North American Actuarial Journal最新文献

{"title":"Distributionally Robust Goal-Reaching Optimization in the Presence of Background Risk","authors":"Yichun Chi, Z. Xu, S. Zhuang","doi":"10.1080/10920277.2021.1966805","DOIUrl":"https://doi.org/10.1080/10920277.2021.1966805","url":null,"abstract":"In this article, we examine the effect of background risk on portfolio selection and optimal reinsurance design under the criterion of maximizing the probability of reaching a goal. Following the literature, we adopt dependence uncertainty to model the dependence ambiguity between financial risk (or insurable risk) and background risk. Because the goal-reaching objective function is nonconcave, these two problems bring highly unconventional and challenging issues for which classical optimization techniques often fail. Using a quantile formulation method, we derive the optimal solutions explicitly. The results show that the presence of background risk does not alter the shape of the solution but instead changes the parameter value of the solution. Finally, numerical examples are given to illustrate the results and verify the robustness of our solutions.","PeriodicalId":46812,"journal":{"name":"North American Actuarial Journal","volume":"26 1","pages":"351 - 382"},"PeriodicalIF":1.4,"publicationDate":"2021-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45376793","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":"Alcohol and Mortality: An Actuarial Issue","authors":"S. Gutterman","doi":"10.1080/10920277.2021.1946660","DOIUrl":"https://doi.org/10.1080/10920277.2021.1946660","url":null,"abstract":"Despite some favorable global trends in the prevalence of heavy episodic drinking, alcohol-related mortality and morbidity since 2010, and the prevalence of youth drinking in certain developed countries, there has been limited progress in reducing total per-capita alcohol consumption. The burden of disease attributable to alcohol remains high, particularly at pre-retirement ages, and is increasing in some countries and for some causes of death. This article describes the status and trends in alcohol consumption, both worldwide and in the United States. It also describes the adverse consequences of heavy and binge drinking, which are significant to the individual, family and friends, and society. Although the overall effect on mortality of moderate alcohol drinking compared with no drinking at all has generally been viewed to be somewhat favorable due to the effect of certain cardiovascular risks, this view is not shared by all—the arguments involved are examined in this article. The recognition and need for active management of the adverse effects of heavy and binge alcohol consumption, remain essential to favorable health and longevity. Possible public interventions are also described. Actuaries involved in assessing mortality trends and product design need to assess trends in drivers and consequences of historical, current, and expected future alcohol-attributable mortality and morbidity patterns on a regular basis.","PeriodicalId":46812,"journal":{"name":"North American Actuarial Journal","volume":"26 1","pages":"184 - 204"},"PeriodicalIF":1.4,"publicationDate":"2021-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/10920277.2021.1946660","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45985356","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":"Tail Moments of Compound Distributions","authors":"Jiandong Ren","doi":"10.2139/ssrn.3880127","DOIUrl":"https://doi.org/10.2139/ssrn.3880127","url":null,"abstract":"In this article, we study the moment transform of both univariate and multivariate compound sums. We first derive simple explicit formulas for the first and second moment transforms when the (loss) frequency distribution is in the so-called class. Then we show that the derived formulas can be used to efficiently compute risk measures such as the tail conditional expectation (TCE), the tail variance (TV), and higher tail moments. The results generalize those in Denuit (North American Actuarial Journal, 24 (4):512–32, 2020).","PeriodicalId":46812,"journal":{"name":"North American Actuarial Journal","volume":"26 1","pages":"336 - 350"},"PeriodicalIF":1.4,"publicationDate":"2021-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44835084","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":"Extreme Data Breach Losses: An Alternative Approach to Estimating Probable Maximum Loss for Data Breach Risk","authors":"Kwangmin Jung","doi":"10.1080/10920277.2021.1919145","DOIUrl":"https://doi.org/10.1080/10920277.2021.1919145","url":null,"abstract":"This study proposes a measure of the data breach risk’s probable maximum loss, which stands for the worst data breach loss likely to occur, using an alternative approach to estimating the potential loss degree of an extreme event with one of the largest private databases for data breach risk. We determine stationarity, the presence of autoregressive feature, and the Fréchet type of generalized extreme value distribution (GEV) as the best fit for data breach loss maxima series and check robustness of the model with a public dataset. We find that the predicted data breach loss likely to occur in the next five years is substantially larger than the loss estimated by the recent literature with a Pareto model. In particular, the comparison between the estimates from the recent data (after 2014) and those for the old data (before 2014) shows a significant increase with a break in the loss severity. We design a three-layer reinsurance scheme based on the probable maximum loss estimates with public–private partnership. Our findings are important for risk managers, actuaries, and policymakers concerned about the enormous cost of the next extreme cyber event.","PeriodicalId":46812,"journal":{"name":"North American Actuarial Journal","volume":"25 1","pages":"580 - 603"},"PeriodicalIF":1.4,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/10920277.2021.1919145","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48293207","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 Model Averaging to Determine Suitable Risk Measure Estimates","authors":"T. Miljkovic, B. Grün","doi":"10.1080/10920277.2021.1911668","DOIUrl":"https://doi.org/10.1080/10920277.2021.1911668","url":null,"abstract":"Recent research in loss modeling resulted in a growing number of classes of statistical models as well as additional models being proposed within each class. Empirical results indicate that a range of models within or between model classes perform similarly well, as measured by goodness-of-fit or information criteria, when fitted to the same data set. This leads to model uncertainty and makes model selection a challenging task. This problem is particularly virulent if the resulting risk measures vary greatly between and within the model classes. We propose an approach to estimate risk measures that accounts for model selection uncertainty based on model averaging. We exemplify the application of the approach considering the class of composite models. This application considers 196 different left-truncated composite models previously used in the literature for loss modeling and arrives at point estimates for the risk measures that take model uncertainty into account. A simulation study highlights the benefits of this approach. The data set on Norwegian fire losses is used to illustrate the proposed methodology.","PeriodicalId":46812,"journal":{"name":"North American Actuarial Journal","volume":"25 1","pages":"562 - 579"},"PeriodicalIF":1.4,"publicationDate":"2021-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/10920277.2021.1911668","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43749675","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":"Discounting the Discounted Projection Approach","authors":"D. Buckner, K. Dowd","doi":"10.1080/10920277.2021.1916537","DOIUrl":"https://doi.org/10.1080/10920277.2021.1916537","url":null,"abstract":"U.K. equity release actuaries are using a flawed approach to value the no-negative equity guarantees in their equity release mortgages. The approach they use, the discounted projection approach, incorrectly uses projected future house prices as the underlying prices in their put option pricing equations. The correct approach uses forward house prices. The discounted projection approach entails significant undervaluations of no-negative equity guarantees and overvaluations of equity release mortgages and can produce valuations that violate rational pricing principles. The discounted projection approach is also inconsistent with both actuarial and accounting standards. Our results have significant ramifications for equity release industry practice and prudential regulation.","PeriodicalId":46812,"journal":{"name":"North American Actuarial Journal","volume":"26 1","pages":"521 - 536"},"PeriodicalIF":1.4,"publicationDate":"2021-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/10920277.2021.1916537","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47488311","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":"Reply to Jiandong Ren on Their Discussion on the Paper Titled “Size-Biased Risk Measures of Compound Sums”","authors":"M. Denuit","doi":"10.1080/10920277.2021.1925823","DOIUrl":"https://doi.org/10.1080/10920277.2021.1925823","url":null,"abstract":"I am grateful to Jiandong Ren for providing readers with a unified treatment of compound sums with frequency component in the ða, b, 0Þ class of counting distributions, which is central to insurance studies. This offers a deeper understanding of the underlying structure of this family, compared to the separate treatment of the Poisson and negative binomial cases in the paper (the latter being treated as a Poisson mixture). Therefore, I sincerely thank Jiandong Ren for having supplemented the initial work with these brilliant ideas. As stressed at the end of the discussion, the Panjer algorithm is particularly useful to compute tail risk measures. In addition to exact calculations, the approximations derived by Denuit and Robert (2021) in terms polynomial expansions (with respect to the Gamma distribution and its associated Laguerre orthonormal polynomials or with respect to the Normal distribution and its associated Hermite polynomials when the size of the pool gets larger) may also be useful in the present context. Depending on the thickness of the tails of the loss distributions, the latter may be replaced with their Esscher transform (or exponential tilting) of negative order. Compound sums with ða, b, 0Þ frequency component are also considered as an application in that paper and the proposed method is compared with the well-established Panjer recursive algorithm.","PeriodicalId":46812,"journal":{"name":"North American Actuarial Journal","volume":"25 1","pages":"643 - 643"},"PeriodicalIF":1.4,"publicationDate":"2021-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/10920277.2021.1925823","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42673797","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":"Jiandong Ren's Discussion on “Size-Biased Risk Measures of Compound Sums,” by Michel Denuit, January 2020","authors":"Jiandong Ren","doi":"10.1080/10920277.2021.1914666","DOIUrl":"https://doi.org/10.1080/10920277.2021.1914666","url":null,"abstract":"2. SIZE-BIASED TRANSFORM FOR DISTRIBUTIONS IN ða,b, 0Þ CLASS The concept of ða, b, 0Þ class distributions is well known to actuaries, mainly because of the popularity of Panjer’s recursive formulas for calculating the distribution of the corresponding compound sums. For detailed introductions and applications, refer to Klugman, Panjer, and Willmot (2019) and Sundt and Vernic (2009). In this section, we present a result for the sizebiased transform of distributions in the class. For completeness, we begin with two definitions. Definition 1. Let PNðkÞ denote the probability function of a discrete random variable N; it is a member of the ða, b, 0Þ class of distributions if there exist constants a and b such that","PeriodicalId":46812,"journal":{"name":"North American Actuarial Journal","volume":"25 1","pages":"639 - 642"},"PeriodicalIF":1.4,"publicationDate":"2021-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/10920277.2021.1914666","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41323897","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 Systematic Review and Qualitative Assessment of Fraud Detection Methodologies in Health Care","authors":"Jing Ai, Jennifer Russomanno, Skyla Guigou, Rachel Allan","doi":"10.1080/10920277.2021.1895843","DOIUrl":"https://doi.org/10.1080/10920277.2021.1895843","url":null,"abstract":"Health care fraud is a costly, challenging problem in health insurance. This study provides a systematic evaluation and synthesis of the methodologies and data samples used in current peer-reviewed studies from different academic fields on characterizing health care fraud. The Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) statement was used to guide reviewing the literature. In addition, a qualitative case study approach was employed to assess the studies included in the review in order to independently confirm the conclusions of the systematic review. Out of the 450 articles that were identified by the search criteria, 27 studies were deemed as relevant and included in the analysis. Using 24 variables designed from the literature to synthesize the fraud detection methodologies, the systematic review showed an inability to compare studies quantitatively because few studies reported the accuracy of their detection methods or the overall rate of fraud. The qualitative assessment independently confirmed that prior studies are highly diverse, with the only common characteristic being widespread use of data mining methods. Applying a previously validated approach that has not been taken by prior health care fraud reviews, our qualitative method showed high validity in terms of reviewers’ agreement on the classification of fraud detection methods (r = 93%). Two limitations of this study are that the strength of the evidence is reliant on the quality and number of studies previously performed on the topic, and our systematic review and qualitative results were limited to the text of the final studies as published in peer-reviewed journals. The main gaps we identified are the need to validate existing methods, lack of proof of intent to commit fraud, absence of a fraud rate estimate in the studies analyzed, and inability to use prior evidence to select the best fraud detection method(s). Additional research designed to address these gaps would be of value to researchers, policymakers, and health care practitioners who aim to select the best fraud detection methods for their specific area of practice.","PeriodicalId":46812,"journal":{"name":"North American Actuarial Journal","volume":"26 1","pages":"1 - 26"},"PeriodicalIF":1.4,"publicationDate":"2021-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/10920277.2021.1895843","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48266263","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":"How Much Telematics Information Do Insurers Need for Claim Classification?","authors":"Francis Duval, J. Boucher, M. Pigeon","doi":"10.1080/10920277.2021.2022499","DOIUrl":"https://doi.org/10.1080/10920277.2021.2022499","url":null,"abstract":"It has been shown several times in the literature that telematics data collected in motor insurance help to better understand an insured’s driving risk. Insurers who use these data reap several benefits, such as a better estimate of the pure premium, more segmented pricing, and less adverse selection. The flip side of the coin is that collected telematics information is often sensitive and can therefore compromise policyholders’ privacy. Moreover, due to their large volume, this type of data is costly to store and hard to manipulate. These factors, combined with the fact that insurance regulators tend to issue more and more recommendations regarding the collection and use of telematics data, make it important for an insurer to determine the right amount of telematics information to collect. In addition to traditional contract information such as the age and gender of the insured, we have access to a telematics dataset where information is summarized by trip. We first derive several features of interest from these trip summaries before building a claim classification model using both traditional and telematics features. By comparing a few classification algorithms, we find that logistic regression with lasso penalty is the most suitable for our problem. Using this model, we develop a method to determine how much information about policyholders’ driving should be kept by an insurer. Using real data from a North American insurance company, we find that telematics data become redundant after about 3 months or 4000 km of observation, at least from a claim classification perspective.","PeriodicalId":46812,"journal":{"name":"North American Actuarial Journal","volume":"26 1","pages":"570 - 590"},"PeriodicalIF":1.4,"publicationDate":"2021-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46495534","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}