Susanna Levantesi, Massimiliano Menzietti, Anna Kamille Nyegaard
{"title":"De-risking in multi-state life and health insurance","authors":"Susanna Levantesi, Massimiliano Menzietti, Anna Kamille Nyegaard","doi":"10.1017/s1748499524000083","DOIUrl":"https://doi.org/10.1017/s1748499524000083","url":null,"abstract":"The calculation of life and health insurance liabilities is based on assumptions about mortality and disability rates, and insurance companies face systematic insurance risks if assumptions about these rates change. In this paper, we study how to manage systematic insurance risks in a multi-state setup by considering securities linked to the transition intensities of the model. We assume there exists a market for trading two securities linked to, for instance, mortality and disability rates, the de-risking option and the de-risking swap, and we describe the optimization problem to find the de-risking strategy that minimizes systematic insurance risks in a multi-state setup. We develop a numerical example based on the disability model, and the results imply that systematic insurance risks significantly decrease when implementing de-risking strategies.","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140635614","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":"Smoothness and monotonicity constraints for neural networks using ICEnet","authors":"Ronald Richman, Mario V. Wüthrich","doi":"10.1017/s174849952400006x","DOIUrl":"https://doi.org/10.1017/s174849952400006x","url":null,"abstract":"<p>Deep neural networks have become an important tool for use in actuarial tasks, due to the significant gains in accuracy provided by these techniques compared to traditional methods, but also due to the close connection of these models to the generalized linear models (GLMs) currently used in industry. Although constraining GLM parameters relating to insurance risk factors to be smooth or exhibit monotonicity is trivial, methods to incorporate such constraints into deep neural networks have not yet been developed. This is a barrier for the adoption of neural networks in insurance practice since actuaries often impose these constraints for commercial or statistical reasons. In this work, we present a novel method for enforcing constraints within deep neural network models, and we show how these models can be trained. Moreover, we provide example applications using real-world datasets. We call our proposed method <span>ICEnet</span> to emphasize the close link of our proposal to the individual conditional expectation model interpretability technique.</p>","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140574264","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}
Alex Jose, Angus S. Macdonald, George Tzougas, George Streftaris
{"title":"Interpretable zero-inflated neural network models for predicting admission counts","authors":"Alex Jose, Angus S. Macdonald, George Tzougas, George Streftaris","doi":"10.1017/s1748499524000058","DOIUrl":"https://doi.org/10.1017/s1748499524000058","url":null,"abstract":"<p>In this paper, we construct interpretable zero-inflated neural network models for modeling hospital admission counts related to respiratory diseases among a health-insured population and their dependants in the United States. In particular, we exemplify our approach by considering the zero-inflated Poisson neural network (ZIPNN), and we follow the combined actuarial neural network (CANN) approach for developing zero-inflated combined actuarial neural network (ZIPCANN) models for modeling admission rates, which can accommodate the excess zero nature of admission counts data. Furthermore, we adopt the LocalGLMnet approach (Richman & Wüthrich (2023). <span>Scandinavian Actuarial Journal</span>, 2023(1), 71–95.) for interpreting the ZIPNN model results. This facilitates the analysis of the impact of a number of socio-demographic factors on the admission rates related to respiratory disease while benefiting from an improved predictive performance. The real-life utility of the methodologies developed as part of this work lies in the fact that they facilitate accurate rate setting, in addition to offering the potential to inform health interventions.</p>","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140301621","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":"Genetic testing and actuarial science","authors":"A. Macdonald","doi":"10.1017/s1748499524000034","DOIUrl":"https://doi.org/10.1017/s1748499524000034","url":null,"abstract":"","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140277211","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":"GEMAct: a Python package for non-life (re)insurance modeling","authors":"Gabriele Pittarello, Edoardo Luini, Manfred Marvin Marchione","doi":"10.1017/s1748499524000022","DOIUrl":"https://doi.org/10.1017/s1748499524000022","url":null,"abstract":"This paper introduces gemact, a Python package for actuarial modeling based on the collective risk model. The library supports applications to risk costing and risk transfer, loss aggregation, and loss reserving. We add new probability distributions to those available in scipy, including the (a, b, 0) and (a, b, 1) discrete distributions, copulas of the Archimedean family, the Gaussian, the Student t and the Fundamental copulas. We provide an implementation of the AEP algorithm for calculating the cumulative distribution function of the sum of dependent, nonnegative random variables, given their dependency structure specified with a copula. The theoretical framework is introduced at the beginning of each section to give the reader with a sufficient understanding of the underlying actuarial models.","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139757709","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":"The discrete-time arbitrage-free Nelson-Siegel model: a closed-form solution and applications to mixed funds representation","authors":"Ramin Eghbalzadeh, Frédéric Godin, Patrice Gaillardetz","doi":"10.1017/s1748499524000010","DOIUrl":"https://doi.org/10.1017/s1748499524000010","url":null,"abstract":"A closed-form solution for zero-coupon bonds is obtained for a version of the discrete-time arbitrage-free Nelson-Siegel model. An estimation procedure relying on a Kalman filter is provided. The model is shown to produce adequate fit when applied to historical Canadian spot rate data and to improve distributional predictive performance over benchmarks. An adaptation of the mixed fund return model from Augustyniak <jats:italic>et al</jats:italic>. ((2021). <jats:italic>ASTIN Bulletin: The Journal of the IAA</jats:italic>, <jats:italic>51</jats:italic>(1), 131–159.) is also provided to include the discrete-time arbitrage-free Nelson-Siegel model as one of its building blocks.","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139757858","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 clustering levels of a hierarchical categorical risk factor","authors":"Bavo D.C. Campo, Katrien Antonio","doi":"10.1017/s1748499523000283","DOIUrl":"https://doi.org/10.1017/s1748499523000283","url":null,"abstract":"<p>Handling nominal covariates with a large number of categories is challenging for both statistical and machine learning techniques. This problem is further exacerbated when the nominal variable has a hierarchical structure. We commonly rely on methods such as the random effects approach to incorporate these covariates in a predictive model. Nonetheless, in certain situations, even the random effects approach may encounter estimation problems. We propose the data-driven Partitioning Hierarchical Risk-factors Adaptive Top-down algorithm to reduce the hierarchically structured risk factor to its essence, by grouping similar categories at each level of the hierarchy. We work top-down and engineer several features to characterize the profile of the categories at a specific level in the hierarchy. In our workers’ compensation case study, we characterize the risk profile of an industry via its observed damage rates and claim frequencies. In addition, we use embeddings to encode the textual description of the economic activity of the insured company. These features are then used as input in a clustering algorithm to group similar categories. Our method substantially reduces the number of categories and results in a grouping that is generalizable to out-of-sample data. Moreover, we obtain a better differentiation between high-risk and low-risk companies.</p>","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139657706","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":"Boosted Poisson regression trees: a guide to the BT package in R","authors":"Gireg Willame, Julien Trufin, Michel Denuit","doi":"10.1017/s174849952300026x","DOIUrl":"https://doi.org/10.1017/s174849952300026x","url":null,"abstract":"<p>Thanks to its outstanding performances, boosting has rapidly gained wide acceptance among actuaries. Wüthrich and Buser (Data Analytics for Non-Life Insurance Pricing. Lecture notes available at SSRN. http://dx.doi.org/10.2139/ssrn.2870308, 2019) established that boosting can be conducted directly on the response under Poisson deviance loss function and log-link, by adapting the weights at each step. This is particularly useful to analyze low counts (typically, numbers of reported claims at policy level in personal lines). Huyghe et al. (Boosting cost-complexity pruned trees on Tweedie responses: The ABT machine for insurance ratemaking. Scandinavian Actuarial Journal. https://doi.org/10.1080/03461238.2023.2258135, 2022) adopted this approach to propose a new boosting machine with cost-complexity pruned trees. In this approach, trees included in the score progressively reduce to the root-node one, in an adaptive way. This paper reviews these results and presents the new <span>BT</span> package in <span>R</span> contributed by Willame (Boosting Trees Algorithm. https://cran.r-project.org/package=BT; https://github.com/GiregWillame/BT, 2022), which is designed to implement this approach for insurance studies. A numerical illustration demonstrates the relevance of the new tool for insurance pricing.</p>","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139469134","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":"Epidemic modelling and actuarial applications for pandemic insurance: a case study of Victoria, Australia","authors":"Chang Zhai, Ping Chen, Zhuo Jin, Tak Kuen Siu","doi":"10.1017/s1748499523000246","DOIUrl":"https://doi.org/10.1017/s1748499523000246","url":null,"abstract":"With the recent outbreak of COVID-19, evaluating the epidemic risk appears to be a pressing issue of global concern and one of the major challenges recently. In the fight against pandemics, the ability to understand, model, and forecast the transmission dynamics of infectious diseases plays a crucial role. This paper provides an overview of foundational compartment models and introduces the Susceptible-Exposed-Infected-Containing-3-Substates-Recovered-Dead model to study the dynamics of COVID-19. A meticulous data calibration procedure is employed to study the evolution trend of an actual pandemic using real-world data from Victoria, Australia. Additionally, the paper discusses innovative applications of epidemic models to the insurance industry, which are currently under investigation. Through the use of the newly developed analytically tractable model, insurance companies are able to determine fair premium levels during an outbreak. Moreover, the paper provides practical guidance for insurance companies by examining the variation in reserve levels over time.","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139411981","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":"Nonparametric intercept regularization for insurance claim frequency regression models","authors":"Gee Y. Lee, Himchan Jeong","doi":"10.1017/s1748499523000271","DOIUrl":"https://doi.org/10.1017/s1748499523000271","url":null,"abstract":"In a subgroup analysis for an actuarial problem, the goal is for the investigator to classify the policyholders into unique groups, where the claims experience within each group are made as homogenous as possible. In this paper, we illustrate how the alternating direction method of multipliers (ADMM) approach for subgroup analysis can be modified so that it can be more easily incorporated into an insurance claims analysis. We present an approach to penalize adjacent coefficients only and show how the algorithm can be implemented for fast estimation of the parameters. We present three different cases of the model, depending on the level of dependence among the different coverage groups within the data. In addition, we provide an interpretation of the credibility problem using both random effects and fixed effects, where the fixed effects approach corresponds to the ADMM approach to subgroup analysis, while the random effects approach represents the classic Bayesian approach. In an empirical study, we demonstrate how these approaches can be applied to real data using the Wisconsin Local Government Property Insurance Fund data. Our results show that the presented approach to subgroup analysis could provide a classification of the policyholders that improves the prediction accuracy of the claim frequencies in case other classifying variables are unavailable in the data.","PeriodicalId":44135,"journal":{"name":"Annals of Actuarial Science","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139373310","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}