North American Actuarial Journal最新文献

{"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":"26 1","pages":"591 - 609"},"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}

{"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":"26 1","pages":"537 - 569"},"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}

{"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":"27 1","pages":"242 - 252"},"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}

{"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":"26 1","pages":"456 - 469"},"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}

{"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":"26 1","pages":"428 - 455"},"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}

{"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":"27 1","pages":"211 - 241"},"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}

{"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":"26 1","pages":"252 - 282"},"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}

{"title":"A Tractable Class of Multivariate Phase-Type Distributions for Loss Modeling","authors":"Martin Bladt","doi":"10.1080/10920277.2023.2167833","DOIUrl":"https://doi.org/10.1080/10920277.2023.2167833","url":null,"abstract":"Phase-type (PH) distributions are a popular tool for the analysis of univariate risks in numerous actuarial applications. Their multivariate counterparts (MPH$^ast$), however, have not seen such a proliferation, due to lack of explicit formulas and complicated estimation procedures. A simple construction of multivariate phase-type distributions -- mPH -- is proposed for the parametric description of multivariate risks, leading to models of considerable probabilistic flexibility and statistical tractability. The main idea is to start different Markov processes at the same state, and allow them to evolve independently thereafter, leading to dependent absorption times. By dimension augmentation arguments, this construction can be cast into the umbrella of MPH$^ast$ class, but enjoys explicit formulas which the general specification lacks, including common measures of dependence. Moreover, it is shown that the class is still rich enough to be dense on the set of multivariate risks supported on the positive orthant, and it is the smallest known sub-class to have this property. In particular, the latter result provides a new short proof of the denseness of the MPH$^ast$ class. In practice this means that the mPH class allows for modeling of bivariate risks with any given correlation or copula. We derive an EM algorithm for its statistical estimation, and illustrate it on bivariate insurance data. Extensions to more general settings are outlined.","PeriodicalId":46812,"journal":{"name":"North American Actuarial Journal","volume":"1 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2021-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43493969","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}

{"title":"Risk-Seeking Behavior and Its Implications for the Optimal Decision Making of Annuity Insurers","authors":"Cuixia Chen, Yi-Jia Lin, Minghe Zhou","doi":"10.1080/10920277.2021.1977144","DOIUrl":"https://doi.org/10.1080/10920277.2021.1977144","url":null,"abstract":"This study investigates risk-seeking and optimal decisions of annuity providers. On the basis of a sample of U.S. life and annuity (L/A) insurers between 1997 and 2016, the results show clear performance-dependent risk attitudes. Specifically, insurers with returns below aspiration levels take more risks, whereas those with returns above reference levels decrease their risk-seeking, which supports the basic propositions of the cumulative prospect theory (CPT). Given initial evidence of mixed risk preferences in the L/A insurance industry, we derive an annuity insurer’s optimal investment and business strategies in a CPT decision-making framework. We show that changing risk preferences considerably affect an annuity provider’s decisions. We further illustrate how risk management changes an annuity insurer’s optimal strategies. Our results suggest that risk management lowers downside risk and allows a loss-averse decision maker to assume more risk and achieve a higher level of utility.","PeriodicalId":46812,"journal":{"name":"North American Actuarial Journal","volume":"27 1","pages":"25 - 46"},"PeriodicalIF":1.4,"publicationDate":"2021-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45228951","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}

{"title":"Dynamic Fund Protection for Property Markets","authors":"T. Siu, H. Nguyen, Ning Wang","doi":"10.1080/10920277.2021.1948430","DOIUrl":"https://doi.org/10.1080/10920277.2021.1948430","url":null,"abstract":"This article aims to investigate, from an academic perspective, a potential application of dynamic fund protection to protect a mortgagor of a property against the downside risk due to falling property price. The valuation of the dynamic fund protection is discussed through modeling the property price and interest rate, which may be considered to be two key factors having a material impact on the mortgagor. Specifically, a mean-reverting process is used to describe the property price and the Heath-Jarrow-Morton theory is used to model the interest rate. The valuation is done via the use of a forward measure approach. The numerical solution to the pricing partial differential equation is obtained via applying the finite difference method. Numerical results with some model parameters being estimated from the data on an Australian residential property index and Australian zero-coupon yields and forward rates are provided. The implications of the numerical results for the potential implementation of the dynamic fund protection are discussed.","PeriodicalId":46812,"journal":{"name":"North American Actuarial Journal","volume":"26 1","pages":"383 - 402"},"PeriodicalIF":1.4,"publicationDate":"2021-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47705780","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}