United Kingdom, France, Italy, Spain, and Australia, we show that CSVAR consistently outperforms the LC, SVAR, and STAR models with respect to forecasting accuracy. The estimates and forecasts of the CSVAR model also demonstrate important demographic differences between these five countries.
{"title":"Age-Coherent Mortality Modeling and Forecasting Using a Constrained Sparse Vector-Autoregressive Model","authors":"Le Chang, Yanlin Shi","doi":"10.1080/10920277.2021.2018614","DOIUrl":"https://doi.org/10.1080/10920277.2021.2018614","url":null,"abstract":"Accurate forecasts and analyses of mortality rates are essential to many practical issues, such as population projections and the design of pension schemes. Recent studies have considered a spatial–temporal autoregressive (STAR) model, in which the mortality rates of each age depend on their own historical values (temporality) and the neighboring cohort ages (spatiality). Despite the realization of age coherence and improved forecasting accuracy over the famous Lee-Carter (LC) model, the assumption of STAR that only the effects of the same and the neighboring cohorts exist can be too restrictive. In this study, we adopt a data-driven principle, as in a sparse vector autoregressive (SVAR) model, to improve the flexibility of the parametric structure of STAR and develop a constrained SVAR (CSVAR) model. To solve its objective function consisting of non-standard L2 and L1 penalties subject to constraints, we develop a new algorithm and prove the existence of the desirable age-coherence in CSVAR. Using empirical data from the United Kingdom, France, Italy, Spain, and Australia, we show that CSVAR consistently outperforms the LC, SVAR, and STAR models with respect to forecasting accuracy. The estimates and forecasts of the CSVAR model also demonstrate important demographic differences between these five countries.","PeriodicalId":46812,"journal":{"name":"North American Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46635591","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 : 2022-01-20DOI: 10.1080/10920277.2021.2014891
Guohui Guan, Xiang Hu
In this study, we investigate the competition among insurers under the mean–variance criterion. The optimization problems are formulated for finite and infinite insurers. The surplus processes of the insurers are characterized by jump-diffusion processes with common and idiosyncratic insurance risks. The insurers can purchase a reinsurance business to divide the insurance risk. In the financial market, the insurers decide the proportion of their fund to be retained as cash and to be invested in a stock characterized by a jump-diffusion process with common and idiosyncratic financial risks. The insurers compete with each other and are concerned with the relative performance. By the extended Hamilton-Jacobi-Bellman equation, the explicit forms of the n-agent equilibrium and mean-field equilibrium (MFE) are obtained in the n-agent case and mean-field case, respectively. Our results show that the MFE of the reinsurance strategy is composed of two parts, one part associated with the individual preference and the other associated with the common insurance shock. Meanwhile, the MFE of the investment strategy is composed of three parts: the individual preference, common market risks, and common shocks. Numerical examples are presented at the end of this article to demonstrate the effects of different parameters on the MFE. The results reveal that the insurers become convergent in a competitive environment.
{"title":"Time-Consistent Investment and Reinsurance Strategies for Mean–Variance Insurers in N-Agent and Mean-Field Games","authors":"Guohui Guan, Xiang Hu","doi":"10.1080/10920277.2021.2014891","DOIUrl":"https://doi.org/10.1080/10920277.2021.2014891","url":null,"abstract":"In this study, we investigate the competition among insurers under the mean–variance criterion. The optimization problems are formulated for finite and infinite insurers. The surplus processes of the insurers are characterized by jump-diffusion processes with common and idiosyncratic insurance risks. The insurers can purchase a reinsurance business to divide the insurance risk. In the financial market, the insurers decide the proportion of their fund to be retained as cash and to be invested in a stock characterized by a jump-diffusion process with common and idiosyncratic financial risks. The insurers compete with each other and are concerned with the relative performance. By the extended Hamilton-Jacobi-Bellman equation, the explicit forms of the n-agent equilibrium and mean-field equilibrium (MFE) are obtained in the n-agent case and mean-field case, respectively. Our results show that the MFE of the reinsurance strategy is composed of two parts, one part associated with the individual preference and the other associated with the common insurance shock. Meanwhile, the MFE of the investment strategy is composed of three parts: the individual preference, common market risks, and common shocks. Numerical examples are presented at the end of this article to demonstrate the effects of different parameters on the MFE. The results reveal that the insurers become convergent in a competitive environment.","PeriodicalId":46812,"journal":{"name":"North American Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46081360","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 : 2022-01-14DOI: 10.1080/10920277.2021.1993927
I. Duncan, A. Mackenzie, Elise Bonfiglio, T. Wrigley, Xiyue Liao
The Centers for Medicare and Medicaid Services (CMS) introduced the Medicare Shared Savings Program (MSSP) for accountable care organizations (ACOs) as part of the Affordable Care Act. Participating ACOs accept risk for the financial outcomes of their assigned populations and share in gains (and, depending on the ACO model, losses) when these are generated. Gains and losses are calculated by comparing actual costs of the ACO population against a benchmark cost based on the historical performance of members in the ACO. Participating ACOs are at risk of model error. Because of stochastic variance in cost distributions and the imperfect operation of the risk-adjustment process, there is a nontrivial probability that an ACO may experience a false positive (gains are calculated where no gains were actually generated) or false negative (a loss is calculated by the model when no losses were actually generated). Using a sample of Medicare fee-for-service data, we model outcomes for typical ACOs and for ACOs consisting of chronic patients. For a typical ACO, the probability of model error resulting in a false positive or false negative outcome is between 5% and 8%. Chronic populations with higher variance have higher probabilities of model error, between 26% and 28% for a diabetes population, and about 23% for a cancer population. In the case of an ACO that generates gains through increased efficiency, model error can result in the ACO failing to realize gains, or even (in a minority of cases) require a reimbursement to the payer. From the perspective of the payer with a number of ACOs, the average overpayment or recovery will be minor. The percentage overpayment (recovery) increases as the prevalence of chronic patients increases. For a population of cancer patients a payer can expect to pay (or recover) between 1.0% and 2.0% of claims, while for a diabetes population the range is 1.5–2.5%. For an individual ACO the loss or gain is more significant because the ACO gains or loses the full amount, with a relatively high probability. While this study has focused on the Medicare Shared Savings Program, the MSSP is just an example of a class of gainsharing models that is increasingly prevalent in value-based contracts. Payers and providers who negotiate value-based contracts need to be aware of and account for model risk in their contracts, particularly as the sizes of populations under management become smaller.
{"title":"Shared Savings Model Risk in the MSSP Program","authors":"I. Duncan, A. Mackenzie, Elise Bonfiglio, T. Wrigley, Xiyue Liao","doi":"10.1080/10920277.2021.1993927","DOIUrl":"https://doi.org/10.1080/10920277.2021.1993927","url":null,"abstract":"The Centers for Medicare and Medicaid Services (CMS) introduced the Medicare Shared Savings Program (MSSP) for accountable care organizations (ACOs) as part of the Affordable Care Act. Participating ACOs accept risk for the financial outcomes of their assigned populations and share in gains (and, depending on the ACO model, losses) when these are generated. Gains and losses are calculated by comparing actual costs of the ACO population against a benchmark cost based on the historical performance of members in the ACO. Participating ACOs are at risk of model error. Because of stochastic variance in cost distributions and the imperfect operation of the risk-adjustment process, there is a nontrivial probability that an ACO may experience a false positive (gains are calculated where no gains were actually generated) or false negative (a loss is calculated by the model when no losses were actually generated). Using a sample of Medicare fee-for-service data, we model outcomes for typical ACOs and for ACOs consisting of chronic patients. For a typical ACO, the probability of model error resulting in a false positive or false negative outcome is between 5% and 8%. Chronic populations with higher variance have higher probabilities of model error, between 26% and 28% for a diabetes population, and about 23% for a cancer population. In the case of an ACO that generates gains through increased efficiency, model error can result in the ACO failing to realize gains, or even (in a minority of cases) require a reimbursement to the payer. From the perspective of the payer with a number of ACOs, the average overpayment or recovery will be minor. The percentage overpayment (recovery) increases as the prevalence of chronic patients increases. For a population of cancer patients a payer can expect to pay (or recover) between 1.0% and 2.0% of claims, while for a diabetes population the range is 1.5–2.5%. For an individual ACO the loss or gain is more significant because the ACO gains or loses the full amount, with a relatively high probability. While this study has focused on the Medicare Shared Savings Program, the MSSP is just an example of a class of gainsharing models that is increasingly prevalent in value-based contracts. Payers and providers who negotiate value-based contracts need to be aware of and account for model risk in their contracts, particularly as the sizes of populations under management become smaller.","PeriodicalId":46812,"journal":{"name":"North American Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48011737","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 : 2021-12-17DOI: 10.1080/10920277.2021.2000876
M. Rosenberg, Fanghao Zhong
This article extends prior work that used only social determinants to create clusters that are labeled using an external measure of average total expenditures. In this article we show that these clusters can identify a reasonable percentage of the top 5% utilizers of health care and compare two methods of clustering (PAM and k-means). We include two independent cohorts to show the consistency of the use of clusters across cohorts. We find that the three clusters with the highest average total expenditure (labeled from the intial studies) identify approximately 40% of those who are among the top 5% utilizers and from 25% to over 50% of the expenditures of the top 5% utilizers for each of the three cohorts. By identifying characteristics of individuals who are consistently in the top 5%, third-party payors and other stakeholders have a better opportunity to prospectively apply effective interventions. Social determinants such whether the individual is not working, on food stamps, or homeless are more frequent in those top 5% utilizers compared to the overall population.
{"title":"Using Clusters Based on Social Determinants to Identify the Top 5% Utilizers of Health Care","authors":"M. Rosenberg, Fanghao Zhong","doi":"10.1080/10920277.2021.2000876","DOIUrl":"https://doi.org/10.1080/10920277.2021.2000876","url":null,"abstract":"This article extends prior work that used only social determinants to create clusters that are labeled using an external measure of average total expenditures. In this article we show that these clusters can identify a reasonable percentage of the top 5% utilizers of health care and compare two methods of clustering (PAM and k-means). We include two independent cohorts to show the consistency of the use of clusters across cohorts. We find that the three clusters with the highest average total expenditure (labeled from the intial studies) identify approximately 40% of those who are among the top 5% utilizers and from 25% to over 50% of the expenditures of the top 5% utilizers for each of the three cohorts. By identifying characteristics of individuals who are consistently in the top 5%, third-party payors and other stakeholders have a better opportunity to prospectively apply effective interventions. Social determinants such whether the individual is not working, on food stamps, or homeless are more frequent in those top 5% utilizers compared to the overall population.","PeriodicalId":46812,"journal":{"name":"North American Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46027116","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 : 2021-11-05DOI: 10.1080/10920277.2021.1953536
Xin Che, Andre P. Liebenberg, Jianren Xu
Insurers are increasingly embracing the InsurTech ecosystem. The most important InsurTech-related trend in automobile insurance is usage-based insurance (UBI), which enables insurers to access and incorporate drivers’ behavioral risk factors in actuarial pricing. Using a difference-in-difference research design with firm fixed effects, we provide evidence that UBI improves private passenger auto liability (PPAL) insurers’ underwriting performance by reducing their loss ratio. However, the improvement in underwriting performance is only significant among early UBI adopters, highlighting the early-mover advantage in InsurTech. Also, UBI produces benefits only when it matures. Our findings are robust to analyses that address potential reverse causality and self-selection bias. Additional tests show that early UBI adopters experience a significant increase in their market share, implying UBI’s advantage to attract low-risk drivers from other insurers. The overall performance effect of UBI programs for early adopters is a 1% increase in ROA and a 3% increase in ROE. The policy implications of our findings from the perspective of insurers should be of interest to firms’ management, actuaries, investors, and rating agencies.
{"title":"Usage-Based Insurance—Impact on Insurers and Potential Implications for InsurTech","authors":"Xin Che, Andre P. Liebenberg, Jianren Xu","doi":"10.1080/10920277.2021.1953536","DOIUrl":"https://doi.org/10.1080/10920277.2021.1953536","url":null,"abstract":"Insurers are increasingly embracing the InsurTech ecosystem. The most important InsurTech-related trend in automobile insurance is usage-based insurance (UBI), which enables insurers to access and incorporate drivers’ behavioral risk factors in actuarial pricing. Using a difference-in-difference research design with firm fixed effects, we provide evidence that UBI improves private passenger auto liability (PPAL) insurers’ underwriting performance by reducing their loss ratio. However, the improvement in underwriting performance is only significant among early UBI adopters, highlighting the early-mover advantage in InsurTech. Also, UBI produces benefits only when it matures. Our findings are robust to analyses that address potential reverse causality and self-selection bias. Additional tests show that early UBI adopters experience a significant increase in their market share, implying UBI’s advantage to attract low-risk drivers from other insurers. The overall performance effect of UBI programs for early adopters is a 1% increase in ROA and a 3% increase in ROE. The policy implications of our findings from the perspective of insurers should be of interest to firms’ management, actuaries, investors, and rating agencies.","PeriodicalId":46812,"journal":{"name":"North American Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46580174","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 : 2021-10-30DOI: 10.1080/10920277.2021.1978850
G. Tzougas, Alice Pignatelli di Cerchiara
The main purpose of this article is to present a new class of bivariate mixed Poisson regression models with varying dispersion that offers sufficient flexibility for accommodating overdispersion and accounting for the positive correlation between the number of claims from third-party liability bodily injury and property damage. Maximum likelihood estimation for this family of models is achieved through an expectation-maximization algorithm that is shown to have a satisfactory performance when three members of this family, namely, the bivariate negative binomial, bivariate Poisson–inverse Gaussian, and bivariate Poisson–Lognormal distributions with regression specifications on every parameter are fitted on two-dimensional motor insurance data from a European motor insurer. The a posteriori, or bonus-malus, premium rates that are determined by these models are calculated via the expected value and variance principles and are compared to those based only on the a posteriori criteria. Finally, we present an extension of the proposed approach with varying dispersion by developing a bivariate Normal copula-based mixed Poisson regression model with varying dispersion and dependence parameters. This approach allows us to consider the influence of individual and coverage-specific risk factors on the mean, dispersion, and copula parameters when modeling different types of claims from different types of coverage. For expository purposes, the Normal copula paired with negative binomial distributions for marginals and regressors on the mean, dispersion, and copula parameters is fitted on a simulated dataset via maximum likelihood.
{"title":"Bivariate Mixed Poisson Regression Models with Varying Dispersion","authors":"G. Tzougas, Alice Pignatelli di Cerchiara","doi":"10.1080/10920277.2021.1978850","DOIUrl":"https://doi.org/10.1080/10920277.2021.1978850","url":null,"abstract":"The main purpose of this article is to present a new class of bivariate mixed Poisson regression models with varying dispersion that offers sufficient flexibility for accommodating overdispersion and accounting for the positive correlation between the number of claims from third-party liability bodily injury and property damage. Maximum likelihood estimation for this family of models is achieved through an expectation-maximization algorithm that is shown to have a satisfactory performance when three members of this family, namely, the bivariate negative binomial, bivariate Poisson–inverse Gaussian, and bivariate Poisson–Lognormal distributions with regression specifications on every parameter are fitted on two-dimensional motor insurance data from a European motor insurer. The a posteriori, or bonus-malus, premium rates that are determined by these models are calculated via the expected value and variance principles and are compared to those based only on the a posteriori criteria. Finally, we present an extension of the proposed approach with varying dispersion by developing a bivariate Normal copula-based mixed Poisson regression model with varying dispersion and dependence parameters. This approach allows us to consider the influence of individual and coverage-specific risk factors on the mean, dispersion, and copula parameters when modeling different types of claims from different types of coverage. For expository purposes, the Normal copula paired with negative binomial distributions for marginals and regressors on the mean, dispersion, and copula parameters is fitted on a simulated dataset via maximum likelihood.","PeriodicalId":46812,"journal":{"name":"North American Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49622543","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 : 2021-10-28DOI: 10.1080/10920277.2021.1973507
Yawen Hwang, L. Chan, C. Tsai
Understanding the causes of voluntary terminations is important to the service quality, profitability, and risk management of the life insurer. This article extends the literature on the determinants of the termination propensities in four aspects. First, we decompose voluntary terminations into surrender and lapse and build models accordingly. This decomposition is important because the motives, causes, and consequences of lapse and surrender are distinct. Second, we construct models for the surrender and lapse propensities by product type. Without such construction, one would overlook the diverse motivations of buying different types of product and distinct behaviors of terminating product holding. Third, we introduce new explanatory variables (commission ratio and occupation of the insured) in modeling the propensities and these variables are found to be significant. Fourth, this is the first article on the determinants of voluntary terminations for the market of Taiwan with implications for other regions having significant Chinese people presence.
{"title":"On Voluntary Terminations of Life Insurance: Differentiating Surrender Propensity From Lapse Propensity Across Product Types","authors":"Yawen Hwang, L. Chan, C. Tsai","doi":"10.1080/10920277.2021.1973507","DOIUrl":"https://doi.org/10.1080/10920277.2021.1973507","url":null,"abstract":"Understanding the causes of voluntary terminations is important to the service quality, profitability, and risk management of the life insurer. This article extends the literature on the determinants of the termination propensities in four aspects. First, we decompose voluntary terminations into surrender and lapse and build models accordingly. This decomposition is important because the motives, causes, and consequences of lapse and surrender are distinct. Second, we construct models for the surrender and lapse propensities by product type. Without such construction, one would overlook the diverse motivations of buying different types of product and distinct behaviors of terminating product holding. Third, we introduce new explanatory variables (commission ratio and occupation of the insured) in modeling the propensities and these variables are found to be significant. Fourth, this is the first article on the determinants of voluntary terminations for the market of Taiwan with implications for other regions having significant Chinese people presence.","PeriodicalId":46812,"journal":{"name":"North American Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43850638","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：